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Diffstat (limited to 'Engineering_Physics')
25 files changed, 17415 insertions, 9 deletions
diff --git a/Engineering_Physics/Chapter_1.ipynb b/Engineering_Physics/Chapter_1.ipynb new file mode 100755 index 00000000..4dd3b7b8 --- /dev/null +++ b/Engineering_Physics/Chapter_1.ipynb @@ -0,0 +1,2094 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Interference" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1, Page 1.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " # Given \n", + "l = 6.6e-7 # wavelength of light in meter\n", + "L = 1.32e-5 # coherence length in meter\n", + "\n", + "#Calculation\n", + "coherence_time = L / (3 * 10 ** 8)#calculation for coherence time\n", + "\n", + "#Result\n", + "print \"Coherence time = %.1e sec\"%coherence_time" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence time = 4.4e-14 sec\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.2, Page 1.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.896e-7 # wavelength of light in meter\n", + "L = 2.945e-2 # coherence length in meter\n", + "\n", + "#Calculations\n", + "coherence_time = L / (3 * 10**8) # calculation for coherence time\n", + "n = L / l # calculation for number of oscillations \n", + "\n", + "#Results\n", + "print \"Coherence time = %.3e sec.\"%coherence_time\n", + "print \"No. of oscillations = %.2e\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence time = 9.817e-11 sec.\n", + "No. of oscillations = 4.99e+04\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3, Page 1.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given\n", + "l = 6.058e-7 # wavelength of light in meter\n", + "L = 0.2 # coherence length in meter\n", + "\n", + "#Calculations\n", + "line_width = (l**2) / L#calculation for line width\n", + "f_spread = (3 * 10**8) / L# calculation for frequency spread\n", + "f = (3 * 10**8) / l # calculation for frequency\n", + "f_stability = f_spread / f # calculation for frequency stability\n", + "coherence_time = L / (3 * 10 ** 8) # calculation for coherence time\n", + "\n", + "#Results\n", + "print(\"Coherence time = %.3e sec\"%coherence_time)\n", + "print(\"Line width = %.3e meter\"%line_width)\n", + "print(\"Frequency stability = %.1e\"%f_stability) #incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence time = 6.667e-10 sec\n", + "Line width = 1.835e-12 meter\n", + "Frequency stability = 3.0e-06\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.4, Page 1.41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lambda_D = 5.5e-13 # Doppler width of orange light in meter\n", + "l = 6.058e-7 # wavelength of light in meter\n", + "\n", + "#Calculation\n", + "coherence_length = (l ** 2) / lambda_D# calculation for coherence light\n", + "\n", + "#Result\n", + "print(\"Coherence length = %.4f meter\"%coherence_length)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence length = 0.6673 meter\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5, Page 1.41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lambda1 = 5.461e-7 # wavelength of light emitted by mercury vapour lamp in meter\n", + "band_width1 = 6e8 # band width for mercury vapour lamp in Hz\n", + "lambda2 = 6.328e-7 # the operating wavelength of light for He Ne laser \n", + "band_width2 = 1e6 # band width for laser in Hz\n", + "\n", + "#Calculations\n", + "delta_lambda1 = (lambda1**2 * band_width1) / 3e8 # calculation for difference between two wavelength for mercury vapour\n", + "delta_L1 = lambda1**2 / delta_lambda1 # calculation for coherence length for mercury vapour lamp\n", + "delta_lambda2 = (lambda2**2 * band_width2) / 3e8 # calculation for difference between two wavelength for He Ne laser\n", + "delta_L2 = lambda2**2 / delta_lambda2 # calculation for coherence length for He Ne laser\n", + "R = delta_L1/delta_L2 # calculation for ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser\n", + "\n", + "#Result\n", + "print(\"The ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser = 1:%d\"%(1./R))\n", + "#Answer differes due to rounding-off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser = 1:600\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6, Page 1.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "band_width = 3000 # band width of laser in hertz\n", + " \n", + "#Calculation\n", + "coherence_length = (3 * 10 ** 8) / band_width#calculation for coherence length \n", + "\n", + "#Result\n", + "print(\"Coherence length of laser = %.f meter\"%(coherence_length))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence length of laser = 100000 meter\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.7, Page 1.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given\n", + "l = 6.328e-7 # wavelength of monochromatic light in meter\n", + "t = 10**-10 # chopping time in sec\n", + "\n", + "#Calculations\n", + "coherence_length = (3 * 10 ** 8) * t # calculation for coherence length of monochromatic light \n", + "band_width = 1 / t # calculation for band width \n", + "line_width = ((l ** 2) * band_width) / (3 * 10 ** 8) # calculation for line width \n", + "\n", + "#Result\n", + "print(\"Coherence length of monochromatic light = %.e meter. \\nband width = %.f Hz. \\nline width = %.4f A.\"%(coherence_length, band_width, line_width*1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence length of monochromatic light = 3e-02 meter. \n", + "band width = 10000000000 Hz. \n", + "line width = 0.1335 A.\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.8, Page 1.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given\n", + "l = 6.438e-7 # wavelength of red cadmium line in meter\n", + "L = 3.8e-1 # coherence length in meter\n", + "\n", + "#Calculations\n", + "coherence_time = L / (3 * 10 ** 8)# calculation for coherence time\n", + "spectral_line_width = (l**2) / L # calculation for spectral line width\n", + "\n", + "#Result\n", + "print(\"Coherence time of red cadmium line = %.3e sec. \\nSpectral line width = %.2e meter.\"%(coherence_time,spectral_line_width))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coherence time of red cadmium line = 1.267e-09 sec. \n", + "Spectral line width = 1.09e-12 meter.\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.9, Page 1.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "from sympy import *\n", + "\n", + "# Given \n", + "ratio = 16 # ratio of intensities of two waves\n", + "\n", + "#Calculation\n", + "a1 = sqrt(ratio) # by the formula amplitude = sqrt(intensity)\n", + "a2 = 1\n", + "R = ((a1 + a2) ** 2) / ((a1 - a2) ** 2)# calculation for ratio of maximum intensity with minimum intensity\n", + "R = nsimplify(R)\n", + "\n", + "#Result\n", + "print \"Ratio of maximum intensity with minimum intensity =\",R" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of maximum intensity with minimum intensity = 25/9\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.10, Page 1.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d = 0.0001 # distance between two slits in meter\n", + "Beta = 0.005 # width of the fringes formed in meter\n", + "D = 1 # distance between slit and screen in meter\n", + "\n", + "#Calculation\n", + "l = (Beta * d) / D # calculation for wavelength of light = %e meter\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A. \"%(l*1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 5000 A. \n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.11, Page 1.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "alpha = pi / 180 # angle of bi prism in radian\n", + "mu = 1.5 # refractive index of biprism \n", + "a = 0.4 # distance of bi prism from slit in meter\n", + "b = 0.6 # distance of bi prism from screen in meter\n", + "l = 5.893e-7 # wavelength of light in meter\n", + "\n", + "#Calculation\n", + "D = a + b # calculation for distance between slits and screen\n", + "fringe_width = (l * D) / (2 * a * (mu - 1) * alpha) # calculation for fringe width\n", + "\n", + "#Result\n", + "print(\"Fringe width = %.3e meter.\"%(fringe_width))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fringe width = 8.441e-05 meter.\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.12, Page 1.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "d1 = 4.05e-3 # distance between slits in first position in meter\n", + "d2 = 2.90e-3 # distance between slits in second position in meter\n", + "l = 5.893e-7 # wavelength of light in meter\n", + "D = 1 # distance between slit and screen\n", + "\n", + "#Calculations\n", + "d = sqrt(d1 * d2)# calculation for distance between fringe\n", + "fringe_width = (l * D) / d # calculation for fringe width\n", + "\n", + "#Result\n", + "print(\"Fringe width = %.3f mm\"%(fringe_width*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fringe width = 0.172 mm\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.13, Page 1.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import floor\n", + "\n", + "# Given \n", + "fringe_width = 3.42e-4 # fringe width in meter\n", + "mu = 1.542 # refractive index of glass\n", + "Xn = 2.143e-3 # shift of central fringe in meter\n", + "l = 5.89e-7 # wavelength of light in meter\n", + "\n", + "#Calculations\n", + "n = Xn / fringe_width # calculation for order of the fringe\n", + "t = (floor(n) * l) / (mu - 1) # calculation for thickness of the glass\n", + "\n", + "#Result\n", + "print(\"Thickness of glass sheet = %.2e meter. \"%t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of glass sheet = 6.52e-06 meter. \n" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.14, Page 1.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "fringe_width = 9e-4 # fringe width in meter\n", + "a = 0.1 # distance of bi prism from slit in meter\n", + "b = 0.9 # distance of bi prism from screen in meter\n", + "l = 5.896e-7 # wavelength of light in meter\n", + "\n", + "#Calculation\n", + "D = a + b # calculation for distance between slits and screen\n", + "d = (l * D) / fringe_width # calculation for distance between coherent sources\n", + "\n", + "#Result\n", + "print(\"Distance between coherent sources = %.2e meter. \"%d)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance between coherent sources = 6.55e-04 meter. \n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.15, Page 1.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi,degrees\n", + "\n", + "# Given \n", + "fringe_width = 0.0135 # fringe width in meter\n", + "a = 0.5 # distance of bi prism from slits in meter\n", + "b = 0.5 # distance of bi prism from screen in meter\n", + "mu = 1.5 # refractive index of bi prism \n", + "alpha = pi / 360 # angle of bi prism in radian \n", + "\n", + "#Calculations\n", + "D = a + b # calculation for distance between slits and screen \n", + "l = (2. * a * (mu - 1) * alpha * fringe_width) / D # calculation for wavelength of light = %e meter\n", + "\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A \"%(l*1e8))\n", + "#Answer differs due to rounding-off errors\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 5890 A \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.16, Page 1.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "a = 45 # distance between slit and bi prism in cm\n", + "alpha = pi / 180 # angle of bi prism in radian\n", + "Mu = 1.5 # refractive index of bi prism\n", + "fringe_width = 15.6e-3 # fringe width in meter \n", + "D = 90 #cm\n", + "\n", + "#Calculations\n", + "d2 = (2*a*(Mu-1)*alpha) # calculation for distance between screen and slit\n", + "l = (fringe_width * d2) / D # calculation for wavelength\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A.\"%(l/1e-8))\n", + "#Answer differs due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 13614 A.\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.17, Page 1.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "D = 1.20 # distance between source and eye piece in meter\n", + "Xn = 1.9e-2 # distance move by eye piece for 20 fringe in meter\n", + "n = 20 # no. of fringes\n", + "d = 6e-4 # distance between slits in meter \n", + "\n", + "#Calculation\n", + "l = (Xn * d) / (D * n)# calculation for wavelength\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A.\"%(l*1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 4750 A.\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.18, Page 1.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import floor\n", + "\n", + "# Given \n", + "lambda1 = 5.890e-7 # wavelength of first light in meter\n", + "lambda2 = 4.358e-7 # wavelength of second light in meter\n", + "n1 = 40 # no. of fringes observed in the field of in first case \n", + "\n", + "#Calculation\n", + "n2 = (n1 * lambda1) / lambda2 # by using formula n1*lambda1=n2*lambda2\n", + "\n", + "#Result\n", + "print(\"No. of fringes observed in field of view in second case = %d. \"%(floor(n2)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of fringes observed in field of view in second case = 54. \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.19, Page 1.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos\n", + "\n", + "# Given \n", + "l = 5.893e-7 # wavelength of light in meter\n", + "Mu = 1.42 # refractive index of soap film \n", + "i = 0 # incidence angle in radian \n", + "r = 0 # refracted angle in radian\n", + "n = 1 # for smallest thickness\n", + "\n", + "#Calculations\n", + "t1 = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for east thickness of soap film for bright fringe\n", + "t2 = (n * l) / (2 * Mu * cos(r)) # calculation for east thickness of soap film for dark fringe\n", + "\n", + "#Result\n", + "print(\"Least thickness of soap film -\\n (a) For bright fringe = %.3e mm. \\n (b) For dark fringe = %.3e mm.\"%(t1*1000,t2*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Least thickness of soap film -\n", + " (a) For bright fringe = 1.038e-04 mm. \n", + " (b) For dark fringe = 2.075e-04 mm.\n" + ] + } + ], + "prompt_number": 97 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.20, Page 1.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,pi,sin,asin\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "Mu_o = 1.4 # refractive index of oil film \n", + "Mu_w = 1.33 # refractive index of water\n", + "i = pi / 6 # incidence angle in radian \n", + "n = 6 # no. of fringes seen\n", + "\n", + "#Calculation\n", + "r = asin(sin(i) / Mu_o) # calculation for angle of refraction\n", + "t = (n * l) / (2 * Mu_o * cos(r)) # calculation for thickness of film\n", + "\n", + "#Result\n", + "print(\"Thickness of oil film = %.3e mm.\"%(t*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of oil film = 1.351e-03 mm.\n" + ] + } + ], + "prompt_number": 98 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.21, Page 1.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos\n", + "\n", + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "Mu = 1.463 # refractive index of soap film \n", + "i = 0 # incidence angle in radian \n", + "r = 0 # refracted angle in radian\n", + "n = 1 # for smallest thickness\n", + "\n", + "#Calculation\n", + "t = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for least thickness of soap film for bright fringe\n", + "\n", + "#Result\n", + "print(\"Least thickness of soap film for bright fringe = %.3e mm. \"%(t*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Least thickness of soap film for bright fringe = 1.025e-04 mm. \n" + ] + } + ], + "prompt_number": 99 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.22, Page 1.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,pi,sin\n", + "\n", + "# Given That\n", + "l = 5.89e-7 # wavelength of light \n", + "Mu_o = 1.46 # refractive index of oil film \n", + "i = pi / 6 # incidence angle in radian \n", + "n = 8 # no. of fringe is seen\n", + "\n", + "#Calculations\n", + "r = asin(sin(i) / Mu_o) # calculation for angle of refraction\n", + "t = (n * l) / (2 * Mu_o * cos(r)) # calculation for thickness of oil film\n", + "\n", + "#Result\n", + "print(\"Thickness of oil film = %.2e mm. \"%(t*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of oil film = 1.72e-03 mm. \n" + ] + } + ], + "prompt_number": 100 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.23, Page 1.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,pi,floor\n", + "\n", + "# Given That\n", + "lambda1 = 4e-7 # max. wavelength of light in meter\n", + "lambda2 = 5e-7 # min. wavelength of light in meter\n", + "Mu = 1.4 # refractive index of soap film \n", + "i = pi / 4 # incidence angle in radian \n", + "t = 1e-5 # thickness of oil film in meter\n", + "\n", + "#Calculations\n", + "r = asin(sin(i) / Mu) # calculation for angle of refraction\n", + "n1 = (2 * Mu * t * cos(r)) / lambda1 # calculation for no. of dark bands seen in the case of max. wavelength \n", + "n2 = (2 * t * Mu * cos(r)) / lambda2 # calculation for no. of dark seen in the case of min. wavelength \n", + "n = floor(n1) - floor(n2) # claculation for no. of dark bands seen between wavelengths\n", + "\n", + "#Result\n", + "print(\"No. of dark bands seen between wavelengths = %d\"%n)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of dark bands seen between wavelengths = 12\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.24, Page 1.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,pi\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "Mu = 1.5 # refractive index of soap film \n", + "r = pi / 3 # refracted angle in radian\n", + "n = 1 # for smallest thickness\n", + "\n", + "#Calculation\n", + "t = (n * l) / (2 * Mu * cos(r)) # calculation for least thickness of soap film for bright fringe\n", + "\n", + "#Result\n", + "print(\"Least thickness of soap film for bright fringe = %.3e meter \"%t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Least thickness of soap film for bright fringe = 3.927e-07 meter \n" + ] + } + ], + "prompt_number": 104 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.25, Page 1.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,pi,sin\n", + "\n", + "# Given That\n", + "lambda1 = 6.1e-7 # max. wavelength of light in meter\n", + "lambda2 = 6e-7 # min. wavelength of light in meter\n", + "Mu = 1.333 # refractive index of film \n", + "i = pi / 4 # incidence angle in radian \n", + "\n", + "#Calculation\n", + "r = asin(sin(i) / Mu) # calculation for angle of refraction\n", + "n = lambda2 / (lambda1 - lambda2) # calculation for no. of bright band\n", + "t = (n * lambda1) / (2 * Mu * cos(r)) # calculation for thickness of the film\n", + "\n", + "#Result\n", + "print(\"Thickness of the film = %.2e meter \"%t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of the film = 1.62e-05 meter \n" + ] + } + ], + "prompt_number": 105 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.26, Page 1.49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos\n", + "\n", + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "Mu = 1.463 # refractive index of soap film \n", + "i = 0 # incidence angle in radian \n", + "r = 0 # refracted angle in radian\n", + "n = 1 # for smallest thickness\n", + "\n", + "#Calculation\n", + "t = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for thickness of soap film\n", + "\n", + "#Result\n", + "print(\"\\n Least thickness of soap film for bright fringe = %.3e meter. \"%t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Least thickness of soap film for bright fringe = 1.025e-07 meter. \n" + ] + } + ], + "prompt_number": 106 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.27, Page 1.49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos,sin,asin,pi,degrees,radians\n", + "\n", + "# Given \n", + "lambda1 = 6.1e-7 # max. wavelength of light in meter\n", + "lambda2 = 6e-7 # min. wavelength of light in meter\n", + "Mu = 4. / 3 # refractive index of film \n", + "i = asin(4. / 5) # incidence angle in radian \n", + "\n", + "#Calculation\n", + "r = asin(sin(i) / Mu)*180/pi # calculation for angle of refraction\n", + "n = lambda2 / (lambda1 - lambda2) # calculation for order of fringe\n", + "t = (n * lambda1) / (2 * Mu * cos(r*pi/180)) # calculation for thickness of film\n", + "\n", + "#Result\n", + "print(\"Thickness of the film = %.3e mm. \"%(t*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of the film = 1.716e-02 mm. \n" + ] + } + ], + "prompt_number": 127 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.28, Page 1.50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.893e-7 # wavelenth of light in meter\n", + "n = 20 # no. of interference fringes are observed \n", + "Mu = 1 # refractive index of air\n", + "i = 0 # incidence angle in radian \n", + "r = 0 # refracted angle in radian \n", + "\n", + "#Calculation\n", + "t = (n * l) / (2 * Mu) # calculation for thickness of fringe\n", + "\n", + "#Result\n", + "print(\"Thickness of wire = %.3e mm. \"%(t*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of wire = 5.893e-03 mm. \n" + ] + } + ], + "prompt_number": 128 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.29, Page 1.50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 6e-7 # wavelength of light in meter\n", + "Mu = 1 # refractive index of air film\n", + "l = 0.06e-3 # diameter of wire in meter\n", + "L = 0.15 # distance of wire from edge in meter\n", + "\n", + "#Calculation\n", + "theta = l / L #calculation for theta\n", + "fringe_width = (lamda * L)/ (2 * Mu * l) # calculation for fringe width\n", + "\n", + "#Result\n", + "print(\"Fringe width = %.1e mm.\"%fringe_width)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fringe width = 7.5e-04 mm.\n" + ] + } + ], + "prompt_number": 140 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.30, Page 1.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 4.56e-7 # wavelength of light in meter\n", + "theta = 1.9e-4 # angle of wedge in radian \n", + "Mu = 1 # refractive index of air\n", + "\n", + "#Calculation\n", + "fringe_width = l / (2 * Mu * theta)# calculation for fringe width \n", + "\n", + "#Result\n", + "print(\"Fringe width = %.1f mm.\"%(fringe_width*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fringe width = 1.2 mm.\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.31, Page 1.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 6e-7 # wavelength of light in meter\n", + "Mu = 1 # refractive index of air film\n", + "l = 0.03*10**-3 # diameter of wire in meter\n", + "L = 0.15 # distance of wire from edge in meter\n", + "i = 0 # incidence angle in radian \n", + "r = 0 # refracted angle in radian \n", + "\n", + "#Calculation\n", + "theta = l / L # calculation for theta\n", + "fringe_width = lamda / (2 * Mu * theta) # calculation for fringe width \n", + "\n", + "#Result\n", + "print(\"Fringe width = %.1f mm.\"%(fringe_width*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fringe width = 1.5 mm.\n" + ] + } + ], + "prompt_number": 141 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.32, Page 1.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.890e-7 # wavelength of light in meter\n", + "theta = 1e-2 # angle of wedge in radian \n", + "n = 12 # no. of dark fringe\n", + "Mu = 1 # refractive index of air\n", + "i = 0 # incidence angle in radian\n", + "r = 0 # refracted angle in radian\n", + "\n", + "#Calculatiom\n", + "x = ( n * l) / (2 * theta) # calculation for distance\n", + "\n", + "#Result\n", + "print(\"Distance = %.2f mm. \"%(x*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance = 0.35 mm. \n" + ] + } + ], + "prompt_number": 142 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.33, Page 1.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "w = 2e-5 # fringe width in meter\n", + "Mu = 1.5 # refractive index of film\n", + "i = 0 # incidence angle in radian\n", + "r = 0 # refracted angle in radian\n", + "\n", + "#Calculation\n", + "theta = l / (2 * Mu * w)# calculation for the angle of the film\n", + "\n", + "#Result\n", + "print(\"Angle of wedge = %.3f degree. \"%(theta * 180/pi))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of wedge = 0.525 degree. \n" + ] + } + ], + "prompt_number": 143 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + " Example 1.34, Page 1.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d1 = 5.9e-3 # diameter of 15th ring in meter\n", + "d2 = 3.36e-3 # diameter of 5th ring in meter\n", + "R = 1 # radius of the plano-convex lens in meter\n", + "\n", + "#Calculations\n", + "p = 15 - 5\n", + "l = ((d1**2) - (d2**2)) / (4 * p * R) # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A.\"%(l*1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 5880 A.\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.35, Page 1.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d1 = 2e-3 # diameter of 10th ring in meter\n", + "d2 = 3e-3 # diameter of 20th ring in meter\n", + "f = 0.9 # focal length of the plano-convex lens in meter\n", + "mu = 1.5 # refractive index of lens\n", + "\n", + "#Calculations\n", + "p = 20 - 10\n", + "R = (f * (mu - 1)) # calculation for radius of convex surface of lens\n", + "l = ((d2**2) - (d1**2)) / (4 * p * R)\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f nm.\"%(l*1e9))\n", + "#Incorrect answer in the textbook\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 2778 nm.\n" + ] + } + ], + "prompt_number": 145 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.36, Page 1.53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt \n", + "\n", + "# Given \n", + "l = 5.896e-7 # wavelength of light in meter\n", + "f = 1 # focal length of the plano-convex lens in meter\n", + "mu = 1.5 # refractive index of lens \n", + "n = 7 # no. of bright ring\n", + "\n", + "#Calculations\n", + "p = 20 - 10\n", + "R = (f * (mu - 1)) * 2 # calculation for radius of lens\n", + "D = sqrt(4 * n * l * R) # calculation for diameter of 7th ring \n", + "\n", + "#Result\n", + "print(\"Diameter of 7th bright ring = %.3e meter.\"%(D))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of 7th bright ring = 4.063e-03 meter.\n" + ] + } + ], + "prompt_number": 146 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.37, Page 1.53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given That\n", + "lambda1 = 6e-7 # wavelength of first light in meter\n", + "lambda2 = 4.8e-7 # wavelength of second light in meter\n", + "r = 0.96 # radius of curvature of curved surface of lens in meter\n", + "\n", + "#Calculations\n", + "n = lambda2 / (lambda1 - lambda2) # calculation for order of fringe\n", + "D = sqrt(4 * (n + 1) * lambda2 * r) # calculation for diameter of ring\n", + "\n", + "#Result\n", + "print(\"Diameter of (n +1)th dark ring of lambda2. = %.2e meter.\"%D)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of (n +1)th dark ring of lambda2. = 3.04e-03 meter.\n" + ] + } + ], + "prompt_number": 147 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.38, Page 1.54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "lambda1 = 6e-7 # wavelength of first light in meter\n", + "lambda2 = 5.9e-7 # wavelength of second light in meter\n", + "r = 0.9 # radius of curvature of curved surface of lens in meter\n", + "\n", + "#Calculations\n", + "n = lambda2 / (lambda1 - lambda2) # calculation for order of ring\n", + "D = sqrt(4 * (n + 1) * lambda1 * r) # calculation for diameter of ring\n", + "\n", + "#Result\n", + "print(\"Diameter of nth dark ring of lambda1 = %.4f meter.\"%D)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of nth dark ring of lambda1 = 0.0114 meter.\n" + ] + } + ], + "prompt_number": 148 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.39, Page 1.54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.896e-7 # wavelength of light in meter\n", + "D = 4e-3 # diameter of 7th brighter fringe in m\n", + "R = 1 # radius of curvature in m\n", + "n = 7 # for seventh brighter fringe\n", + "\n", + "#Calculation\n", + "mu = 2*(2*n-1)*l*R / D**2 # calculation for refractive index of liquid\n", + "\n", + "#Result\n", + "print(\"Refractive index of liquid = %.2f.\"%mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of liquid = 0.96.\n" + ] + } + ], + "prompt_number": 149 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.40, Page 1.54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "D1 = 3e-3 # diameter of nth dark fringe when liquid is absent between the lens and the plate in m\n", + "D2 = 2.5e-3 # diameter of nth dark fringe when liquid is introduced between the lens and the plate in m\n", + "c = 3e8 # velocity of light in vacuum in m/sed\n", + "\n", + "#Calculations\n", + "mu = D1**2 / D2**2# calculation for refractive index\n", + "v = 3e8 / mu # calculation for velocity of light \n", + "\n", + "#Result\n", + "print(\"Refractive index of liquid = %.2f.\\n velocity of light in the liquid = %.2e m/sec.\"%(mu,v))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of liquid = 1.44.\n", + " velocity of light in the liquid = 2.08e+08 m/sec.\n" + ] + } + ], + "prompt_number": 150 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.41, Page 1.55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.896e-7 # wavelength of light in meter\n", + "D = 5.1e-3 # diameter of 16th brighter fringe in m\n", + "R = 1 # radius of curvature in m\n", + "n = 16 # for sixteenth brighter fringe\n", + "\n", + "#Calculation\n", + "mu = 4*n*l*R / D**2 # calculation for refractive index of liquid\n", + "\n", + "#Result\n", + "print(\"Refractive index of liquid = %.2f\"%mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of liquid = 1.45\n" + ] + } + ], + "prompt_number": 170 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.42, Page 1.55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 6.3e-7 # wavelength of light in meter\n", + "mu = 1.63 # refractive index of liquid \n", + "R = 0.9 # the radius of curvature of convex lens in meter\n", + "\n", + "#Calculation\n", + "r = sqrt(l*R/mu) # calculation for the radius of smallest dark ring\n", + "\n", + "#Result\n", + "print(\"The radius of smallest dark ring = %.2f mm.\"%(r*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The radius of smallest dark ring = 0.59 mm.\n" + ] + } + ], + "prompt_number": 171 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.43, Page 1.55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "r = 10./7 # ratio of nth ring diameter for two media\n", + "\n", + "#Calculation\n", + "R = (1/r)**2 # calculation for the ratio of refractive index of media\n", + "\n", + "#Result\n", + "print(\"The ratio refractive index of media = %.f:100.\"%(R*100))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio refractive index of media = 49:100.\n" + ] + } + ], + "prompt_number": 173 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.44, Page 1.56" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "R = 0.9 # radius of curvature of the lower face of the lens in meter\n", + "D = 4.8e-3 # diameter of the 10th dark ring in meter\n", + "n = 10 # for 10th dark ring\n", + "\n", + "#Calculation\n", + "l = D**2 / (4 * n * R) # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A.\"%(l * 1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 6400 A.\n" + ] + } + ], + "prompt_number": 174 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.45, Page 1.56" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "r = 1./2 # ratio of 5th ring diameter \n", + "\n", + "#Calculatio\n", + "R = (1/r)**2 # calculation for refractive index of liquid\n", + "\n", + "#Result\n", + "print(\"Refractive index of liquid = %.f. \"%R)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of liquid = 4. \n" + ] + } + ], + "prompt_number": 175 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.46, Page 1.56" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given That\n", + "R = 1 # radius of curvature of lens of both side in meter\n", + "l = 5.4e-7 # wavelength of monochromatic light in meter\n", + "n1 = 5 # for 5th dark ring\n", + "n2 = 15 # for 10th dark ring\n", + "\n", + "#Calculation\n", + "r1 = sqrt((n1*l)/(1/R + 1/R)) # calculation for radius of 5th dark ring\n", + "r2 = sqrt((n2*l)/(1/R + 1/R)) # calculation for radius of 15th dark ring\n", + "d = r2 - r1 # calculation for distance between 5th and 15th dark ring\n", + "\n", + "#Result\n", + "print(\"Distance between 5th and 15th dark ring = %.3f cm.\"%(d * 100))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance between 5th and 15th dark ring = 0.085 cm.\n" + ] + } + ], + "prompt_number": 177 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.47, Page 1.57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "x = 2.5e-5 # distance moved by movable mirror in meter\n", + "t = 5e-5 # thickness of mica sheet in meter\n", + "\n", + "#Calculation\n", + "mu = x / t + 1 # calculation for refractive index of mica\n", + "\n", + "#Result\n", + "print(\"Refractive index of mica = %.1f\"%mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of mica = 1.5\n" + ] + } + ], + "prompt_number": 179 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.48, Page 1.57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "x = 6e-5 # distance moved by movable mirror in meter\n", + "N = 200 # no. of fringes crossed the field of view \n", + "\n", + "#Calculation\n", + "l = (2 * x) / N # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.f A.\"%(l * 1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 6000 A.\n" + ] + } + ], + "prompt_number": 180 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.49, Page 1.57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 50 # no. of bands crosses the line of observation \n", + "l = 5.896e-7 # wavelength of light in meter\n", + "mu = 1.4 # refractive index \n", + "\n", + "#Calculation\n", + "t = n*l / (2*(mu-1)) # calculation for thickness of the plate\n", + "\n", + "#Result\n", + "print(\"Thickness of the plate = %.2e m.\"%t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of the plate = 3.69e-05 m.\n" + ] + } + ], + "prompt_number": 181 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.50, Page 1.57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 50 # no. of bands crosses the line of observation \n", + "lambda1 = 5.896e-7 # max. wavelength of light in meter\n", + "lambda2 = 5.89e-7 # min. wavelength of light in meter\n", + "\n", + "#Calculation\n", + "x = lambda1 * lambda2 /(lambda1 - lambda2) # calculation for the path difference\n", + "\n", + "#Result\n", + "print(\"The path difference = %.4f mm.\"%(x*10**3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The path difference = 0.5788 mm.\n" + ] + } + ], + "prompt_number": 182 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.51, Page 1.58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "x = 2.948e-5 # distance moved by movable mirror in meter\n", + "n = 100 # no. of fringes cross the field of view \n", + "\n", + "#Calculation\n", + "l = 2*x/n # calculation for wavelength of monochromatic light\n", + "\n", + "#Result\n", + "print(\"Wavelength of monochromatic light = %.f A.\"%(l * 1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of monochromatic light = 5896 A.\n" + ] + } + ], + "prompt_number": 183 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.52, Page 1.58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lambda1 = 5.896e-7 # max. wavelength of light in meter\n", + "lambda2 = 5.89e-7 # min. wavelength of light in meter\n", + "\n", + "#Calculation\n", + "x = lambda1 * lambda2 /(2*(lambda1 - lambda2)) # calculation for the path difference\n", + "\n", + "#Result\n", + "print(\"The distance through which the movable mirror is move = %.3f mm.\"%(x*10**3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The distance through which the movable mirror is move = 0.289 mm.\n" + ] + } + ], + "prompt_number": 184 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.53, Page 1.58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "x = 2.945e-4 # distance moved by movable mirror in meter\n", + "l = 5.893e-7 # mean wavelength of light in meter\n", + "\n", + "#Calculation\n", + "delta_lambda = l**2 / (2*x) # calculation for difference between two wavelengths\n", + "\n", + "#Result\n", + "print(\"Difference between two wavelengths = %.3f A.\"%(delta_lambda*1e10))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Difference between two wavelengths = 5.896 A.\n" + ] + } + ], + "prompt_number": 185 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.54, Page 1.58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 140 # no. of shift in fringe\n", + "l = 5.46e-7 # wavelength of light in meter\n", + "t = 0.2 # length of tube in meter\n", + "\n", + "#Calculation\n", + "mu = (n*l)/(2*t) + 1 # calculation for refractive index of gas\n", + "\n", + "#Result\n", + "print(\"Refractive index of gas = %.5f\"%mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of gas = 1.00019\n" + ] + } + ], + "prompt_number": 188 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_10.ipynb b/Engineering_Physics/Chapter_10.ipynb new file mode 100755 index 00000000..39a354b1 --- /dev/null +++ b/Engineering_Physics/Chapter_10.ipynb @@ -0,0 +1,613 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10: Electromagnetism" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.15, Page 10.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 2000 # flux lines enter in given volume in Vm\n", + "n_ = 4000 # flux lines diverge from given volume in Vm\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculations\n", + "fi = n_ - n\n", + "q = e0 * fi\n", + "\n", + "#Result\n", + "print 'The total charge within volume(in C) = ',q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total charge within volume(in C) = 1.77e-08\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.16, Page 10.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 20000 # flux lines entering in given volume in Vm\n", + "n_ = 45000 # flux lines entering out from given volume in Vm\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculations\n", + "fi = n_ - n\n", + "q = e0 * fi\n", + "\n", + "#Result\n", + "print \"The total charge enclosed by closed surface is %.3e C\"%q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total charge enclosed by closed surface is 2.212e-07 C\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.17, Page 10.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "q = 13.5e-6 # charge enclosed at the centre of cube in C\n", + "l = 6 # length of the side of cube in cm\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculations\n", + "fi = q / e0\n", + "fi_ = fi / 6\n", + "q = e0 * fi\n", + "\n", + "#Results\n", + "print \"Electric flux through the whole volume of the cube is %.3e Nm^2/C\\nElectric flux through one face of the cube is %.2e Nm^2/C\"%(fi,fi_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electric flux through the whole volume of the cube is 1.525e+06 Nm^2/C\n", + "Electric flux through one face of the cube is 2.54e+05 Nm^2/C\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.18, Page 10.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "q = 11 # charge enclosed at the centre of cube in C\n", + "l = 5 # length of the side of cube in cm\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculation\n", + "fi_ = (q / e0) / 6\n", + "\n", + "#Result\n", + "print \" Electric flux through each surface of the cube = %.2e Nm^2/C\"%fi_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Electric flux through each surface of the cube = 2.07e+11 Nm^2/C\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.19, Page 10.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "q = 1e-8 # charge uniformly spread over metallic sphere in C\n", + "r = .1 #radius of sphere in m\n", + "d = 7 # distance of a point from centre of the sphere in cm\n", + "d_ = .5 # distance of another point from centre of the sphere in m\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#calculations\n", + "E1 = (1 / (4 * pi * e0) * (q / r**2))\n", + "E2 = 0 #because sphere is metallic\n", + "E3 = (1 / (4 * pi * e0) * (q / d_**2))\n", + "\n", + "#Result\n", + "print \"Electric field intensity-\\n(1) On the surface of the sphere = %.e N/C\\n(2) At first point = %d N/C\\n(3)At second point = %.2e N/C\"%(E1,E2,E3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electric field intensity-\n", + "(1) On the surface of the sphere = 9e+03 N/C\n", + "(2) At first point = 0 N/C\n", + "(3)At second point = 3.60e+02 N/C\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.20, Page 10.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "q = 1.6e-19 # charge on a proton in C\n", + "d = 1e-10 # distance of a point from proton in m\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculation\n", + "E = (1 / (4 * pi * e0)) * (q / d**2)\n", + "\n", + "#Result\n", + "print \"Electric field = %.2e V/m\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electric field = 1.44e+11 V/m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.21, Page 10.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "v = 1000 # potential through which alpha particle accelerated in V\n", + "q = 3.2e-19 # charge on an alpha particle in C\n", + "e0 = 8.85e-12 # electric permittivity of space\n", + "\n", + "#calculation\n", + "E = q * v\n", + "\n", + "#Result\n", + "print \"Energy gained by alpha particle = %.1e J\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy gained by alpha particle = 3.2e-16 J\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.22, Page 10.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "q = 1.6e-19 # charge on a proton in C\n", + "d = 1e-10 # distance of a point from proton in m\n", + "d_ = 2e-11 # distance of another point from proton in m\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#calculations\n", + "v = (1 / (4 * pi * e0)) * (q / d)#calculation for potential at first point\n", + "E = -q * v#calculation for energy at first point in J\n", + "delta_v = (1 / (4 * pi * e0)) * q * ((1 / d_) - (1 / d))#calculation for potential difference between points\n", + "\n", + "#Result\n", + "print \"Potential energy at first point = %.1f eV\\nPotential difference between points = %.1f V\"%(E/q,delta_v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential energy at first point = -14.4 eV\n", + "Potential difference between points = 57.5 V\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.23, Page 10.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, ceil\n", + "\n", + "# Given \n", + "q = 1.5e-6 # charge in C\n", + "v = 30 # potential of a surface in V\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculation\n", + "r = (1 / (4 * pi * e0)) * (q / v)\n", + "\n", + "#Result\n", + "print \"Radius of equipotential surface = %d m\"%ceil(r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of equipotential surface = 450 m\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.24, Page 10.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "p = 3.8e26 # power radiated by sun in W\n", + "r = 7e8 # radius of sun in m\n", + "e0 = 8.85e-12 # permittivity of space\n", + "\n", + "#Calculation\n", + "s = p / (4 * pi * r**2)\n", + "\n", + "#Result\n", + "print \"The value of poynting vector at the surface of the sun = %.3e W/m^2\"%s" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The value of poynting vector at the surface of the sun = 6.171e+07 W/m^2\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.25, Page 10.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "Se = (2*4.2)/(60*10**-4) #J/m^2-sec\n", + "c = 3*10**8 #m/s\n", + "res = 1.4*10**11 #m\n", + "rs = 7*10**7 #W/m^2\n", + "\n", + "#Calculations\n", + "Prad_e = Se/c\n", + "Ss = Se*((res/rs)**2)\n", + "Prad_s = Ss/c\n", + "\n", + "#Results\n", + "print \"Radiation pressure at the surface of the earth =%.2e N/m^2\"%Prad_e\n", + "print \"Radiation pressure at the surface of the sun =%.3e N/m^2\"%Prad_s" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radiation pressure at the surface of the earth =4.67e-06 N/m^2\n", + "Radiation pressure at the surface of the sun =1.867e+01 N/m^2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.28, Page 10.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "s = 2 # energy received by the earth in cal/cm^2.min\n", + "e0 = 8.85e-12 # electric permittivity of space\n", + "mu0 = 1.2567e-6 # magnetic permittivity of space\n", + "c = 3e8 # speed of light in meter/sec\n", + "\n", + "#calculations\n", + "r = sqrt(mu0 / e0)\n", + "P = s*4.2/(60*1e-4)\n", + "E = sqrt(P*r)\n", + "H = E/r\n", + "\n", + "#Result\n", + "print \"Magnitude of electric field vector = %.1f v/m\\nMagnitude of magnetic field vector = %.3f A/m\"%(E * sqrt(2),H*sqrt(2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnitude of electric field vector = 1027.2 v/m\n", + "Magnitude of magnetic field vector = 2.726 A/m\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.29, Page 10.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "H = 1 # magnitude of magnetic field vector A/m\n", + "e0 = 8.85e-12 # electric permittivity of space\n", + "mu0 = 1.2567e-6 # magnetic permittivity of space\n", + "c = 3e8 # speed of light in meter/sec\n", + "\n", + "#Calculations\n", + "r = sqrt(mu0 / e0) # ratio of E,H\n", + "E = H * r\n", + "\n", + "#Result\n", + "print \"Magnitude of electric field vector = %.2f v/m.\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnitude of electric field vector = 376.83 v/m.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.31, Page 10.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "p = 1000 # power of lamp in W\n", + "d = 2 # distance of a point from lamp in meter\n", + "e0 = 8.85e-12 # electric permittivity of space\n", + "mu0 = 1.2567e-6 # magnetic permittivity of space\n", + "c = 3e8 # speed of light in meter/sec\n", + "\n", + "#Calculations\n", + "s = p / (4 * pi * d**2) #calculation for \n", + "r = sqrt(mu0 / e0) # ratio of E,H\n", + "E = sqrt(s * r)#calculation for average value of intensity of electric field of radiation\n", + "\n", + "#Result\n", + "print \"Average value of the intensity of electric field of radiation = %.2f v/m.\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Average value of the intensity of electric field of radiation = 86.58 v/m.\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.32, Page 10.49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "k = 81 # relative permittivity of water \n", + "c = 3e8 # speed of light in meter/sec\n", + "\n", + "#Calculations\n", + "mu = sqrt(k)\n", + "v = c / mu\n", + "\n", + "#Result\n", + "print \"Refractive index of distilled water is %d \\nSpeed of light in water is %.2e m/sec\"%(mu,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of distilled water is 9 \n", + "Speed of light in water is 3.33e+07 m/sec\n" + ] + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_11.ipynb b/Engineering_Physics/Chapter_11.ipynb new file mode 100755 index 00000000..0cd9f3f6 --- /dev/null +++ b/Engineering_Physics/Chapter_11.ipynb @@ -0,0 +1,1203 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11: Theory of Relativity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.5, Page 11.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "# Given \n", + "x = 100 # in meter\n", + "y = 10 # in meter\n", + "z = 5 # in meter\n", + "t = 1e-4 # in sec\n", + "# coordinates of point in frame F\n", + "v = 2.7e8 # velocity of frame F_ w.r.t. frame F in m/sed\n", + "c=3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "# according to Galilean transformation\n", + "x__ = x-v*t\n", + "y__=y\n", + "z__=z\n", + "t__=t\n", + "# according to Lorentz transformation\n", + "x_ = (x-v*t)/sqrt(1-(v/c)**2)\n", + "y_=y\n", + "z_=z\n", + "t_=(t-(v*x/c**2))/sqrt(1-(v/c)**2)\n", + "\n", + "#Results\n", + "print \"Coordinate of the event in reference frame F_ using \\n(a)Galilean transformation-x=%.f m, y=%.f m, z = %.f m, t = %.e sec\"%(x__,y__,z__,t__) \n", + "print \"(b)Lorentz transformation-x=%.f m,y =%.f m, z = %.f m, t=%.e sec \"%(x_,y_,z_,t_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coordinate of the event in reference frame F_ using \n", + "(a)Galilean transformation-x=-26900 m, y=10 m, z = 5 m, t = 1e-04 sec\n", + "(b)Lorentz transformation-x=-61713 m,y =10 m, z = 5 m, t=2e-04 sec \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.6, Page 11.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 4 # ratio of mass of particle to the rest mass\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / r)**2)\n", + "\n", + "#Result\n", + "print \"Speed of particle is %.e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of particle is 3e+08 meter/sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.7, Page 11.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 1.2 # ratio of mass of particle to the rest mass\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / r)**2)\n", + "\n", + "#Results\n", + "print \"Speed of particle is %.3f c\"%(v/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of particle is 0.553 c\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.9, Page 11.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E = 2 # kinetic energy of electron in Mev\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / (1 + (1.6e-19 * 2e6) / (9.1e-31 * 3e8**2)))**2)\n", + "m = (9.1e-31) / sqrt(1 - (v / 3e8)**2)\n", + "\n", + "#Results\n", + "print \"Speed of electron is %.2f c\\nMass of electron is %.2e kg\"%(v/3e8,m)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of electron is 0.98 c\n", + "Mass of electron is 4.47e-30 kg\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11, Page 11.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "r = 2.25 # ratio of mass of particle to the rest mass\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / r)**2)\n", + "\n", + "#Result\n", + "print \"Speed of particle is %.2e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of particle is 2.69e+08 meter/sec\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.12, Page 11.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 2. # ratio of kinetic energy of body to its rest mass\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / (r + 1))**2)\n", + "\n", + "#Result\n", + "print \"Velocity of particle is %.2f c\"%(v/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of particle is 0.94 c\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.13, Page 11.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 11. # ratio of mass of particle to the rest mass of electron\n", + "\n", + "#Calculations\n", + "KE = (r - 1) * 9.1e-31 * 3e8**2 / (1.6e-19)\n", + "m = 3e8 * sqrt(1 - (1 / r)**2) * 9.1e-31 * 11\n", + "\n", + "#Result\n", + "print \"Kinetic energy of electron is %.1f MeV\\nMomentum of particle is %.2e N-sec\"%(KE/1e6,m)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Kinetic energy of electron is 5.1 MeV\n", + "Momentum of particle is 2.99e-21 N-sec\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.14, Page 11.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "m = 1.67e-27 # mass of electron in kg\n", + "m_ = 9.1e-31 # rest mass of electron in kg\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (m_ / m)**2)\n", + "\n", + "#Result\n", + "print \"Velocity of electron is %.3e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of electron is 3.000e+08 meter/sec\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.15, Page 11.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 0.1 # kinetic speed of electron in Mev\n", + "\n", + "#Calculations\n", + "v_ = sqrt(2 * (E * 1.6e-13) / 9.1e-31)\n", + "v = 3e8 * sqrt(1 - (1 / (1 + (1.6e-13 * E) / (9.1e-31 * 3e8**2)))**2)\n", + "\n", + "#Results\n", + "print \"Speed according to classical mechanics is %.2e meter/sec\\nSpeed according to relativistic mechanics is %.2e meter/sec\"%(v_,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed according to classical mechanics is 1.88e+08 meter/sec\n", + "Speed according to relativistic mechanics is 1.64e+08 meter/sec\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.17, Page 11.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r1 = 3. # ratio of kinetic energy of body to its rest mass in first case\n", + "r2 = 1. # ratio of kinetic energy of body to its rest mass in second case\n", + "\n", + "#Calculations\n", + "v1 = 3e8 * sqrt(1 - (1 / (r1 + 1))**2)\n", + "v2 = 3e8 * sqrt(1 - (1 / (r2 + 1))**2)\n", + "\n", + "#Results\n", + "print \"Velocity of particle if kinetic energy is %d times of rest mass energy is %.2e meter/sec\\nVelocity of particle if kinetic energy is %.1e times of rest mass energy is %e meter/sec\"%(r1,v1,r2,v2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of particle if kinetic energy is 3 times of rest mass energy is 2.90e+08 meter/sec\n", + "Velocity of particle if kinetic energy is 1.0e+00 times of rest mass energy is 2.598076e+08 meter/sec\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.19, Page 11.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 1.5 # kinetic energy of electron in Mev\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / (1 + (1.6e-19 * 2e6) / (9.1e-31 * 3e8**2)))**2)\n", + "m = (E * 1.6e-13 / (3e8)**2) + 9.1e-31\n", + "\n", + "#Results\n", + "print \"Speed of electron is %.2e meter/sec\\nMass of electron is %.1e kg\"%(v,m)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of electron is 2.94e+08 meter/sec\n", + "Mass of electron is 3.6e-30 kg\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.20, Page 11.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "r = 3. / 2 # ratio of mass of metre stick to the rest mass of metre stick\n", + "\n", + "#Calculations\n", + "l = 1 * (1. / r)\n", + "\n", + "#Result\n", + "print \"Length of meter stick is %.2f meter if mass is %.2f times of its rest mass\"%(l,r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length of meter stick is 0.67 meter if mass is 1.50 times of its rest mass\n" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.21, Page 11.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "# Given \n", + "r = 1. / 2 # ratio of area of circular lamina in frame S_ to the ratio of area of circular lamina in frame S\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - r**2)\n", + "\n", + "#Result\n", + "print \"Velocity of frame S_ w.r.t. frame S is %.1e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of frame S_ w.r.t. frame S is 2.6e+08 meter/sec\n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.22, Page 11.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import * \n", + "# Given \n", + "t = 1 # lose in time in an hour in minute\n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - ((60. - t) / 60)**2)\n", + "\n", + "#Result\n", + "print \"Speed of clock is %.2e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of clock is 5.45e+07 meter/sec\n" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.23, Page 11.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "# Given \n", + "t_ = 2.5e-8 # proper life of pi+ mesons in sec\n", + "v = 2.4e8 # velocity of beam of mesons in m/sec\n", + "r = 1. / exp(2) # ratio of final flux to initial flux of the meson beam\n", + "\n", + "#Calculations\n", + "t = t_ / sqrt(1 - (v / 3e8)**2)\n", + "T = t * log(1. / r)\n", + "d = T * v\n", + "\n", + "#Result\n", + "print \"Distance travel by the beam is %.2f meter\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance travel by the beam is 20.00 meter\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.24, Page 11.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "v = 1.8e8 # velocity of space ship away from the earth in m/sec\n", + "v1 = 2.1e8 # velocity of rocket w.r.t. space ship away from the earth in first case in m/sec\n", + "v2 = -2.1e8 # velocity of rocket w.r.t. space ship away from the earth in second case in m/sec\n", + "\n", + "#Calculations\n", + "u1 = (v1 + v) / (1 + ((v1 * v) / (3e8)**2))\n", + "u2 = (v2 + v) / (1 + ((v2 * v) / (3e8)**2))\n", + "\n", + "#Results\n", + "print \"Velocity of rocket w.r.t. earth in first case = %.2f c away from the earth\\nVelocity of rocket w.r.t. earth in second case = %.2f c away from the earth \"%(u1/3e8,u2/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of rocket w.r.t. earth in first case = 0.92 c away from the earth\n", + "Velocity of rocket w.r.t. earth in second case = -0.17 c away from the earth \n" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.25, Page 11.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "l = 1 # length of the rod in meter\n", + "v = 1.8e8 # speed of rod along its length in meter/sec\n", + "\n", + "#Calculations\n", + "L = l * sqrt(1- (v / 3e8)**2)\n", + "\n", + "#Result\n", + "print \"Length as it appear to the observer is %.1f meter\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length as it appear to the observer is 0.8 meter\n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.26, Page 11.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "l = 2 # length of the rod in meter\n", + "v = 2.7e8 # speed of rod along its length in meter/sec\n", + "\n", + "#Calculations\n", + "L = l * sqrt(1- (v / 3e8)**2)\n", + "\n", + "#Result\n", + "print \"Length as it appear to the observer is %.3f meter\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length as it appear to the observer is 0.872 meter\n" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.27, Page 11.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "l = 100. # consider the length of the rod in meter\n", + "v = 2.4e8 # speed of rod in meter/sec\n", + "theta = pi / 3 # direction of velocity of rod along its length in radian\n", + "\n", + "#Calculations\n", + "Lx = l * cos(theta)\n", + "Ly = l * sin(theta)\n", + "L_x = Lx * sqrt(1 - (v / 3e8)**2)\n", + "L_y = Ly \n", + "L = sqrt(L_x**2 + L_y**2)\n", + "p_l = ((l - L) / l) * 100 \n", + "\n", + "#Result\n", + "print \"Percentage length contraction is %.1f percent\"%p_l" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage length contraction is 8.3 percent\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.28, Page 11.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "# Given \n", + "r = 0.5 # ratio of length of rod when it is in motion to the length of the rod when it is in rest \n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - r**2)\n", + "\n", + "#Result\n", + "print \"Speed of the rod relative to observer is %.3f c\"%(v/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of the rod relative to observer is 0.866 c\n" + ] + } + ], + "prompt_number": 53 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.29, Page 11.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "l = 5 # length of the rod in meter\n", + "v = 1.8e8 # speed of rod in meter/sec\n", + "theta = pi / 6 # direction of velocity of rod along its length in radian\n", + "\n", + "#Calculations\n", + "Lx = l * cos(theta)\n", + "Ly = l * sin(theta)\n", + "L_x = Lx * sqrt(1 - (v / 3e8)**2)\n", + "L_y = Ly \n", + "L = sqrt(L_x**2 + L_y**2)\n", + "orientation = atan(L_y / L_x) * (180 / pi)\n", + "\n", + "#Results\n", + "print \"Length of the rod in moving frame is %.2f meter\\nOrientation of the rod is %.2f degree\"%(L,orientation)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length of the rod in moving frame is 4.27 meter\n", + "Orientation of the rod is 35.82 degree\n" + ] + } + ], + "prompt_number": 55 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.30, Page 11.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "T = 17.8e-9 # half-life of prticle at rest in sec\n", + "v = 2.4e8 # speed of particle in meter/sec\n", + "\n", + "#Calculations\n", + "t = T / (sqrt(1 - (v / 3e8)**2))\n", + "\n", + "#Result\n", + "print \"New half-life of particle is %.2f nanosec\"%(t/1e-9)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "New half-life of particle is 29.67 nanosec\n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.31, Page 11.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "T = 24 # no. of hours in a day\n", + "v = 1e8 # speed of spaceship in meter/sec\n", + "\n", + "#Calculations\n", + "t = T * (sqrt(1 - (v / 3e8)**2))\n", + "T_ = T - t\n", + "m=(T_-1)*60\n", + "s=(m-22)*60\n", + "\n", + "#Result\n", + "print \"Time lost per day is %d hours %d minute %d sec\"%(T_,m,s)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time lost per day is 1 hours 22 minute 21 sec\n" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.32, Page 11.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "T = 4. # no. of year when rocket is moving corresponding to one year \n", + "\n", + "#Calculations\n", + "v = 3e8 * sqrt(1 - (1 / T)**2)\n", + "\n", + "#Result\n", + "print \"Speed of rocket is %.2f c\"%(v/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of rocket is 0.97 c\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.33, Page 11.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 4 # distance of star from the earth in light years\n", + "v = 3e8 * sqrt(0.9999) # speed of rocket in meter/sec\n", + "\n", + "#Calculations\n", + "t = (2 * d * 3e8) / v\n", + "T_ = t * sqrt(1 - (v / 3e8)**2)\n", + "\n", + "#Result\n", + "print \"Time taken by the rocket is %.2f year\"%T_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time taken by the rocket is 0.08 year\n" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.34, Page 11.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 2e-7 # life time of particle when it is moving in sec\n", + "v = 2.8e8 # speed of particle in meter/sec\n", + "\n", + "#Calculations\n", + "T_ = t * sqrt(1 - (v / 3e8)**2)\n", + "\n", + "#Result\n", + "print \"Proper life time of particle is %.2e sec\"%T_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Proper life time of particle is 7.18e-08 sec\n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.35, Page 11.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "v1 = 2.7e8 # velocity of first electron beam in meter/sec\n", + "v2 = -2.7e8 # velocity of second electron beam in meter/sec\n", + "\n", + "#Calculations\n", + "u = v1 - v2\n", + "u_ = (v1 - v2) / (1 - (v1 * v2) / (3e8)**2)\n", + "\n", + "#Results\n", + "print \"Velocity of electrons beam w.r.t. another electron beam according to Newtonian mechanics is %.1f c\\nVelocity of electrons beam measured by the observer moving with other electron beam = %.2f c\"%(u/3e8,u_/3e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of electrons beam w.r.t. another electron beam according to Newtonian mechanics is 1.8 c\n", + "Velocity of electrons beam measured by the observer moving with other electron beam = 0.99 c\n" + ] + } + ], + "prompt_number": 63 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.37, Page 11.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E = 900 # total relativistic energy of proton in Mev\n", + "m = 1.63-27 # rest mass of proton in kg\n", + "c = 3e8 # velocity of photon in meter/sec\n", + "\n", + "#Calculations\n", + "m_ = (E * 1.6e-13) / (c)**2\n", + "\n", + "#Results\n", + "print \"Relativistic mass of proton is %.2e kg\\nHere relativistic mass is same as rest mass\\n hence proton is at rest and speed and kinetic energy of proton will be zero\"%(m_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relativistic mass of proton is 1.60e-27 kg\n", + "Here relativistic mass is same as rest mass\n", + " hence proton is at rest and speed and kinetic energy of proton will be zero\n" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.38, Page 11.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E = 5.4e6 # energy liberates during dynamite explosion in J/kg\n", + "c = 3e8 # velocity of photon in meter/sec\n", + "\n", + "#Calculations\n", + "E_ = 1 * c**2 # energy liberated by 1 kg content in J\n", + "f = E / E_\n", + "\n", + "#Result\n", + "print \"Fraction of total energy content in it is %.1e per kg\"%f" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fraction of total energy content in it is 6.0e-11 per kg\n" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.39, Page 11.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import * \n", + "# Given \n", + "k = 1.02 # kinetic energy of electron in Mev\n", + "E_ = 0.51 # rest mass energy of electron in Mev\n", + "c = 3e8 # velocity of photon in meter/sec\n", + "\n", + "#Calculations\n", + "E = k + E_\n", + "v = c * sqrt(1 - (E_ / E)**2)\n", + "\n", + "#Result\n", + "print \"Speed of the electron is %.2e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of the electron is 2.83e+08 meter/sec\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.40, Page 11.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 1400 # solar energy receives by the earth in W/square meter\n", + "d = 1.5e11 # distance between earth and the sun in meter\n", + "c = 3e8 # velocity of photon in meter/sec\n", + "\n", + "#Calculations\n", + "E_ = 4 * pi * d**2 * E\n", + "m = E_ / c**2\n", + "\n", + "#Result\n", + "print \"Rate of decrement of mass of the sun is %.2e kg/sec\"%m" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rate of decrement of mass of the sun is 4.40e+09 kg/sec\n" + ] + } + ], + "prompt_number": 67 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_12.ipynb b/Engineering_Physics/Chapter_12.ipynb new file mode 100755 index 00000000..1b8c5610 --- /dev/null +++ b/Engineering_Physics/Chapter_12.ipynb @@ -0,0 +1,1613 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12: Applied Nuclear Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.1, Page 12.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log\n", + "\n", + "# Given \n", + "E = 1.14 # energy of gamma radiation in Mev\n", + "l = 0.2 # length of aluminium in meter\n", + "p = 0.03 # reduce in intensity in beam\n", + "d = 2700 # density of aluminium in kg/m^3 \n", + "\n", + "#Calculations\n", + "mu = (1 / l) * log(1 / p)\n", + "k = mu / d\n", + "x = 0.693 / mu\n", + "\n", + "#Result\n", + "print \"Mass absorption coeffiecient of Al for this radiation is %f m^2/kg\\nHalf value thickness is %.4f meter\"%(k,x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass absorption coeffiecient of Al for this radiation is 0.006494 m^2/kg\n", + "Half value thickness is 0.0395 meter\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.2, Page 12.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given that\n", + "E = 1.1 # energy of gamma radiation in Mev\n", + "l = 0.25 # length of aluminium in meter\n", + "p = 0.02 # reduce in intensity in beam\n", + "d = 2700 # density of aluminium in kg/m^3 \n", + "\n", + "#Calculations\n", + "mu = (1 / l) * log(1 / p)\n", + "k = mu / d\n", + "x = 0.693 / mu\n", + "\n", + "#Result\n", + "print \"Mass attenuation coefficient of Al for this radiation is %.1e m^2/kg\\nHalf value thickness is %.4f meter\"%(k,x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass attenuation coefficient of Al for this radiation is 5.8e-03 m^2/kg\n", + "Half value thickness is 0.0443 meter\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.3, Page 12.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 15 # half-life for Na(23) in hours\n", + "r = 93.75 # percentage fraction of sample which decayed \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / t\n", + "T = (1 / lamda) * (log(100 / (100 - r)))\n", + "\n", + "#Result\n", + "print \"Time taken for 93.75 per decay of sample is %d hours\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time taken for 93.75 per decay of sample is 60 hours\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.4, Page 12.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 4 # half-life of radioactive element in years\n", + "r = 1. / 64 # ratio of mass of element present in specimen to the initial mass of element \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / t\n", + "T = (1 / lamda) * log(1 / r)\n", + "\n", + "#Result\n", + "print \"Time after which element present in specimen reduce to 1/64 of its original value is %d years\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time after which element present in specimen reduce to 1/64 of its original value is 24 years\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.5, Page 12.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 15 # half-life of radioactive element in years\n", + "r = 0.025 # ratio of mass of element present in specimen to the intial mass of element \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / t\n", + "T = (1 / lamda) * log(1 / r)\n", + "\n", + "#result\n", + "print \"Period in which 2.5 percent of the initial quantity left over is %.2f years\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Period in which 2.5 percent of the initial quantity left over is 79.85 years\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.6, Page 12.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 3.8 # half-life for radon in days\n", + "r = 60. # percentage fraction of sample which decayed \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / t\n", + "T = (1 / lamda) * (log(100 / (100 - r)))\n", + "\n", + "#Result\n", + "print \"Time taken for 60 percent decay of sample is %.3f days\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time taken for 60 percent decay of sample is 5.024 days\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.7, Page 12.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 4.28e-4 # decay constant in per year\n", + "\n", + "#Calculations\n", + "T = 0.693 / lamda\n", + "t = 1 / lamda\n", + "\n", + "#Result\n", + "print \"Half life time is %.2f years\\nMean life time is %.2f years\"%(T,t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Half life time is 1619.16 years\n", + "Mean life time is 2336.45 years\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.8, Page 12.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 30 # time in years\n", + "r = 1. / 64 # ratio of final mass of element to the intial mass of element \n", + "\n", + "#Calculations\n", + "lamda = log(1 / r) / t\n", + "T = 0.693 / lamda\n", + "\n", + "#Result\n", + "print \"Half life of radioactive material is %d years\"%(ceil(T))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Half life of radioactive material is 5 years\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.9, Page 12.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "t = 2.1 # half life in minute\n", + "r = 60 # percentage fraction of sample which decayed \n", + "\n", + "#Calculation\n", + "lamda = 0.693 / t\n", + "\n", + "#Result\n", + "print \"Decay constant is %.2f per minute\"%lamda" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Decay constant is 0.33 per minute\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.10, Page 12.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 2.7 # half-life of Au(198) in days\n", + "m = 1e-6 # mass of sample in gm\n", + "T = 8 * 86400 # time in seconds\n", + "\n", + "#Calculations\n", + "lamda = 0.693 / (t * 86400)\n", + "N = (m * 6.023e23) / 198 # by the formula (N = mass*Avogadro number/molar mass)\n", + "A_ = lamda * N\n", + "A = A_ * (1 / exp(lamda * T))\n", + "\n", + "#Result\n", + "print \"Activity of sample is %.4e decays/sec\"%A" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Activity of sample is 1.1595e+09 decays/sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.11, Page 12.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 3 # no. of half lives\n", + "\n", + "#Calculation\n", + "f = (1. / 2)**n\n", + "\n", + "#Result\n", + "print \"Fraction of sample left after %d half lives is %.3f \"%(n,f)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fraction of sample left after 3 half lives is 0.125 \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.12, Page 12.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "t = 2 # life period of radioactive substance in years\n", + "T = 4 # time in years\n", + "m = 10. # mass of substance in mg\n", + "\n", + "#Calculation\n", + "N = m / T # in mg\n", + "\n", + "#Result\n", + "print \"Substance remained unchanged after 4 years is %.1f mg\"%N" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Substance remained unchanged after 4 years is 2.5 mg\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.13, Page 12.36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given that\n", + "m = 1. # initial mass of radium in gm\n", + "m_ = 0.0021 # final mass of radium in gm\n", + "t = 5. # time for decay from m to m_ in years\n", + "\n", + "#Calculations\n", + "lamda = log(m / (1 - m_)) / t\n", + "T = 0.693 / lamda\n", + "T_ = 1. / lamda\n", + "\n", + "#Result\n", + "print \"Decay constant is %.4f per year\\nHalf life of sample is %.1f years\\nAverage life of sample is %.3f years\"%(lamda,T,T_)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Decay constant is 0.0004 per year\n", + "Half life of sample is 1648.3 years\n", + "Average life of sample is 2378.452 years\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.14, Page 12.36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 10. # time in days\n", + "r = 15. # percentage fraction of sample which remain \n", + "\n", + "#Calculations\n", + "lamda = log(100. / 15) / t\n", + "T = 0.693 / lamda\n", + "\n", + "#Result\n", + "print \"Half life of sample is %.3f days\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Half life of sample is 3.653 days\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.15, Page 12.36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 12.3 # half life in year\n", + "T = 50 # time in year \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / t\n", + "f = 1 / exp(lamda * T)\n", + "\n", + "#Result\n", + "print \"Fraction of radioactive isotope remained is %.2f \"%f" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fraction of radioactive isotope remained is 0.06 \n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.16, Page 12.37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "R = 1 # radioactivity of Pb(214) in curie\n", + "t = 26.8 # half life in minute \n", + "\n", + "#calculations\n", + "lamda = 0.693 / (t * 60)\n", + "R = 1 * 3.7e10 # in disintegration per sec\n", + "m = (R * 214) / (6.023e23 * lamda)\n", + "\n", + "#Result\n", + "print \"Mass of Pb(214)is %.2e gm\"%m" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass of Pb(214)is 3.05e-08 gm\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.17, Page 12.37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "R = 1e6 # radioactivity of Pb(214) in disintegrations per sec\n", + "t = 26.8 # half life in minute \n", + "\n", + "#Calculations\n", + "lamda = 0.693 / (t * 60)\n", + "m = (R * 214) / (6.023e23 * lamda)\n", + "\n", + "#Result\n", + "print \"Mass of Pb(214) is %.2e gm\"%m" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass of Pb(214) is 8.24e-13 gm\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.18, Page 12.37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "m = 1. # mass of Ra(226) in gm \n", + "R = 1. # radioactivity of Ra(226) in curie\n", + "\n", + "#Calculations\n", + "r = R * 3.7e10 # in disintegrations per sec\n", + "N = 6.023e23 * m / 226\n", + "lamda = r * 226 / 6.023e23\n", + "T = 1. / lamda\n", + "T_ = 0.693 / lamda\n", + "\n", + "#Result\n", + "print \"Mean life of radium is %.2e year\\nHalf life of radium is %.2e year\"%(T,T_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mean life of radium is 7.20e+10 year\n", + "Half life of radium is 4.99e+10 year\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.19, Page 12.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "m = 0.0001 # mass of Sr(90) in gm\n", + "t = 28. # half life of Sr(90) in year\n", + "t_ = 9. # time in sec\n", + "\n", + "#Calculations\n", + "lamda = 0.693 / (t * 86400 * 365)\n", + "N_ = 6.023e23 * m / 90\n", + "n = N_ * lamda * t_\n", + "\n", + "#Result\n", + "print \"Activity of Sr is %.2e disintegration/sec.\"%n\n", + "#Incorrect answer in the textbook\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Activity of Sr is 4.73e+09 disintegration/sec.\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.20, Page 12.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "t = 1600 # the half life of radium(226) in year\n", + "t1 = 3.8 # the half life of radon(222) in days\n", + "m = 1 # mass of Ra(226) in gm\n", + "\n", + "#Calculation\n", + "m_ = (222 * t1 * m) / (226 * 365 * t) # by the formula N1*t = N2*t1\n", + "\n", + "#Result\n", + "print \"Mass of radon is %.2e gm\"%m_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass of radon is 6.39e-06 gm\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.21, Page 12.39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "m1 = 4.002603 # mass of He(4) in a.m.u.\n", + "m2 = 3.016056 # mass of H(3) in a.m.u.\n", + "m3 = 1.007276 # mass of H(1) in a.m.u.\n", + "\n", + "#Calculations\n", + "k = m2 + m3 - m1\n", + "E = k * 931\n", + "\n", + "#Result\n", + "print \"Energy of gamma ray photon is %.3f MeV\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of gamma ray photon is 19.299 MeV\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.22, Page 12.39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 3 # kinetic energy of proton in Mev\n", + "m1 = 1.007276 # mass of H(1) in a.m.u.\n", + "m2 = 3.016056 # mass of H(3) in a.m.u.\n", + "m3 = 1.008665 # mass of neutron in a.m.u.\n", + "m4 = 3.016036 # mass of He(3) in a.m.u.\n", + "\n", + "#calculations\n", + "k = m1 + m2 - m3 - m4\n", + "E = k * 931.5\n", + "\n", + "#Result\n", + "print \"Q value of reaction is %.4f MeV\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Q value of reaction is -1.2752 MeV\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.23, Page 12.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 200 # energy released per fission in Mev\n", + "m = 0.01 # mass of U(235) in gm\n", + "n = 235 # atomic no of sample\n", + "N_0=6.023e23 # Avogadro constant\n", + "\n", + "#calculations\n", + "E_ = E * 1.6e-13\n", + "k = E_ * N_0 * m / n\n", + "H = k / 4.168\n", + "\n", + "#Result\n", + "print \"Heat produce by complete disintegration is %.3e cal\\nEnergy released is %.1e J\"%(H,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat produce by complete disintegration is 1.968e+08 cal\n", + "Energy released is 3.2e-11 J\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.24, Page 12.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 200 # energy released per fission in Mev\n", + "m = 1 # mass of U(235) in kg\n", + "\n", + "#Calculations\n", + "E_ = E * 1.6e-13\n", + "k = E_ * 6.023e26 * m / 235\n", + "\n", + "#Result\n", + "print \"Energy released by fission of 1 kg of U(235)is %.2e J\"%k" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy released by fission of 1 kg of U(235)is 8.20e+13 J\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.25, Page 12.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "P = 1e9 # power required for enlighten the city in watt\n", + "e = 30 # percentage efficiency of nuclear reactor\n", + "E = 3.2e-11 # energy released per fission in J\n", + "\n", + "#Calculations\n", + "E_ = E * 30 / 100\n", + "N = P / E_\n", + "N_ = N * 24 * 3600\n", + "m = N_ * 235 / 6.023e26 \n", + "\n", + "#Result\n", + "print \"Amount of fuel required per day is %.2f kg\"%m" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Amount of fuel required per day is 3.51 kg\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.26, Page 12.41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 200 # energy released per fission of U(235)in Mev\n", + "m = 3.7 # mass of U(235) consumed in a day in kg\n", + "e = 20 # percentage efficiency of reactor\n", + "\n", + "#Calculations\n", + "E_ = E * 1.6e-13\n", + "N = m * 6.023e26 / 235\n", + "H = E_ * e / 100\n", + "k = H * N / (24 * 3600)\n", + "\n", + "#Result\n", + "print \"Power output of reactor is %.3f GW\"%(k * 1e-9)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power output of reactor is 0.702 GW\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.27, Page 12.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "m1 = 4.00260 # mass of He(4) in a.m.u.\n", + "m2 = 0.00055 # mass of electron in a.m.u.\n", + "m3 = 12 # mass of C(12) in a.m.u.\n", + "\n", + "#Calculations\n", + "delta_m = 3 * m1 - m3\n", + "E = delta_m * 931\n", + "\n", + "#Result\n", + "print \"Energy produce by each reaction is %.4f MeV\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy produce by each reaction is 7.2618 MeV\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.28, Page 12.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "P = 5e7 # power in watt\n", + "e = 33. # percentage efficiency of nuclear reactor\n", + "m1 = 2.01478 # mass of H(2) in a.m.u.\n", + "m2 = 4.00388 # mass of He(4) in a.m.u.\n", + "\n", + "#calculations\n", + "m = (2 * m1) - m2\n", + "E = m * 931 * 1.6e-13\n", + "E_O = (E * e) /(2 * 100)\n", + "N = P / E_O\n", + "k = N * m1 / 6.023e26\n", + "M = k * 24 * 3600 \n", + "\n", + "#Result\n", + "print \"Mass of deuterium consumed per day is %.4f kg\"%M" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass of deuterium consumed per day is 0.0229 kg\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.29, Page 12.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given\n", + "d = 1.8 # diameter in meter\n", + "B = 0.8 # magnetic field in tesla\n", + "m = 6.68e-27 # mass of He(4) in kg\n", + "e = 1.6e-19 # charge on an electron in Coulomb\n", + "\n", + "#Calculations\n", + "r = d / 2\n", + "E = (B**2 * (2 * e)**2 * r**2) / (2 * m * 1.6e-19 * 10**6) \n", + "f = B * 2 * e / (2 * pi * m)\n", + "N = f / 2\n", + "\n", + "#Result\n", + "print \"Energy is %.2f MeV\\nNumber of revolution made by particle to obtain above energy is %.2e per sec\"%(E,N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy is 24.83 MeV\n", + "Number of revolution made by particle to obtain above energy is 3.05e+06 per sec\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.30, Page 12.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given\n", + "f = 12e6 # oscillator frequency of cyclotron in Hz\n", + "r = 0.53 # radius of dee in meter\n", + "e = 1.6e-19 # charge on an electron in Coulomb\n", + "\n", + "#Calculations\n", + "B = (2 * pi * f * 2 * 1.67e-27) / e\n", + "\n", + "#Result\n", + "print \"Value of magnetic induction needed to accelerate deuteron in it is %.3f T\"%B" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Value of magnetic induction needed to accelerate deuteron in it is 1.574 T\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.31, Page 12.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "f = 10e6 # frequency of applied Emf in Hz\n", + "r = 0.32 # radius in meter\n", + "m = 3.32e-27 # mass of deuteron in kg\n", + "e = 1.6e-19 # charge on an electron in Coulomb\n", + "\n", + "#Calculations\n", + "B = (2 * pi * f * m) / e\n", + "v = (e * B * r) / m\n", + "\n", + "#Result\n", + "print \"Flux density of the magnetic field is %.3f T\\nVelocity of the deuterons emerging out of the cyclotron is %.2e m/sec \"%(B, v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flux density of the magnetic field is 1.304 T\n", + "Velocity of the deuterons emerging out of the cyclotron is 2.01e+07 m/sec \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.32, Page 12.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "f = 60 # operating frequency in Hz\n", + "d = 1.6 # diameter in meter\n", + "B = 0.5 # magnetic field at the orbit in tesla\n", + "e = 1.6e-19 # charge on an electron in Coulomb\n", + "\n", + "#Calculations\n", + "r = d / 2\n", + "w = 2 * pi * f\n", + "E = 4 * e * w * r**2 * B\n", + "E_ = 3e8 * r * B / 1e6\n", + "\n", + "#Result\n", + "print \"Energy gained per turn is %.1f eV\\nFinal energy is %d MeV\"%(E / e,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy gained per turn is 482.5 eV\n", + "Final energy is 120 MeV\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.33, Page 12.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 70 # energy of betatron synchrotron in Mev\n", + "r = 0.28 # radius in meter\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E_ = E * 1.6e-13\n", + "B = E_ / (3e8 * e * r)\n", + "\n", + "#Result\n", + "print \"Magnitude of magnetic field is %.2f T\"%B" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnitude of magnetic field is 0.83 T\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.34, Page 12.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 4.18 # energy of alpha particle in Mev\n", + "n = 12 # no. of particle enter the chamber per sec\n", + "E_ = 40 # required energy of an ion pair in ev\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "R = n * E * 10**6 # in eV\n", + "N = R / E_\n", + "i = N * e\n", + "\n", + "#Result\n", + "print \"The current produced = %.e Amp\"%i" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The current produced = 2e-13 Amp\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.35, Page 12.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given\n", + "n = 10**8 # no. of electron per discharge counted by GM counter\n", + "r = 500. # counting rate in counts per minutes\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "N = r / 60\n", + "i = N * n * e \n", + "\n", + "#Result\n", + "print \"Average current in the circuit = %.2e Amp\"%i" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Average current in the circuit = 1.33e-10 Amp\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.36, Page 12.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 10 # energy of electron in kev\n", + "B = 5e-5 # magnetic field of earth in tesla\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "f = e * B / 9.1e-31\n", + "E_ = E * 1.6e-16\n", + "v = sqrt((2 * E_) / 9.1e-31)\n", + "r = v / f\n", + "\n", + "#Result\n", + "print \"Frequency of cyclotron = %.3e per sec\\nLarmour radius = %.3f meter\"%(f,r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of cyclotron = 8.791e+06 per sec\n", + "Larmour radius = 6.745 meter\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.37, Page 12.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "B = 5e-9 # magnetic field in tesla\n", + "v = 3e5 # velocity of proton stream in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#calculations\n", + "r = (1.67e-27 * v) / (e * B)\n", + "\n", + "#Result\n", + "print \"Larmour radius is %.2e meter\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Larmour radius is 6.26e+05 meter\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.38, Page 12.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 1. # energy of He+ in kev\n", + "r = 0.188 # Larmour radius in meter\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E_ = E * 1.6e-16\n", + "v = sqrt((2 * E_) / (4 * 1.67e-27))\n", + "B = (4 * 1.67e-27 * v) / (e * r)\n", + "\n", + "#Result\n", + "print \"Magnetic field is %.3e tesla\"%B" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic field is 4.861e-02 tesla\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.39, Page 12.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 3.5 # energy of He++ ash particle in Mev\n", + "B = 8 # magnetic field in tesla\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E_ = E * 1.6e-13\n", + "v = sqrt(2 * E_ / (4 * 1.67e-27))\n", + "r = (4 * 1.67e-27 * v) / (2 * e * B)\n", + "\n", + "#Result\n", + "print \"Larmour radius is %.2e meter\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Larmour radius is 3.38e-02 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.40, Page 12.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 1e12 # electron density in number per m^3\n", + "E = 0.1 # thermal energy in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lamda = sqrt((8.85e-12 * E * e) / (d * e * e))\n", + "omega = sqrt(d * e**2 / (9.1e-31 * 8.85e-12))\n", + "f = omega / (2 * pi)\n", + "\n", + "#Results\n", + "print \"Debye length is %.2e meter\\nPlasma frequency is %.2f MHz\"%(lamda,f / 1e6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Debye length is 2.35e-03 meter\n", + "Plasma frequency is 8.97 MHz\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.41, Page 12.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 1e16 # density in per m^3\n", + "E = 2 # thermal energy in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lamda = sqrt((8.85e-12 * E * e) / (d * e * e))\n", + "omega = sqrt(d * e**2 / (9.1e-31 * 8.85e-12))\n", + "f = omega / (2 * pi)\n", + "\n", + "#Result\n", + "print \"Debye length is %.4e meter\\nPlasma frequency is %.3e Hz\"%(lamda,f)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Debye length is 1.0518e-04 meter\n", + "Plasma frequency is 8.973e+08 Hz\n" + ] + } + ], + "prompt_number": 25 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_13.ipynb b/Engineering_Physics/Chapter_13.ipynb new file mode 100755 index 00000000..db97b36d --- /dev/null +++ b/Engineering_Physics/Chapter_13.ipynb @@ -0,0 +1,995 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 13: Crystal Structure\n" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.1, Page 13.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "x = 2 # intercepts cut by the plane along vector a of crystallographic axes\n", + "y = 3 # intercepts cut by the plane along vector b of crystallographic axes\n", + "z = 1 # intercepts cut by the plane along vector c of crystallographic axes\n", + "\n", + "#Calculations\n", + "x_ = 6 / x\n", + "y_ = 6 / y\n", + "z_ = 6 / z\n", + "\n", + "#Result\n", + "print \"Miller indices of the plane are (%d %d %d)\"%(x_,y_,z_)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Miller indices of the plane are (3 2 6)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.2, Page 13.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "x = 1 # intercepts cut by the plane along vector a of crystallographic axes\n", + "y = 2 # intercepts cut by the plane along vector b of crystallographic axes\n", + "z = -3. / 2 # intercepts cut by the plane along vector c of crystallographic axes\n", + "\n", + "#Calculations\n", + "x_ = 6 / x\n", + "y_ = 6 / y\n", + "z_ = 6 / z\n", + "\n", + "print \"Miller indices of the plane are (%d %d %d)\"%(x_,y_,z_)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Miller indices of the plane are (6 3 -4)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.3, Page 13.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "x1 = 3. # intercepts cut by the plane along vector a of crystallographic axes in first case\n", + "y1 = 3. # intercepts cut by the plane along vector b of crystallographic axes in first case \n", + "z1 = 2. # intercepts cut by the plane along vector c of crystallographic axes in first case\n", + "x2 = 1. # intercepts cut by the plane along vector a of crystallographic axes in second case\n", + "y2 = 2. # intercepts cut by the plane along vector b of crystallographic axes in second case\n", + "k2 = 0. # raciprocal of intercepts cut by the plane along vector c of crystallographic axes in second case\n", + "x3 = 1. # intercepts cut by the plane along vector a of crystallographic axes in third case\n", + "y3 = 1./2 # intercepts cut by the plane along vector b of crystallographic axes in third case\n", + "z3 = 1. # intercepts cut by the plane along vector c of crystallographic axes in third case\n", + "\n", + "#Calculations\n", + "x_1 = 6. / x1\n", + "y_1 = 6. / y1\n", + "z_1 = 6. / z1\n", + "x_2 = 2. / x2\n", + "y_2 = 2. / y2\n", + "z_2 = 2*k2\n", + "x_3 = 2 * x3\n", + "y_3 = 2 * y3\n", + "z_3 = 2 * z3\n", + "\n", + "#Result\n", + "print \"Miller indices of the plane (i) In first case are (%d %d %d)\\n(ii) In second case are (%d %d %d)\\n(iii)In the third case are (%d %d %d).\"%(x_1,y_1,z_1,x_2,y_2,z_2,x_3,y_3,z_3)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Miller indices of the plane (i) In first case are (2 2 3)\n", + "(ii) In second case are (2 1 0)\n", + "(iii)In the third case are (2 1 2).\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.4, Page 13.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "x1 = 1 # coordinate on x axis for first plane\n", + "y1 = 0 # coordinate on y axis for first plane\n", + "z1 = 0 # coordinate on z axis for first plane\n", + "x2 = 1 # coordinate on x axis for second plane\n", + "y2 = 1 # coordinate on y axis for second plane\n", + "z2 = 1 # coordinate on z axis for second plane\n", + "\n", + "#Calculations\n", + "d1 = 1 / sqrt(x1**2 + y1**2 + z1**2)\n", + "d2 = 1 / sqrt(x2**2 + y2**2 + z2**2)\n", + "\n", + "#Result\n", + "print \"Spacing between the plane in first case is a / %d\\nSpacing between the plane in second case is a / %f\"%(d1,d2)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Spacing between the plane in first case is a / 1\n", + "Spacing between the plane in second case is a / 0.577350\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.5, Page 13.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given that\n", + "x = 1. # intercepts cut by the plane along vector a of crystallographic axes\n", + "y = 2. # intercepts cut by the plane along vector b of crystallographic axes\n", + "k = 0. # raciprocal of intercepts cut by the plane along vector c of crystallographic axes\n", + "a = 5. # length of vector a of crystallographic axes in angstrom\n", + "b = 5. # length of vector b of crystallographic axes in angstrom \n", + "c = 5. # length of vector c of crystallographic axes in angstrom\n", + "\n", + "#Calculations\n", + "x_ = 2. / x\n", + "y_ = 2. / y\n", + "z_ = 2 * k\n", + "d = a / sqrt(x_**2 + y_**2 + z_**2)\n", + "D=d**2\n", + "\n", + "#Result\n", + "print \"Miller indices of the plane are (%d %d %d)\\nInter planar distance is sqrt(%d) angstrom\"%(x_,y_,z_,D)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Miller indices of the plane are (2 1 0)\n", + "Inter planar distance is sqrt(0) angstrom\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.6, Page 13.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "x = 2 # intercepts cut by the plane along vector a of crystallographic axes\n", + "y = 2. / 3 # intercepts cut by the plane along vector b of crystallographic axes\n", + "k = 0 # raciprocal of intercepts cut by the plane along vector c of crystallographic axes\n", + "\n", + "#Calculations\n", + "x_ = 2. / x\n", + "y_ = 2. / y\n", + "z_ = 2 * k\n", + "\n", + "#Result\n", + "print \"Miller indices of the plane are (%d %d %d)\"%(x_,y_,z_)\n", + "\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Miller indices of the plane are (1 3 0)\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.7, Page 13.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "x1 = 2 # coordinate on x axis \n", + "y1 = 3 # coordinate on y axis \n", + "z1 = 1 # coordinate on z axis \n", + "r = 0.175 # atomic radius of fcc structure in nm\n", + "\n", + "#Calculations\n", + "a = (4 * r) / sqrt(2)\n", + "d = a / sqrt(x1**2 + y1**2 + z1**2)\n", + "\n", + "#Result\n", + "print \"Inter planar spacing is %.3f nm\"%d\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Inter planar spacing is 0.132 nm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.8, Page 13.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "x1 = 1 # coordinate on x axis in first case\n", + "y1 = 2 # coordinate on y axis in first case \n", + "z1 = 3 # coordinate on z axis in first case\n", + "x2 = 1\n", + "y2 = 1\n", + "z2 = 0\n", + "# coordinate of first plane in second case\n", + "x3 = 1\n", + "y3= 1\n", + "z3 = 1\n", + "# coordinate of second plane in second case\n", + "\n", + "#Calculations\n", + "x_=6/x1\n", + "y_=6/y1\n", + "z_=6/z1\n", + "d1 = 1 / sqrt(x2^2 + y2^2 + z2^2)\n", + "d2= 1/ sqrt(x3^2 + y3^2 + z3^2)\n", + "d = d1/d2\n", + "\n", + "#Results\n", + "print \"The ratio of intercepts of three axes by the point are %d : %d : %d\\nThe ratio of spacing between two planes is %.3f\"%(x_,y_,z_,d)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of intercepts of three axes by the point are 6 : 3 : 2\n", + "The ratio of spacing between two planes is 1.225\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.9, Page 13.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "a = 5 # the lattice constant of the structure in angstrom\n", + "\n", + "#Calculations\n", + "d = (sqrt(3) / 4) * a\n", + "\n", + "#Result\n", + "print \"Distance between two atoms is %.2f A\"%d\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance between two atoms is 2.17 A\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.10, Page 13.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given that\n", + "a = 3.56 # the length of cube edge in angstrom\n", + "\n", + "#Calculations\n", + "d = a / sqrt(2)\n", + "\n", + "#Result\n", + "print \"Permitive translation vector is %.2f A\"%d\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permitive translation vector is 2.52 A\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.11, Page 13.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "w = 207.2 # atomic weight of Pb\n", + "d = 11.36e3 # density of Pb in kg/m^3\n", + "a = 3.2e-10 # length of cube edge in meter\n", + "N = 6.023e26 # Avogadro's no. in per kg mole\n", + "\n", + "#Calculations\n", + "n = (a**3 * d * N) / w\n", + "\n", + "#Result\n", + "print \"Number of atom per unit cell is %d\"%n\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of atom per unit cell is 1\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.12, Page 13.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "M = 60.2 # molecular weight\n", + "d = 6250 # density in kg/m^3\n", + "N = 6.023e+26 # Avogadro's no. in per kg mole\n", + "n = 4. # for fcc lattice\n", + "\n", + "#Calculations\n", + "a = (((4 * M) / (N * d))**(1. / 3)) * 1e10\n", + "\n", + "#Result\n", + "print \"Lattice constant is %.f A\"%a\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant is 4 A\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.13, Page 1329" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "x1 = 1 # coordinate on x axis of plane\n", + "y1 = 0 # coordinate on y axis of plane\n", + "z1 = 0 # coordinate on z axis of plane\n", + "d = 2.82 # the space between successive plane in angstrom\n", + "theta = 8.8 # glancing angle in degree\n", + "\n", + "#Calculations\n", + "n = 1\n", + "lamda = 2 * d * sin(theta*pi/180) / n\n", + "\n", + "#Result\n", + "print \"Wavelength of x-ray is %.3f A\"%lamda\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of x-ray is 0.863 A\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.14, Page 13.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 2.51 # the space between adjacent plane in angstrom\n", + "theta = 9 # glancing angle in degree\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "lamda = 2 * d * sin(theta*pi/180) / n\n", + "n = 2 # for n=2\n", + "theta = degrees(asin(lamda / d))\n", + "\n", + "#Result\n", + "print \"Wavelength of x-ray is %.4f A\\nGlancing angle for second order diffraction is %.1f degree\"%(lamda,theta)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of x-ray is 0.7853 A\n", + "Glancing angle for second order diffraction is 18.2 degree\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.15, Page 13.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 1.5 # wavelength of x-ray in angstrom\n", + "theta = 60 # glancing angle in degree\n", + "\n", + "#Calculations\n", + "n = 1 # for first order\n", + "d = ( n * lamda) / (2 * sin(theta*pi/180))\n", + "\n", + "#Result\n", + "print \"Lattice constant of NaCl is %.2f A\"%d\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice constant of NaCl is 0.87 A\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.16, Page " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 1.4 # wavelength of x-ray in angstrom\n", + "x1 = 1 # coordinate on x axis of plane\n", + "y1 = 1 # coordinate on y axis of plane\n", + "z1 = 1 # coordinate on z axis of plane\n", + "a = 5. # lattice parameter of of crystal in angstrom\n", + "\n", + "#Calculations\n", + "n = 1 # for first order\n", + "d = a / sqrt(x1**2 + y1**2 + z1**2)\n", + "theta = degrees(asin((n * lamda) / (2 * d)))\n", + "\n", + "#Result\n", + "print \"Angle of incidence of x-ray on the plane is %.f degree\"%theta\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of incidence of x-ray on the plane is 14 degree\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.17, Page 13.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 0.710 # wavelength of x-ray in angstrom\n", + "x1 = 1 # coordinate on x axis of plane\n", + "y1 = 0 # coordinate on y axis of plane\n", + "z1 = 0 # coordinate on z axis of plane\n", + "a = 2.814 # lattice parameter of of crystal in angstrom\n", + "\n", + "#Calculations\n", + "n = 2 # for second order\n", + "d = a / sqrt(x1**2 + y1**2 + z1**2)\n", + "theta = degrees(asin((n * lamda) / (2 * d)))\n", + "\n", + "#Result\n", + "print \"Glancing angle is %.1f degree\"%theta\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Glancing angle is 14.6 degree\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.18, Page 13.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 1 # order of brag reflection \n", + "d = 3.84e-10 # the space between successive plane in m\n", + "theta = 30. # glancing angle in degree\n", + "\n", + "#Calculations\n", + "lamda = 2 * d * sin(theta*pi/180) / n\n", + "v = 6.62e-34 / (1.67e-27 * lamda)\n", + "\n", + "#Result\n", + "print \"Wavelength of neutron beam is %.2f A\\nSpeed of neutron beam is %.2e meter/sec\"%(lamda * 10**10,v)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of neutron beam is 3.84 A\n", + "Speed of neutron beam is 1.03e+03 meter/sec\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.19, Page 13.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 120 # voltage at which electron is accelerated in v\n", + "n = 1 # order of Bragg reflection \n", + "x1 = 1 # coordinate on x axis of plane\n", + "y1 = 1 # coordinate on y axis of plane\n", + "z1 = 1 # coordinate on z axis of plane\n", + "theta = 22 # angle at which maximum reflection is obtain in degree\n", + "n = 1 # order of reflection\n", + "\n", + "#Calculations\n", + "lamda = 6.62e-34 / sqrt(2 * 9.1e-31 * 1.6e-19 * v)\n", + "d = (n * lamda) / (2 * sin(theta*pi/180))\n", + "a = d * sqrt(3) \n", + "\n", + "#Result\n", + "print \"Lattice parameter is %.3f A\"%(a * 10**10) " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice parameter is 2.589 A\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.20, Page 13.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 1.24e-10 # wavelength of X-ray in A\n", + "x1 = 1 # coordinate on x axis of first plane\n", + "y1 = 0 # coordinate on y axis of first plane\n", + "z1 = 0 # coordinate on z axis of first plane\n", + "x2 = 1 # coordinate on x axis of second plane\n", + "y2 = 1 # coordinate on y axis of second plane\n", + "z2 = 0 # coordinate on z axis of second plane\n", + "x3 = 1 # coordinate on x axis of third plane\n", + "y3 = 1 # coordinate on y axis of third plane\n", + "z3 = 1 # coordinate on z axis of third plane\n", + "M = 74.5 # molecular weight of KCl\n", + "d = 1980 # density of KCl in kg/m^3\n", + "N = 6.023e+26 # Avogadro's No per Kg mole\n", + "\n", + "#Calculations\n", + "a = (4*M / (N*d))**(1./3)\n", + "D1 = a/sqrt(x1**2 + y1**2 + z1**2)\n", + "D2 = a/sqrt(x2**2 + y2**2 + z2**2)\n", + "D3 = a/sqrt(x3**2 + y3**2 + z3**2)\n", + "\n", + "#Result\n", + "print \"Inter planner distances are - \\n(1) in first case %.1f A \\n(2) in second case %.2f A \\n(3) in third case %.2f A\"%(D1*10**10,D2*10**10,D3*10**10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Inter planner distances are - \n", + "(1) in first case 6.3 A \n", + "(2) in second case 4.45 A \n", + "(3) in third case 3.64 A\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.21, Page 13.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 0.15e-9 # distance between K(+) and Cl(-) in m\n", + "\n", + "#Calculations\n", + "v = -1.6e-19 / (4 * pi * 8.85e-12 * d)\n", + "\n", + "#Result\n", + "print \"Potential energy of molecule is %.1f eV\"%v\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential energy of molecule is -9.6 eV\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.22, Page 13.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 0.32e-9 # equilibrium separation in m\n", + "alpha = 1.748 \n", + "n = 9\n", + "e = 4 # ionization energy in eV\n", + "a = -2.16 # electron affinity in eV\n", + "\n", + "#Calculations\n", + "E = -((alpha * 1.6e-19) / (4 * pi * 8.85e-12 * d)) * (1 - (1. / n))\n", + "\n", + "#Result\n", + "print \"Cohesive energy of Nacl is %f eV\"%E\n", + "#Incorrect answer in the textbook " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Cohesive energy of Nacl is -6.985633 eV\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.23, Page 13.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 2.02 # average energy required to produce a Schottky defect at room temperature in eV\n", + "k = 1.38e-23 # Boltzmann constant in J/k\n", + "T = 300 # room temperature in K\n", + "\n", + "#Calculations\n", + "r = exp(-(E * 1.6e-19) / (2 * k * T))\n", + "\n", + "#Result\n", + "print \"Ratio of number of Schottky defects to total number of cation-anion pairs is %.2e\"%r\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of number of Schottky defects to total number of cation-anion pairs is 1.12e-17\n" + ] + } + ], + "prompt_number": 44 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_14.ipynb b/Engineering_Physics/Chapter_14.ipynb new file mode 100755 index 00000000..498814f0 --- /dev/null +++ b/Engineering_Physics/Chapter_14.ipynb @@ -0,0 +1,1951 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 14: Development of Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.1, Page 14.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 75 # energy of photon in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in J \n", + "\n", + "#Calculations\n", + "f = E * e / h\n", + "lamda = c / f\n", + " \n", + "#Result\n", + "print \"Frequency is %.2e Hz\\nWavelength is %.1f A\"%(f,lamda * 10**10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency is 1.81e+16 Hz\n", + "Wavelength is 165.5 A\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.2, Page 14.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "P = 2e5 # radiated power in W\n", + "f = 98e6 # frequency in Hz \n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "\n", + "#Calculations\n", + "E = h * f\n", + "n = P / E\n", + "\n", + "#Result\n", + "print \"Number of quanta emitted per sec is %.2e\"%n\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of quanta emitted per sec is 3.08e+30\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.3, Page 14.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 4e-7 # wavelength of spectral line in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "\n", + "#Calculations\n", + "E = (h * c) / lamda\n", + "\n", + "#Result\n", + "print \"Energy of photon is %.3e J\"%E\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of photon is 4.965e-19 J\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.4, Page 14.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "lamda = 5e-7 # wavelength of green light in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "P = 1. # energy in erg\n", + "\n", + "#Calculations\n", + "E = ((h * c) / lamda) * (10**7)\n", + "n = P / E\n", + "\n", + "#Result\n", + "print \"Number of photons of green light emitted is %.2e\"%n\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of photons of green light emitted is 2.52e+11\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.5, Page 14.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "E = 5e-19 # energy of photon in J\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lamda = (c * h) / E\n", + "\n", + "#Result\n", + "print \"Wavelength is %.f A\"%(lamda * 10**10)\n", + "#Incorrect answer in the textbook " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength is 3972 A\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.6, Page 14.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 4.35e-7 # wavelength of green light in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "P = 1 # energy in erg\n", + "\n", + "#Calculations\n", + "E = ((h * c) / lamda)\n", + "\n", + "#Result\n", + "print \"Energy of an electron is %.3e J\"%E\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of an electron is 4.566e-19 J\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.7, Page 14.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 5.6e-7 # wavelength of light in meter\n", + "n = 120 # no. of photons per second\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "\n", + "#Calculations\n", + "E = ((h * c) / lamda)\n", + "p = E * n\n", + "\n", + "#Result\n", + "print \"Energy received by the eye per second is %.3e W\"%p\n", + "#Incorrect answer in the textbook " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy received by the eye per second is 4.256e-17 W\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.8, Page 14.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 5.5e-7 # wavelength of light in meter\n", + "E = 1.5 # energy in J\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "\n", + "#Calculations\n", + "E_ = ((h * c) / lamda)\n", + "n = E / E_\n", + "\n", + "#Result\n", + "print \"Number of photons of yellow light = %.3e\"%n\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of photons of yellow light = 4.154e+18\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.9, Page 14.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 4.35e-7 # wavelength of light in meter\n", + "lambda_ = 5.42e-7 # threshold wavelength of photoelectron in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "w = ((h * c) / lambda_)\n", + "v = sqrt(((2 * h * c) / m) * (1 / lamda - 1 / lambda_))\n", + "V = m * v**2 / (2 * e)\n", + "\n", + "#Result\n", + "print \"Work function is %.3e J\\nStopping potential is %.2f V\\nMaximum velocity is %.3e m/sec\"%(w,V,v)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work function is 3.664e-19 J\n", + "Stopping potential is 0.56 V\n", + "Maximum velocity is 4.451e+05 m/sec\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.10, Page 14.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "f = 1.2e15 # frequency of light in Hz\n", + "f_ = 1.1e+15 # threshold frequency of photoelectron emission in copper in Hz\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E = h * (f - f_) / e\n", + "\n", + "#Result\n", + "print \"Maximum energy of photoelectron is %.3f eV\"%E\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum energy of photoelectron is 0.414 eV\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.11, Page 14.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 6.2e-7 # threshold wavelength of photoelectron in first case in meter\n", + "lambda_ = 5e-7 # threshold wavelength of photoelectron in second case in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "w = ((h * c) / lamda) * (1 / e)\n", + "w_ = ((h * c) / lambda_) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Work function for wavelength %.e A is %.f eV\\nWork function for wavelength %.e A is %.2f eV\"%(lamda,w,lambda_,w_)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work function for wavelength 6e-07 A is 2 eV\n", + "Work function for wavelength 5e-07 A is 2.48 eV\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.12, Page 14.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "lamda = 3.132e-7 # wavelength of light in meter\n", + "V = 1.98 # stopping potential in V\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "E = e * V\n", + "lambda_ = 1. / ((1. / lamda) - (E / (h * c)))\n", + "f = c / lambda_\n", + "w = ((h * c) / lambda_)\n", + "\n", + "#Result\n", + "print \"Work function is %.3e J\\nMaximum energy is %.3e J\\nThreshold frequency is %.3e Hz\"%(w,E,f)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Work function is 3.173e-19 J\n", + "Maximum energy is 3.168e-19 J\n", + "Threshold frequency is 4.793e+14 Hz\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.13, Page 14.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "w = 4.8 # work function in eV\n", + "lambda1 = 5e-7 # wavelength of incident radiation in first case in meter\n", + "lambda2 = 2e-7 # wavelength of incident radiation in second case in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E_k1 = h*c/lambda1\n", + "E_k2 = h*c / lambda2\n", + "\n", + "#Result\n", + "print \"The energy corresponding to wavelength 5000 A is %.2f which is found to be less than the work function 4.8 eV\"%(E_k1/e) \n", + "print \"The energy corresponding to wavelength 2000 A %.2f is found to be greater than the work function\"%(E_k2/e)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy corresponding to wavelength 5000 A is 2.48 which is found to be less than the work function 4.8 eV\n", + "The energy corresponding to wavelength 2000 A 6.21 is found to be greater than the work function\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.14, Page 14.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 5.893e-7 # wavelength of light in meter\n", + "V = 0.36 # stopping potential for emitted electron in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "E = h * c / lamda\n", + "w = ((h * c) / lamda) * (1 / e) - V\n", + "f = w * e / h\n", + "\n", + "#Result\n", + "print \"Maximum energy is %.2f eV\\nWork function is %.2f eV\\nThreshold frequency is %.2e cycles/sec\"%(E/e,w,f)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum energy is 2.11 eV\n", + "Work function is 1.75 eV\n", + "Threshold frequency is 4.22e+14 cycles/sec\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.15, Page 14.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "lamda = 5.89e-7 # wavelength of light in meter\n", + "lambda_ = 7.32e-7 # threshold wavelength of photoelectron in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "E = (h * c) * (1 / lamda - 1 / lambda_)\n", + "V = E / e\n", + "\n", + "#Result\n", + "print \"Stopping potential is %.3f V\\nMaximum kinetic energy is %.3e J\"%(V,E)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Stopping potential is 0.412 V\n", + "Maximum kinetic energy is 6.587e-20 J\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.16, Page 14.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E = 1.5 # maximum energy in eV\n", + "lambda_ = 2.3e-7 # threshold wavelength of photoelectron in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "lamda = 1 / ((E * e / (h * c)) + (1 / lambda_))\n", + "\n", + "#Resuult\n", + "print \"Wavelength of light is %.1f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light is 1799.8 A\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.17, Page 14.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 1.5e-7 # wavelength of light in in meter\n", + "w = 4.53 # work function of tungsten in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "E = ((h * c) / lamda) * (1 / e)\n", + "k = E - w\n", + "\n", + "#Result\n", + "print \"Energy of incident photon is %.2f eV,which is greater than the work function \\nSo it causes photoelectric emission.\\nKinetic energy of the emitted electron is %.2f eV\"%(E,k)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of incident photon is 8.28 eV,which is greater than the work function \n", + "So it causes photoelectric emission.\n", + "Kinetic energy of the emitted electron is 3.75 eV\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.18, Page 14.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "w = 2.3 # work function of sodium in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lamda = ((h * c) / w) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Longest wavelength required for photoemission is %.2f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Longest wavelength required for photoemission is 5396.74 A\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.19, Page 14.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "w = 2 # work function of sodium in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lamda = ((h * c) / w) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Threshold wavelength for photo emission is %d A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Threshold wavelength for photo emission is 6206 A\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.20, Page 14.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "k = 4 # maximum kinetic energy of electron in eV\n", + "w = 2.2 # work function of sodium in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "lambda_ = ((h * c) / (w * e)) \n", + "lamda = (1 / ((((k * e) / (h * c))) + (1 / lambda_)))\n", + "\n", + "#Result\n", + "print \"Threshold wavelength is %d A\\nIncident electromagnetic wavelength is %.f A\"%(lambda_ * 1e10,lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Threshold wavelength is 5642 A\n", + "Incident electromagnetic wavelength is 2002 A\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.21, Page 14.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 3.5e-7 # wavelength of light in meter\n", + "i = 1 # intensity in W/m^2\n", + "p = 0.5 # percent of incident photon produce electron\n", + "a = 1 # surface area of potassium in cm^2\n", + "w = 2.1 # work function of potassium in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of an electron in kg \n", + "\n", + "#Calculations\n", + "E = (((h * c) / lamda) * (1 / e) - w) * e\n", + "E_ = (p * a * 1e-4) / 100 # in W/cm^2\n", + "n = E_ / E\n", + "\n", + "#Result\n", + "print \"Maximum kinetic energy is %.3e J\\nNumber of electrons emitted per sec from 1cm^2 area is %.2e\"%(E,n)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum kinetic energy is 2.314e-19 J\n", + "Number of electrons emitted per sec from 1cm^2 area is 2.16e+12\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.22, Page 14.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 5.896e-7 # wavelength of first light in meter\n", + "lambda_ = 2.83e-7 # wavelength of second light in meter\n", + "V1 = 0.12 # stopping potential for emitted electrons for first light in V\n", + "V2 = 2.2 # stopping potential for emitted electrons for second light in V\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "\n", + "#Calculations\n", + "h = (e * (V2 - V1) / c) / (1 / lambda_ - 1 / lamda)\n", + "\n", + "#Result\n", + "print \"Value of Planck constant is %.2e J-sec\"%h\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Value of Planck constant is 6.04e-34 J-sec\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.23, Page 14.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 1e-10 # wavelength of light in meter\n", + "theta = 90 # angle at which scattered radiation is viewed in degree\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "delta_lambda = (h * (1 - cos(theta*pi/180))) / (m * c)\n", + "\n", + "#Result\n", + "print \"Compton shift is %.3f A\"%(delta_lambda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Compton shift is 0.024 A\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.24, Page 14.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import * \n", + "# Given \n", + "lamda = 1e-10 # wavelength of light in meter\n", + "theta = 90 # angle in degree\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "delta_lambda = (h * (1 - cos(theta*pi/180))) / (m * c)\n", + "E = (h * c) / delta_lambda\n", + "\n", + "#Result\n", + "print \"Compton shift is %.3f A\\nEnergy of incident beam is %.3f MeV\"%(delta_lambda * 1e10,E / 1.6e-13)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Compton shift is 0.024 A\n", + "Energy of incident beam is 0.512 MeV\n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.25, Page 14.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + " \n", + "# Given \n", + "E = 4 # enrgy of recoil electron in KeV\n", + "theta = 180 # scattered angle of photon in degree\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "p = sqrt(2 * E * 10**3 * e * m)\n", + "lamda = (2 * h * c) / (p * c + E * 10**3 * e)\n", + "\n", + "#Result\n", + "print \"Wavelength of incident beam is %.3f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of incident beam is 0.365 A\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.26, Page 14.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 1e-10 # wavelength of light in meter\n", + "theta = 90 # angle in degree\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "delta_lambda = (h * (1 - cos(theta*pi/180))) / (m * c)\n", + "E = (h * c) * ((1 / lamda) - (1 / (lamda + delta_lambda)))\n", + "\n", + "#Result\n", + "print \"Compton shift is %.3e m\\nKinetic energy is %.f eV\"%(delta_lambda,E / 1.6e-19)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Compton shift is 2.425e-12 m\n", + "Kinetic energy is 294 eV\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.27, Page 14.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 0.144e-10 # wavelength of x-ray in meter\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "theta = 180 # for maximum shift\n", + "d_lamda = (h * (1 - cos(theta*pi/180))) / (m * c)\n", + "E = (h * c) * ((1. / lamda) - (1. / (d_lamda+lamda)))\n", + "\n", + "#Result\n", + "print \"Maximum Compton shift is %.4f A\\nKinetic energy is %.2f KeV\"%(delta_lambda * 1e10,E / 1.6e-16)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum Compton shift is 0.0485 A\n", + "Kinetic energy is 21.72 KeV\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.28, Page 14.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "lamda = 0.2e-10 # wavelength of x-ray in meter\n", + "theta = 45 # scattered angle in degree\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "delta_lambda = (h * (1 - cos(theta*pi/180))) / (m * c)\n", + "E = (h * c) * ((1 / lamda) - (1 / (lamda + delta_lambda)))\n", + "theta_ = 180 # for maximum\n", + "delta_lambda_ = (h * (1 - cos(theta_*pi/180))) / (m * c)\n", + "lambda_ = lamda + delta_lambda_\n", + "E_k = h*c*(1/lamda - 1/lambda_)\n", + "\n", + "#Result\n", + "print \"Wavelength of x-ray is %.4f A\\nMaximum kinetic energy %.2e J\"%(lambda_ * 1e10,E_k)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of x-ray is 0.2485 A\n", + "Maximum kinetic energy 1.94e-15 J\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.29, Page 14.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "v = 96 # speed of automobile in km/hr\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 2e3 # mass of automobile in kg\n", + "\n", + "#Calculations\n", + "v_ = v * (5. / 18)\n", + "lamda = h / (m * v_)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength is %.2e m\"%lamda\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength is 1.24e-38 m\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.30, Page 14.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 50 # potential differece in volt\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of an electron in kg\n", + "\n", + "#Calculations\n", + "lamda = h / sqrt(2 * m * v * e)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength is %.2f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength is 1.73 A\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.31, Page 14.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 300 # temperature in K\n", + "k = 1.37e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of neutron in kg\n", + "\n", + "#Calculations\n", + "lamda = h / sqrt(3 * m * k * t)\n", + "\n", + "#Result\n", + "print \"Wavelength of thermal neutron is %.3f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of thermal neutron is 1.459 A\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.32, Page 14.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "v = 2e8 # speed of proton in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of proton in kg\n", + "\n", + "#Calculations\n", + "lamda = h / (m * v)\n", + "\n", + "#Result\n", + "print \"Wavelength of matter wave associated with proton is %.2e m\"%lamda\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of matter wave associated with proton is 1.98e-15 m\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.33, Page 14.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 0.1e-10 # DE Broglie wavelength associated with electron in M\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "V = h**2 / (2 * m* e * lamda**2)\n", + "\n", + "#Result\n", + "print \"Potential difference is %.2f KV\"%(V * 10**-3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential difference is 15.05 KV\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.34, Page 14.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 200 # potential differece in volt\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "q = 3.2e-19 # charge on an alpha particle in C \n", + "m = 4 * 1.67e-27 # mass of alpha particle in kg\n", + "\n", + "#Calculations\n", + "lamda = h / sqrt(2 * m * v * q)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength = %.2e m\"%lamda\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength = 7.16e-13 m\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.35, Page 14.34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 400 # temperature in K\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 4 * 1.67e-27 # mass of helium atom in kg\n", + "\n", + "#Calculations\n", + "lamda = h / sqrt(3 * m * k * t)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength = %.4f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength = 0.6294 A\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.36, Page 14.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "v = 2000 # velocity of neutron in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of neutron in kg\n", + "\n", + "#Calculations\n", + "lamda = h / (m * v)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength is %.2f A\"%(lamda * 1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength is 1.98 A\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.37, Page 14.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 1e-10 # wavelength in m\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of electron in kg\n", + "m_ = 1.7e-27 # mass of neutron in kg\n", + "\n", + "#Calculations\n", + "v = h / (m_ * lamda)\n", + "E = h**2 / (2 * m * lamda**2)\n", + "E_ = h**2 / (2 * m_ * lamda**2)\n", + "\n", + "#Result\n", + "print \"Energy for electron is %.f eV\\nEnergy for neutron is %.3f eV\"%(E / e,E_ / e)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy for electron is 150 eV\n", + "Energy for neutron is 0.081 eV\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.38, Page 14.36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E1 = 500 # kinetic energy of electron in first case in eV\n", + "E2 = 50 # kinetic energy of electron in second case in eV\n", + "E3 = 1 # kinetic energy of electron in third case in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "lambda1 = h / sqrt(2 * m * E1 * e)\n", + "lambda2 = h / sqrt(2 * m * E2 * e)\n", + "lambda3 = h / sqrt(2 * m * E3 * e)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength of electron - \\n(1) In first case is %.4f A \\n(2) In second case is %.3f A \\n(3) In third is %.3f A\"%(lambda1*1e10,lambda2*1e10,lambda3*1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength of electron - \n", + "(1) In first case is 0.5486 A \n", + "(2) In second case is 1.735 A \n", + "(3) In third is 12.268 A\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.39, Page 14.36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E1 = 1 # kinetic energy of neutron in first case in eV\n", + "E2 = 510 # kinetic energy of neutron in second case in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of neutron in kg\n", + "\n", + "#Calculations\n", + "lambda1 = h / sqrt(2 * m * E1 * e)\n", + "lambda2 = h / sqrt(2 * m * E2 * e)\n", + "r = lambda1 / lambda2\n", + "\n", + "#Result\n", + "print \"Ratio of de-Broglie wavelengths is %.2f:1\"%r\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of de-Broglie wavelengths is 22.58:1\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.40, Page 14.37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 20 # kinetic energy of proton in MeV\n", + "E2 = 510 # kinetic energy of neutron in second case in eV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of proton in kg\n", + "m_ = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "lambda1 = h / sqrt(2 * m * 10**6 * E * e)\n", + "lambda2 = h / sqrt(2 * m_ * E * 10**6 * e)\n", + "r = lambda2 / lambda1\n", + "\n", + "#Result\n", + "print \"Ratio of de-Broglie wavelengths is 1:%.f\"%r\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of de-Broglie wavelengths is 1:43\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.41, Page 14.37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 1 # kinetic energy of proton in MeV\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of proton in kg\n", + "\n", + "#Calculations\n", + "v = sqrt(2 * E * 1.6e-13 / m)\n", + "\n", + "#Result\n", + "print \"Velocity is %.2e m/sec\"%v\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity is 1.38e+07 m/sec\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.42, Page 14.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "r = 1. / 20 # ratio of velocity of proton to the velocity of light \n", + "c = 3e8 # velocity of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of proton in kg\n", + "\n", + "#Calculations\n", + "v = r * c\n", + "lamda = h / (m * v)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength is %.3e m\"%lamda\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength is 2.643e-14 m\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.43, Page 14.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 5.0e-7 # wavelength in m\n", + "c = 3.e8 # velocity of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 1.67e-27 # mass of proton in kg\n", + "m_ = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E1 = h**2 / (2 * m * lamda**2)\n", + "E2 = h**2 / (2 * m_ * lamda**2)\n", + "\n", + "#Results\n", + "print 'kinetic energy of proton(in J) =%.3e'%E1\n", + "print 'kinetic energy of electron(in J) =%.2e'%E2\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "kinetic energy of proton(in J) =5.248e-28\n", + "kinetic energy of electron(in J) =9.63e-25\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.44, Page 14.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 1 # no. of Bohr's orbit of hydrogen atom\n", + "c = 3e8 # velocity of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E = (13.6 / n**2) * e\n", + "lamda = h / sqrt(2 * m * E)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength is %.1f A\"%(lamda*1e10)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de-Broglie wavelength is 3.3 A\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.45, Page 14.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 300 # temperature in K\n", + "k = 1.376e-23 # Boltzmann's constant in J/K\n", + "c = 3e8 # velocity of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m_ = 4 * 1.67e-27 # mass of helium atom in kg\n", + "m = 1.67e-27 # mass of hydrogen atom in kg\n", + "\n", + "#Calculations\n", + "lambda1 = h / sqrt(3 * m * k * t)\n", + "lambda2 = h / sqrt(3 * m_ * k * t)\n", + "r = lambda1 / lambda2\n", + "\n", + "#Result\n", + "print \"Ratio of de-Broglie wavelengths is %d:1\"%r\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of de-Broglie wavelengths is 2:1\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.47, Page 14.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lamda = 1.2e-10 # DE Broglie wavelength in m\n", + "c = 3e8 # velocity of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C \n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "v1 = h / (m * lamda)\n", + "v2 = h / (2 * m * lamda)\n", + "\n", + "#Result\n", + "print \"Group velocity is %.2e m/sec\\nPhase velocity is %.2e m/sec\"%(v1,v2)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Group velocity is 6.06e+06 m/sec\n", + "Phase velocity is 3.03e+06 m/sec\n" + ] + } + ], + "prompt_number": 41 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_15.ipynb b/Engineering_Physics/Chapter_15.ipynb new file mode 100755 index 00000000..2b3eeafd --- /dev/null +++ b/Engineering_Physics/Chapter_15.ipynb @@ -0,0 +1,983 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 15: Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.1, Page 15.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 1000 # energy of electron in eV\n", + "delta_x = 1e-10 # error in position in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "p = sqrt(2 * m * E * e)\n", + "delta_p = h / (4 * pi * delta_x)\n", + "P = (delta_p / p) * 100\n", + "\n", + "#Result\n", + "print \"Percentage of uncertainty in momentum is %.1f%%\"%P" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage of uncertainty in momentum is 3.1%\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.3, Page 15.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "E = 500 # energy of electron in eV\n", + "delta_x = 2e-10 # error in position in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "p = sqrt(2 * m * E * e)\n", + "delta_p = h / (4 * pi * delta_x)\n", + "P = (delta_p / p) * 100\n", + "\n", + "#Result\n", + "print \"Percentage of uncertainty in momentum is %.2f%%\"%P" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage of uncertainty in momentum is 2.18%\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.4, Page 15.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "delta_lambda = 1e-6 # accuracy in wavelength of its one part\n", + "lamda = 1e-10 # wavelength of x-ray in m\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_x = lamda / (4 * pi * delta_lambda)\n", + "\n", + "#Result\n", + "print \"Uncertainty in position is %.2f micrometer\"%(delta_x*10**6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in position is 7.96 micrometer\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.5, Page 15.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "delta_x = 1e-10 # error in position in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_p = h / (4 * pi * delta_x)\n", + "\n", + "#Result\n", + "print \"Uncertainty in momentum is %.2e kg m/sec\"%delta_p" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in momentum is 5.27e-25 kg m/sec\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.6, Page 15.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "M = 5.4e-26 # momentum of electron in kg-m/sec\n", + "p = 0.05 # percentage accuracy in momentum\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_m = p * M / 100\n", + "delta_x = h / (4 * pi * delta_m)\n", + "\n", + "#Result\n", + "print \"Uncertainty in position is %.3f micrometer\"%(delta_x * 10**6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in position is 1.951 micrometer\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.7, Page 15.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 0.53e-10 # radius of hydrogen atom in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_M = h / (4 * pi * r)\n", + "delta_k = delta_M**2 / (2 * m)\n", + "\n", + "#Result\n", + "print \"Minimum energy of electron is %.3e J\"%delta_k" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum energy of electron is 5.428e-19 J\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.8, Page 15.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 5e3 # speed of electron in m/sec\n", + "a = 0.003 # percentage accuracy in measurement of speed \n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_v = v * a / 100\n", + "delta_p = m * delta_v\n", + "delta_x = h / (4 * pi * delta_p)\n", + "\n", + "#Result\n", + "print \"Uncertainty in determining the position of electron is %.3e m\"%delta_x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in determining the position of electron is 3.859e-04 m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.9, Page 15.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 6.6e4 # speed of electron in m/sec\n", + "a = 0.01 # percentage accuracy in measurement of speed \n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.6e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_v = v * a / 100\n", + "delta_p = m * delta_v\n", + "delta_x = h / (4 * pi * delta_p)\n", + "\n", + "#Result\n", + "print \"Uncertainty in determining the position is %.2e m\"%delta_x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in determining the position is 8.74e-06 m\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.10, Page 15.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "v = 3e7 # speed of electron in m/sec \n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "delta_p = m * v / sqrt(1 - (v/c)**2)\n", + "delta_x = h / (4 * pi * delta_p)\n", + "\n", + "#Result\n", + "print \"Uncertainty in determining the position is %.2e m\"%delta_x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainty in determining the position is 1.92e-12 m\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.11, Page 15.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "t = 2.5e-14 # life time of hydrogen atom in exited state in sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_E = h / (4 * pi * t)\n", + "\n", + "#Result\n", + "print \"Minimum error in measurement of the energy is %.2e J\"%delta_E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum error in measurement of the energy is 2.11e-21 J\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.12, Page 15.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 10**-8 # life time of atom in exited state in sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_f = 1 / (4 * pi * t)\n", + "\n", + "#Result\n", + "print \"Minimum uncertainty in frequency is %.2e sec\"%delta_f" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum uncertainty in frequency is 7.96e+06 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.13, Page 15.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "delta_x = 20e-10 # uncertainty in position in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "m_ = 1.67e-27 # mass of proton in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "delta_v1 = h / (4 * pi * m * delta_x)\n", + "delta_v2 = h / (4 * pi * m_ * delta_x)\n", + "r = delta_v2 / delta_v1\n", + "\n", + "#Result\n", + "print \"Ratio of uncertainty in velocity of a proton and an electron is %.2e\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of uncertainty in velocity of a proton and an electron is 5.45e-04\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.14, Page 15.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "delta_x = 1e-10 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "n = 1 # for n=1\n", + "\n", + "#Calculations\n", + "E = (n**2 * h**2) / (8 * m * delta_x**2)\n", + "n = 2 # for n=2\n", + "E_ = (n**2 * h**2) / (8 * m * delta_x**2)\n", + "\n", + "#Result\n", + "print \"Energy of electron - \\nFor (n=1) energy is %.2e J\\nFor (n=2) energy is %.2e J\"%(E,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron - \n", + "For (n=1) energy is 6.02e-18 J\n", + "For (n=2) energy is 2.41e-17 J\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.15, Page 15.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "l = 1e-10 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "n = 1 # for n=1\n", + "\n", + "#Calculations\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # for n=2\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "d = E_ - E\n", + "\n", + "#Result\n", + "print \"Energy difference is %.2e J\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy difference is 1.81e-17 J\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.16, Page 15.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 3e-10 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "n = 1 # For n=1\n", + "\n", + "#Calculations\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # For n=2\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 3 # For n=3\n", + "E__ = (n**2 * h**2) / (8 * m * l**2)\n", + "\n", + "#Result\n", + "print \"Energy of electron -\\nFor (n=1) is %.1e J\\nFor (n=2) is %.2e J\\nFor (n=3) is %.2e J\"%(E,E_,E__)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron -\n", + "For (n=1) is 6.7e-19 J\n", + "For (n=2) is 2.68e-18 J\n", + "For (n=3) is 6.02e-18 J\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.17, Page 15.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 2.5e-10 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # for n=2\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "\n", + "#Result\n", + "print \"Energy of electron -\\nFor (n=1) is %.2e J\\nFor (n=2) is %.3e J\"%(E,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron -\n", + "For (n=1) is 9.63e-19 J\n", + "For (n=2) is 3.853e-18 J\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.18, Page 15.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1e-14 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 1.67e-27 # mass of neutron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E = (h**2) / (8 * m * l**2)\n", + "\n", + "#Result\n", + "print \"Lowest energy of neutron confined in the nucleus is %.2e J\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lowest energy of neutron confined in the nucleus is 3.28e-13 J\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.19, Page 15.31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1e-10 # width of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.63e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "p1 = (n * h) / (2 * l)\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # for n=2\n", + "p2 = (n * h) / (2 * l)\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "\n", + "#Result\n", + "print \"Energy of electron -\\nFor (n=1) is %.2e J\\nFor (n=2) is %.2e J\"%(E,E_)\n", + "print \"\\nMomentum of electron -\\nFor (n=1) is %.3e kg-m/sec\\nFor (n=2) is %.2e kg-m/sec\"%(p1,p2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron -\n", + "For (n=1) is 6.04e-18 J\n", + "For (n=2) is 2.42e-17 J\n", + "\n", + "Momentum of electron -\n", + "For (n=1) is 3.315e-24 kg-m/sec\n", + "For (n=2) is 6.63e-24 kg-m/sec\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.20, Page 15.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1e-10 # length of box in m\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E1 = (n**2 * h**2) / (8 * m * l**2)\n", + "lambda1 =2*l\n", + "n = 2 # for n=2\n", + "E2 = (n**2 * h**2) / (8 * m * l**2)\n", + "lambda2 =2*l/2\n", + "n = 3 # for n=3\n", + "E3 = (n**2 * h**2) / (8 * m * l**2)\n", + "lambda3 =2*l/3\n", + "\n", + "#Results\n", + "print \"Energy Eigen value of electron -\\nFor (n=1) is %.2e J\\nFor (n=2) is %.2e J\\nFor (n=3) is %.2e J\"%(E1,E2,E3)\n", + "print \"\\nde-Broglie wavelength of electron -\\nFor (n=1) is %.f A\\nFor (n=2) is %.f A \\nFor (n=3) is %.3f A\"%(lambda1*1e10,lambda2*1e10,lambda3*1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy Eigen value of electron -\n", + "For (n=1) is 6.02e-18 J\n", + "For (n=2) is 2.41e-17 J\n", + "For (n=3) is 5.42e-17 J\n", + "\n", + "de-Broglie wavelength of electron -\n", + "For (n=1) is 2 A\n", + "For (n=2) is 1 A \n", + "For (n=3) is 0.667 A\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.21, Page 15.32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E1 = 3.2e-18 # minimum energy possible for a particle entrapped in a one dimensional box in J\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "E1 = E1 / e # in eV\n", + "n = 2 # for n=2\n", + "E2 = n**2 * E1\n", + "n = 3 # for n=3\n", + "E3 = n**2 * E1\n", + "n = 4 # for n=4\n", + "E4 = n**2 * E1\n", + "\n", + "#Result\n", + "print \"Energy Eigen values -\\nFor (n=2) for %.f eV\\nFor (n=3) is %.f eV\\nFor (n=4) is %.f eV\"%(E2,E3,E4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy Eigen values -\n", + "For (n=2) for 80 eV\n", + "For (n=3) is 180 eV\n", + "For (n=4) is 320 eV\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.22, Page 15.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "l = 4e-10 # width of box in m\n", + "E = 9.664e-17 # energy of electron in J\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E1 = (n**2 * h**2) / (8 * m * l**2)\n", + "N = sqrt(E / E1)\n", + "p = ((N) * h) / (2 * l)\n", + "\n", + "#Result\n", + "print \"Order of exited state is %d\\nMomentum of electron is %.2e kg-m/sec\"%(N,p)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Order of exited state is 16\n", + "Momentum of electron is 1.33e-23 kg-m/sec\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15.23, Page 15.33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 10e-10 # width of box containing electron in m\n", + "E = 9.664e-17 # energy of electron in J\n", + "M = 0.001 # mass of glass marble in kg\n", + "l_ = 0.2 # width of box containing marble in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "# For electron\n", + "n = 1 # for n=1\n", + "E1 = (n**2 * h**2) / (8 * m * l**2)\n", + "E2 = 2**2* E1\n", + "E3 = 3**2 * E1\n", + "# For glass marble\n", + "E1_ = h**2/(8*M*l_**2)\n", + "E2_ = 2**2 * E1_\n", + "E3_ = 3**2 *E1_\n", + "\n", + "#Result\n", + "print \"\\nEnergy levels of electron- \\nFor (n=1) is %.2e J\\nFor (n=2) is %.2e J\\n For (n=3) is %.2e J\"%(E1,E2,E3)\n", + "print \"\\nEnergy levels of marble- \\nFor (n=1) is %.2e J\\nFor (n=2) is %.2e J\\nFor (n=3) is %.2e J\"%(E1_,E2_,E3_)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Energy levels of electron- \n", + "For (n=1) is 6.02e-20 J\n", + "For (n=2) is 2.41e-19 J\n", + " For (n=3) is 5.42e-19 J\n", + "\n", + "Energy levels of marble- \n", + "For (n=1) is 1.37e-63 J\n", + "For (n=2) is 5.48e-63 J\n", + "For (n=3) is 1.23e-62 J\n" + ] + } + ], + "prompt_number": 25 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_16.ipynb b/Engineering_Physics/Chapter_16.ipynb new file mode 100755 index 00000000..0fab1922 --- /dev/null +++ b/Engineering_Physics/Chapter_16.ipynb @@ -0,0 +1,467 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 16: Free Electron Theory" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.1, Page 16.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 0 # temperature in K\n", + "E = 10 # Fermi energy of electron in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E_ = E * 3 / 5\n", + "v = sqrt(2 * E_ * e / m)\n", + "\n", + "#Result\n", + "print \"\\nAverage energy of electron is %.f eV\\nSpeed of electron is %.2e m/sec\"%(E_,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Average energy of electron is 6 eV\n", + "Speed of electron is 1.45e+06 m/sec\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.2, Page 16.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 0 # temperature in K\n", + "E = 7.9 # Fermi energy in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E_ = E * 3 / 5\n", + "v = sqrt(2 * E_ * e / m)\n", + "\n", + "#Result\n", + "print \"Average energy of electron is %.2f eV\\nSpeed of electron is %.2e m/sec\"%(E_,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Average energy of electron is 4.74 eV\n", + "Speed of electron is 1.29e+06 m/sec\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.3, Page 16.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 2.5e28 # no. of free electron in per meter cube\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1. / e)\n", + "v = (h / (2 * pi * m)) * (3 * pi**2 * n)**(1./3)\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.2f eV\\nSpeed of electron is %.2e m/sec\"%(E,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 3.12 eV\n", + "Speed of electron is 1.05e+06 m/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.4, Page 16.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 8940 # density of copper in kg/m^3\n", + "w = 63.55 # atomic weight of copper\n", + "t = 0 # temperature in K\n", + "N = 6.02e26 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = w / d\n", + "n = N / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1. / e)\n", + "E_ = 3 * E / 5\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.3f eV\\nAverage energy is %.2f eV\"%(E,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 7.036 eV\n", + "Average energy is 4.22 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.5, Page 16.16\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 10.5e6 # density of silver in g/m^3\n", + "w = 108 # atomic weight of silver\n", + "t = 0 # temperature in K\n", + "N = 6.02e23 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = w / d\n", + "n = N / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Fermi energy is %.1f eV\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 5.5 eV\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.6, Page 16.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "a = 4e-10 # lattice constant in mr\n", + "t = 0 # temperature in K\n", + "N = 6.02e23 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = a**3\n", + "n = 4 / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1 / e)\n", + "k = (3 * pi**2 *n)**(1./3)\n", + "KE = (3 * E / 5) * (n)\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.2f eV\\nFermi vector is %.2e per m\\nTotal kinetic energy is %.2e eV\"%(E,k,KE)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 5.75 eV\n", + "Fermi vector is 1.23e+10 per m\n", + "Total kinetic energy is 2.15e+29 eV\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.7, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "d = 0.9e-3 # diameter of aluminium in m\n", + "i = 6 # current in amp\n", + "n = 4.5e28 # no. of electron available for conduction per meter^3 \n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "J = i * 4 / (pi * (d)**2)\n", + "v = J / (n * e)\n", + "\n", + "#Result\n", + "print \"Drift velocity of electron is %.3e m/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Drift velocity of electron is 1.310e-03 m/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.8, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 8.92e3 # density of copper in kg/m^3\n", + "i = 5 # current in amp\n", + "w = 63.5 # atomic weight of copper\n", + "r = 0.7e-3 # radius in meter\n", + "N = 6.02e28 # Avogadro no.\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = (w / d)\n", + "n = N / V \n", + "J = i / (pi * r**2)\n", + "v = J / (n * e)\n", + "\n", + "#Result\n", + "print \"Current density = %.2e amp/m^2\\nDrift velocity is %.1e m/sec\"%(J,v)\n", + "#Incorrect units in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current density = 3.25e+06 amp/m^2\n", + "Drift velocity is 2.4e-06 m/sec\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.9, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given\n", + "d1= 0.534*10**3 # densiy of Li in kg/m^3\n", + "d2= 0.971*10**3 # densiy of Na in kg/m^3\n", + "d3= 0.86*10**3 # densiy of K in kg/m^3\n", + "w1 = 6.939 # atomic weight of Li \n", + "w2 = 22.99 # atomic weight of Na\n", + "w3 = 39.202 # atomic weight of K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "m = 9.1e-31 # mass of an electron in kg\n", + "NA = 6.023e26 # Avogadro no.\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "# For Li\n", + "n1 = NA * d1/w1\n", + "E1 = h**2/(8*pi**2*m)*(3*pi**2*n1)**(2./3)\n", + "# For Na\n", + "n2 = NA * d2/w2\n", + "E2 = h**2/(8*pi**2*m)*(3*pi**2*n2)**(2./3)\n", + "# For K\n", + "n3 = NA * d3/w3\n", + "E3 = h**2/(8*pi**2*m)*(3*pi**2*n3)**(2./3)\n", + "\n", + "#Results\n", + "print \"Fermi Energy \\nFor Li is %.2f eV\\nFor Na is %.3f eV \\nFor K is %.3f eV\"%(E1/e,E2/e,E3/e)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi Energy \n", + "For Li is 4.71 eV\n", + "For Na is 3.156 eV \n", + "For K is 2.039 eV\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.10, Page 16.18\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1e-10 #length of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # for n=2\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "d = (E_ - E) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Energy difference is %.2f eV\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy difference is 112.87 eV\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_17.ipynb b/Engineering_Physics/Chapter_17.ipynb new file mode 100755 index 00000000..01028f54 --- /dev/null +++ b/Engineering_Physics/Chapter_17.ipynb @@ -0,0 +1,258 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 17: Band Theory of Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.1, Page 17.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "a = 3e-10 # side of square lattice in m\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "p = (h / (2 * a))\n", + "E = (p**2 / (2 * m)) * (1. / e)\n", + "\n", + "#Result\n", + "print \"Electron momentum value at the sides of first Brilloin zone is %.1e kg-m/sec\\nEnergy of free electron is %.1f eV\"%(p,E)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electron momentum value at the sides of first Brilloin zone is 1.1e-24 kg-m/sec\n", + "Energy of free electron is 4.2 eV\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.2, Page 17.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log,pi\n", + "\n", + "# Given \n", + "n = 5e22 # no. of atoms per m^3\n", + "t = 300 # room temperature in K\n", + "k = 1.37e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "d = (k * t) * log(n * h**3 / (2 * (2 * pi * m * k * t)**(3./2)))\n", + "\n", + "#Result\n", + "print \"Position of fermi level is %.3f eV\"%(-d/e)\n", + "#Answer varies due to round-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Position of fermi level is 0.159 eV\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.3, Page 17.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E = 0.3 # Fermi energy in eV\n", + "T = 330 # temperature in K\n", + "t = 300 # room temperature in K\n", + "k = 1.37e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "d = (T / t) * (E)\n", + "\n", + "print \"New position of fermi level is %.2f eV\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "New position of fermi level is 0.30 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.4, Page 17.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given\n", + "E = 0.7 # band gap for semiconductor in eV\n", + "t = 300 # room temperature in K\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "n = 2 * ((2 * pi * k * t * m) / h**2)**(3./2) * exp(-(E * e / (2 * k * t)))\n", + "\n", + "#Result\n", + "print \"Density of holes and electron is %.1e per m^3\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of holes and electron is 3.4e+19 per m^3\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.5, Page 17.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "n = 5e28 # no. of atoms in per m^3\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "R = -(1 / (n * e))\n", + "\n", + "#Resilt\n", + "print \"Hall coefficient is %.3e m^3/C\"%R" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall coefficient is -1.250e-10 m^3/C\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17.6, Page 17.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "a = 4.28e-10 # cell side of Na in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "n = (2 / a**3)\n", + "R = -(1 / (n * e))\n", + "\n", + "#Result\n", + "print \"Hall coefficient is %.3e m^3/C\"%R" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall coefficient is -2.450e-10 m^3/C\n" + ] + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_18.ipynb b/Engineering_Physics/Chapter_18.ipynb new file mode 100755 index 00000000..de6fffda --- /dev/null +++ b/Engineering_Physics/Chapter_18.ipynb @@ -0,0 +1,876 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 18: Magnetic Properties of Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.1, Page 18.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 0.53e-10 # radius of orbit in m\n", + "f = 6.6e15 # frequency of revolution in Hz\n", + "h = 6.6e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "M = e * f * pi * r**2\n", + "mu = (e * h) / (4 * pi * m) \n", + "\n", + "#Result\n", + "print \"Magnetic moment is %.3e Am^2\\nBohr magneton is %.2e J/T\"%(M,mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic moment is 9.319e-24 Am^2\n", + "Bohr magneton is 9.23e-24 J/T\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.2, Page 18.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = -4.2e-6 # magnetic susceptibility\n", + "H = 1.19e5 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "I = X * H\n", + "B = mu_ * (H + I)\n", + "mur = (1 + I/H)\n", + "\n", + "#Results\n", + "print \"Magnetisation is %.2f A/m\\nFlux density is %.3f T\\nRelative permeability is %.2f\"%(I,B,mur)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is -0.50 A/m\n", + "Flux density is 0.150 T\n", + "Relative permeability is 1.00\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.3, Page 18.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "X = 1.2e-5 # magnetic susceptibility of magnesium\n", + "\n", + "#Calculations\n", + "p = 100 * X\n", + "\n", + "#Result\n", + "print \"Percentage increase in magnetic induction is %.4f percent\"%p" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage increase in magnetic induction is 0.0012 percent\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.4, Page 18.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = -0.4e-5 # magnetic susceptibility of material\n", + "H = 1e4 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "\n", + "#Calculations\n", + "I = X * H\n", + "B = mu_ * (H + I)\n", + "\n", + "#Result\n", + "print \"Magnetisation is %.2f A/m\\nMagnetic flux density is %f T\"%(I,B)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is -0.04 A/m\n", + "Magnetic flux density is 0.012566 T\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.5, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = 2.3e-5 # magnetic susceptibility of aluminium\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mur = 1 + X\n", + "mu = mu_ * mur\n", + "\n", + "#Result\n", + "print \"Permeability of aluminium is %.2e N/A^2\"%mu" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability of aluminium is 1.26e-06 N/A^2\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.6, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "X = 9.4e-2 # magnetic susceptibility\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mu_r = 1 + X\n", + "mu = mu_ * mu_r\n", + "\n", + "#Results\n", + "print \"Absolute permeability is %.2e N/A^2\\nRelative permeability is %.3f\"%(mu,mu_r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Absolute permeability is 1.37e-06 N/A^2\n", + "Relative permeability is 1.094\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.7, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "mu = 0.126 # maximum value of the permeability in N/A^2\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mu_r = mu / mu_\n", + "X = mu_r - 1\n", + "\n", + "#Results\n", + "print \"Magnetic susceptibility is %.f\\nRelative permeability is %e\"%(X,mu_r)\n", + "#Answers differ due to rounding off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic susceptibility is 100267\n", + "Relative permeability is 1.002676e+05\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.8, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "r = 0.6e-10 # radius of the atom\n", + "N = 28e26 # no. of electron in per m^3\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "Z = 2 # atomic no. of helium\n", + "m = 9.1e-31 # mass of an electron in kg\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "Chi = -(mu_ * Z * N * r**2 * e**2) / (6 * m)\n", + "\n", + "#Result\n", + "print \"Diamagnetic susceptibility is %.3e\"%Chi" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diamagnetic susceptibility is -1.188e-07\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.9, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "H = 1e3 # magnetisation field in A/m\n", + "phi = 2e-5 # magnetic flux in Weber\n", + "a = 0.2e-4 # area of cross section in m^2\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "mu = B / H\n", + "X = mu / mu_ - 1\n", + "\n", + "#Results\n", + "print \"Permeability is %.e N/A^2\\nSusceptibility is %.3f\"%(mu,X)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability is 1e-03 N/A^2\n", + "Susceptibility is 794.775\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.10, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1 # length of iron rod in m\n", + "a = 4e-4 # area in m^2\n", + "mu = 50e-4 # permeability of iron in H/m\n", + "Phi = 4e-4 # magnetic flux in Weber\n", + "\n", + "#Calculations\n", + "B = Phi / a\n", + "NI = B / mu\n", + "\n", + "#Result\n", + "print \"Number of ampere turns is %d A/m\"%NI" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of ampere turns is 200 A/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.11, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 200 # no. of turns \n", + "l = 0.5 # the mean length of iron wire in m\n", + "phi = 4e-4 # magnetic flux in Weber\n", + "a = 4e-4 # area of cross section in m^2\n", + "mu = 6.5e-4 # permeability of iron in wb/Am\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "N = n / l\n", + "I = B / (mu * N)\n", + "\n", + "#Result\n", + "print \"Current through the winding is %.2f A\"%I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current through the winding is 3.85 A\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.12, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "X = -5.6e-6 # magnetic susceptibility of material\n", + "a = 2.55e-10 # lattice constant in m\n", + "H = 1e4 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "m = 9.1e-31 # mass of electron in kg\n", + "e = 1.6e-19 # charge in an electron in C\n", + "\n", + "#Calculations\n", + "N = 2 / a**3\n", + "z = 1 \n", + "R = ((-X * 6 * m) / (mu_ * z * e**2 * N))**(1./2)\n", + "\n", + "#Result\n", + "print \"Radius of atom is %.2f A\"%(R * 1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of atom is 0.89 A\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.13, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "N = 6.5e25 # no. of atom per m^3\n", + "T = 300 # room temperature in K\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "m = 9.1e-31 # mass of electron in kg\n", + "e = 1.6e-19 # charge in an electron in C\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "\n", + "#Calculations\n", + "M = (e * h) / (4 * pi * m)\n", + "X = (mu_ * N * M**2) / (3 * k * T)\n", + "\n", + "#Result\n", + "print \"Susceptibility is %.3e\"%X" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Susceptibility is 5.642e-07\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.14, Page 18.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "w = 168.5 # molecular weight \n", + "d = 4370 # density of material in kg/m^3\n", + "H = 2e5 # magnetic field in A/m\n", + "T = 300 # room temperature in K\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space]\n", + "NA = 6.02e26 # Avogadro no. in per kg\n", + "mu_b = 9.24e-24 # Bohr magnetons in Am^2\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "\n", + "#Calculations\n", + "N = d * NA / w\n", + "X = (mu_ * N * (2 * mu_b)**2) / (3 * k * T)\n", + "I = X * H\n", + "\n", + "#Result\n", + "print \"Magnetisation is %.2f A/m\"%I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is 107.89 A/m\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.15, Page 18.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given that\n", + "A = 2500 # area of hysteresis loop \n", + "m = 10000 # weight in kg\n", + "d = 7.5 # density of material in g/cm^3\n", + "f = 50 # frequency in Hz\n", + "\n", + "#Calculations\n", + "E = f * A * 3600\n", + "V = m / d\n", + "L = E * V\n", + "\n", + "#Result\n", + "print \"Total loss of energy per hour is %.e ergs\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total loss of energy per hour is 6e+11 ergs\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.16, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "H = 5e3 # coercivity in A/m\n", + "l = 0.10 # length of solenoid in m\n", + "n = 50 # no. of turns \n", + "\n", + "#Calculations\n", + "N = n / l\n", + "i = H / N\n", + "\n", + "#Result\n", + "print \"Current in solenoid should be %d A\"%i" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current in solenoid should be 10 A\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.17, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 0.50 # length of iron rod in m\n", + "a = 4e-4 # area of cross section of rod in m^2\n", + "mu = 65e-4 # permeability of iron in H/m\n", + "fi = 4e-5 # flux in weber \n", + "\n", + "#Calculations\n", + "B = fi / a\n", + "H = B / mu\n", + "N = H * l\n", + "\n", + "#Result\n", + "print \"Number of turns are %.2f\"%N" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of turns are 7.69\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.18, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "H = 600 # magnetic flux in A/m\n", + "a = 0.2e-4 # area of cross section of rod in m^2\n", + "phi = 2.4e-5 # flux in weber \n", + "mu_ = 4*pi * 1e-7 # permeability of space in N/A^2\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "mu = B / H\n", + "X = mu / mu_ - 1\n", + "\n", + "#Result\n", + "print \"Permeability is %.3f N/A^2\\nSusceptibility is %.f\"%(mu,X)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability is 0.002 N/A^2\n", + "Susceptibility is 1591\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.19, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = 9.5e-9 # susceptibility of medium \n", + "mu_ = 4*pi * 1e-7 # permeability of space in N/A^2\n", + "\n", + "#Calculations\n", + "mu = mu_ * (1 + X)\n", + "mu_r = mu / mu_\n", + "\n", + "#Result\n", + "print \"Relative permeability is 1 + %.3e\"%(mu_r -1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relative permeability is 1 + 9.500e-09\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.20, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "a = 250. # area of the B-H loop in J/m^3\n", + "f = 50. # frequency in Hz\n", + "d = 7.5e3 # density of iron in kg/m^3\n", + "m = 100. # mass of core in kg\n", + "\n", + "#Calculations\n", + "V = m / d\n", + "n = 3600 * f\n", + "A = a * V * n\n", + "\n", + "\n", + "#Result\n", + "print \"Energy loss per hour is %.3e J\"%A\n", + "#Answer varies due to rounding-off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy loss per hour is 6.000e+05 J\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.21, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "B_max = 1.375 # maximum value of B in Wb/m^2\n", + "a = 0.513 # area of the loop in cm^2\n", + "k = 1000 # value of 1 cm on x axis in A/m\n", + "k_ = 1 # value of 1 cm on y axis in Wb/m^2\n", + "B = 1.375 # alternating magnetic flux density in Wb/m^2\n", + "v = 1e-3 # volume of specimen in m^3\n", + "f = 50 # frequency in Hz\n", + "\n", + "#Calculations\n", + "K = a * k * k_\n", + "L = K * v * f\n", + "\n", + "#Result\n", + "print \"Hysteresis loss per sec is %.2f W\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hysteresis loss per sec is 25.65 W\n" + ] + } + ], + "prompt_number": 38 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_19.ipynb b/Engineering_Physics/Chapter_19.ipynb new file mode 100755 index 00000000..8e043325 --- /dev/null +++ b/Engineering_Physics/Chapter_19.ipynb @@ -0,0 +1,333 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 19: Superconductivity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.1, Page 19.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "T_c = 7.2 # critical temperature in K\n", + "T = 5.1 # temperature in K\n", + "lambda_ = 380 # penetration depth at 0 K in A\n", + "\n", + "#Calculations\n", + "lamda = lambda_ * (1 - (T / T_c)**4)**(-1./2)\n", + "\n", + "#Result\n", + "print \"Penetration depth is %.2f A\"%lamda" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Penetration depth is 439.30 A\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.2, Page 19.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "Hc1 = 1.41e5 # first critical field at 14.1K\n", + "Hc2 = 4.205e5 # second critical field at 12.9K \n", + "T1 = 14.11 # temperature in K\n", + "T2 = 12.9 # temperature in K \n", + "T = 4.2 # temperature in K\n", + "lambda_ = 380 # penetration depth at 0 K in A\n", + "\n", + "#Calculations\n", + "Tc = sqrt((Hc2*T1**2 - Hc1*T2**2) / (Hc2 - Hc1))\n", + "H_ = Hc1 / (1 - (T1 / Tc)**2)\n", + "Hc = H_ * (1 - (T/Tc)**2)\n", + "\n", + "#Result\n", + "print \"Transition temperature is %.2f K\\nCritical field at temperate at 4.2 k is %.2e A/m\"%(Tc,Hc)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Transition temperature is 14.68 K\n", + "Critical field at temperate at 4.2 k is 1.69e+06 A/m\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.3, Page 19.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 1e-3 # diameter of wire in m\n", + "T1 = 4.2 # temperature in K\n", + "T2 = 7.18 # temperature in K\n", + "H_ = 6.51e4 # critical magnetic field at 0 K\n", + "\n", + "#Calculations\n", + "r = d / 2\n", + "Hc = H_ * (1 - (T1 / T2)**2)\n", + "Jc = (2 * pi * r * Hc) / (pi * r**2)\n", + "\n", + "#Result\n", + "print \"Critical current density is %.3e A/m^2\"%Jc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical current density is 1.713e+08 A/m^2\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.4, Page 19.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "w = 199.5 # isotopic mass of Hg\n", + "Tc = 4.186 # critical temperature in K \n", + "w_ = 203.4 # increased isotope mass of Hg\n", + "\n", + "#Calculations\n", + "Tc_ = Tc * (w / w_)**(1./2)\n", + "\n", + "#Result\n", + "print \"Critical temperature is %.4f K\"%Tc_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical temperature is 4.1457 K\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.5, Page 19.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "T_c = 4.2 # critical temperature in K\n", + "T = 2.9 # temperature in K\n", + "lamda = 57 # penetration depth at 2.9 K in nm\n", + "\n", + "#Calculations\n", + "lambda_ = lamda * (1 - (T / T_c)**4)**(1./2)\n", + "\n", + "#Result\n", + "print \"Penetration depth at 0 K is %.2f nm\"%lambda_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Penetration depth at 0 K is 50.10 nm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.6, Page 19.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given\n", + "T1 = 2.18 # temperature in first case in K\n", + "lambda1 = 16 # penetration depth at 2.18 K in nm\n", + "T2 = 8.1 # temperature in second case in K\n", + "lambda2 = 96 # penetration depth at 8.1 K in nm\n", + "\n", + "#Calculations\n", + "Tc = (((lambda2**2 * T2**4) - (T1**4 * lambda1**2)) / (lambda2**2 - lambda1**2))**(1./4)\n", + "\n", + "#Result\n", + "print \"Critical temperature is %.2f K\"%Tc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical temperature is 8.16 K\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.7, Page 19.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "w = 26.91 # isotopic mass of superconducting sample\n", + "Tc = 1.19 # first critical temperature in K \n", + "w_ = 32.13 # increased isotope mass of superconducting sample\n", + "\n", + "#Calculations\n", + "Tc_ = Tc * (w / w_)**(1./2)\n", + "\n", + "#Result\n", + "print \"Critical temperature is %.3f K\"%Tc_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical temperature is 1.089 K\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19.8, Page 19.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "Tc = 4.2 # critical temperature of Hg in K\n", + "c = 3e8 # speed of light in m/sec \n", + "\n", + "#Calculations\n", + "E = 3 * k * Tc\n", + "lamda = h * c / E\n", + "\n", + "#Result\n", + "print \"Energy gap is %.2e eV\\nWavelength of photon is %.2e m\"%(E/1.6e-19,lamda)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy gap is 1.09e-03 eV\n", + "Wavelength of photon is 1.14e-03 m\n" + ] + } + ], + "prompt_number": 8 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_2.ipynb b/Engineering_Physics/Chapter_2.ipynb new file mode 100755 index 00000000..dccc71e2 --- /dev/null +++ b/Engineering_Physics/Chapter_2.ipynb @@ -0,0 +1,1712 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Diffraction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1, Page 2.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt,pi\n", + "\n", + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "d = 1 # distance of wavefront received on the screen from the opening in meter\n", + "n = 80 # no. of half period zone\n", + "\n", + "#Calculations\n", + "Rn = sqrt(n * l * d)# calculation for radius of nth half period zone\n", + "A = pi * d * l# calculation for area of half period zone\n", + "\n", + "#Result\n", + "print(\"Radius of 80th half period zone = %.3f cm. \\nArea of half period zone = %.4f square cm.\"%(Rn*100,A*10000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of 80th half period zone = 0.632 cm. \n", + "Area of half period zone = 0.0157 square cm.\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2, Page 2.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "f = 0.6 # focal length of convex lens in meter\n", + "n = 1 # no. of half period zone\n", + "\n", + "#Calculation\n", + "Rn = sqrt(n * l * f)# calculation for radius of half period zone\n", + "\n", + "print(\"Radius of half period zone = %.1f mm \"%(Rn*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of half period zone = 0.6 mm \n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3, Page 2.38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "f = 0.60 #focal length in m\n", + "n = 1 # no. of half period zone\n", + "\n", + "#Calculation\n", + "r1 = sqrt(f* l ) # because at maxima intensity is four time the individual intensity of light\n", + "\n", + "#Result\n", + "print(\"Radius of 80th half period zone = %.4f mm. \"%(r1)) " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of 80th half period zone = 0.0006 mm. \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4, Page 2.39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "d = 0.5 # distance of observation point from circular opening in meter\n", + "r1 = 2e-3 # radius of circular opening in first case in meter\n", + "r2 = 2e-2 # radius of circular opening in second case in meter \n", + "\n", + "#Calculation\n", + "n1 = (r1**2) / (d * l) # calculation for no. of half period zone in first case \n", + "n2 = (r2**2) / (d * l) # calculation for no. of half period zone in second case\n", + "\n", + "print(\"No. of half period zone in first case = %d \\nNo. of half period zone in second case = %d \"%(n1,n2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of half period zone in first case = 13 \n", + "No. of half period zone in second case = 1333 \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5, Page 2.39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "d = 1e-3 # diameter of the first ring of zone plate in meter\n", + "n = 1 # no. of half period zone\n", + "\n", + "#Calculation\n", + "D = (d**2) / (4 * l * n) # calculation for distance of screen from opening\n", + "\n", + "#Result\n", + "print(\"Distance of screen from opening = %.1f meter \"%D)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance of screen from opening = 0.5 meter \n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6, Page 2.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 5.893e-7 # wavelength of light in meter\n", + "f = 1 # focal-length of convex lens in meter\n", + "n1 = 1 # no. of first half period zone\n", + "n2 = 3 # no. of second half period zone\n", + "n3 = 5 # no. of third half period zone\n", + "\n", + "#Calculations\n", + "R1 = sqrt(n1 * l * f) # calculation for Radius of first half period zone\n", + "R2 = sqrt(n2 * l * f) # calculation for Radius of second half period zone\n", + "R3 = sqrt(n3 * l * f) # calculation for Radius of third half period zone\n", + "\n", + "#Result\n", + "print(\"Radius of first ,second and third half period zone = %.3e, %.3e and %.3e meter respectively. \"%(R1,R2,R3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of first ,second and third half period zone = 7.677e-04, 1.330e-03 and 1.717e-03 meter respectively. \n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7, Page 2.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "f = 0.2 # focal length of convex lens in meter\n", + "n = 10 # no. of half period zone\n", + "\n", + "#Calculation\n", + "Rn = sqrt(n * l * f) # calculation for radius of 10th half period zone\n", + "\n", + "#Result\n", + "print(\"Radius of 10th half period zone = %.1f mm. \"%(Rn*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of 10th half period zone = 1.0 mm. \n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8, Page 2.40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "d1 = 1. # distance of wavefront recieved on the screen from the opening in first side in meter\n", + "d2 = 2. # distance of wavefront recieved on the screen from the opening in other side in meter\n", + "\n", + "#Calculations\n", + "f = (d1 * d2) / (d1 + d2)\n", + "p = 1. / f # beacause zone plate act as a convex lens\n", + "n = 1 # for first zone\n", + "Rn = sqrt(n * l * f) # calculation for radius of first zone\n", + "Dn = 2 * Rn # calculation for diameter of first zone\n", + "\n", + "#Result\n", + "print(\"Focal length = %.2f meter. \\n Power = %.1f D. \\n Diameter of first zone = %.3f mm. \"%(f,p,Dn*1000))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Focal length = 0.67 meter. \n", + " Power = 1.5 D. \n", + " Diameter of first zone = 1.253 mm. \n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9, Page 2.41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "lambda1 = 6e-7 # wavelength of first light in meter\n", + "lambda2 = 5e-7 # wavelength of second light in meter\n", + "f1 = 1 # focal length in first case in meter \n", + "\n", + "#Calculation\n", + "f2 = (lambda1 * f1) / lambda2 # calculation for focal length in second case\n", + "\n", + "#Result\n", + "print(\"Focal length in second case = %.1f meter\"%f2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Focal length in second case = 1.2 meter\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10, Page 2.41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 4e-7 # wavelength of light in meter\n", + "u = 0.2 # distance of object from zone plate in meter\n", + "v = 0.2 # distance of brightest image from from zone plate in meter \n", + "r = 0.01 # radius in meter\n", + "\n", + "#Calculations\n", + "f = (u * v) / (u + v) # calculation for focal length\n", + "n = (r**2) / (f * l) # calculation for no. of zone of Fresnel\n", + "\n", + "#Result\n", + "print(\"No. of zone of Fresnel = %.f\"%n)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of zone of Fresnel = 2500\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11, Page 2.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.893e-7 # wavelength of light in meter\n", + "d = 2.3e-3 # diameter of the central zone of zone plate in meter\n", + "u = 6 # distance between point source from zone plate in meter\n", + "n = 1 # for central zone\n", + "\n", + "#Calculations\n", + "r = d/2\n", + "f = (r**2) / (l) # calculation for focal length\n", + "v = (f * u) / (u - f) # calculation for distance of first image from zone plate\n", + "\n", + "#Result\n", + "print(\"Distance of first image from zone plate = %.2f meter \"%v) #answer differs due to rounding-off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance of first image from zone plate = 3.59 meter \n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12, Page 2.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "R = 2 # radius of curvature in meter\n", + "\n", + "#Calculation\n", + "f = R # calculation for principal focal length of zone plate\n", + "\n", + "#Result\n", + "print(\"Principal focal length of zone plate = %.1f meter \"%f)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Principal focal length of zone plate = 2.0 meter \n" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13, Page 2.42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, pi\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "b = 1e-3 # slit-width in meter\n", + "m = 1 # for first minima\n", + "\n", + "#Calculation\n", + "theta = asin((m * l) / b) # calculation for angular spread of the central maxima in radian\n", + "theta_ = theta * (180 / pi) # calculation for angular spread of the central maxima in degree\n", + "\n", + "#Result\n", + "print(\"Angular spread of the central maxima = %.4f degree \"%(2 * theta_))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular spread of the central maxima = 0.0675 degree \n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14, Page 2.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d = 1.2 # distance of screen from slit in meter\n", + "x = 3.7e-3 # distance between first maxima to central maxima in meter\n", + "b = 2e-4 # slit-width in meter\n", + "\n", + "#Calculation\n", + "l = (x * b) / d # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print \"Wavelength of light = \",round(l/1e-10),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 6167.0 A\n" + ] + } + ], + "prompt_number": 70 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15, Page 2.43" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, pi\n", + "\n", + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "b = 2.2e-6 # slit-width in meter\n", + "\n", + "#Calculations\n", + "m2 = 2 # for second minima\n", + "theta2 = asin((m2 * l) / b) * (180 / pi) # calculation for angular position of second minima\n", + "m3 = 3 # for third minima\n", + "theta3 = asin((m3 * l) / b) * (180 / pi) # calculation for angular position of third minima\n", + "\n", + "#Result\n", + "print(\"Angular position of second and third minima = %.f degrees and %.2f degrees respectively \"%(theta2 ,theta3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular position of second and third minima = 30 degrees and 48.59 degrees respectively \n" + ] + } + ], + "prompt_number": 72 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.16, Page 2.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, pi\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "b = 1.2e-6 # slit-width in meter\n", + "\n", + "#Calculation\n", + "m = 1 # for first minima\n", + "theta = asin((m * l) / b) # calculation for half angular width of the central bright maxima in radian\n", + "theta_ = theta * (180 / pi) # calculation for half angular width of the central bright maxima in degree\n", + "\n", + "#Result\n", + "print(\"Half angular width of the central bright maxima = %.2f degrees \"%theta_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Half angular width of the central bright maxima = 29.40 degrees \n" + ] + } + ], + "prompt_number": 74 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.17, Page 2.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin, pi \n", + "\n", + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "theta = pi / 6 # half angular width of central maximum in first case in radian\n", + "theta_ = pi / 2 # half angular width of central maximum in second case in radian\n", + "\n", + "#Calculation\n", + "m = 1 # for first minima\n", + "b1 = (l * m) / sin(theta) # calculation for slit width in first case\n", + "b2 = (l * m) / sin(theta_) # calculation for slit width in second case\n", + "\n", + "#Result\n", + "print(\"Slit width in first case = %.f micro-meter \\nSlit width in second case = %.1f micro-meter\"%(b1*1e6,b2*1e6))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slit width in first case = 1 micro-meter \n", + "Slit width in second case = 0.5 micro-meter\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.18, Page 2.44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, pi\n", + "\n", + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "d = 1 # distance of screen from slit in meter\n", + "b = 1e-4 # slit-width in meter\n", + "\n", + "#Calculations\n", + "theta = (asin(l / b)) * (180 / pi) # calculation for angular spread\n", + "x = (2 * d * l) / b# calculation for linear width\n", + "\n", + "#Result\n", + "print(\"Angular spread = %.3f degree\\nLinear width = %.3f cm \"%(2*theta,x*1e2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular spread = 0.675 degree\n", + "Linear width = 1.178 cm \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.20, Page 2.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, pi\n", + "\n", + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "b = 1.2e-6 # slit-width in meter\n", + "\n", + "#Calculations\n", + "m = 1 # for first minima\n", + "theta = asin((m * l) / b) # calculation for angular width of the central maxima in radian\n", + "theta_ = theta * (180 / pi) # calculation for angular width of the central maxima in degree\n", + "\n", + "#Result\n", + "print(\"Angular width of the central maxima = %.f degree \"%(2 * theta_))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular width of the central maxima = 60 degree \n" + ] + } + ], + "prompt_number": 104 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21, Page 2.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 4.890e-7 # wavelength of light in meter\n", + "b = 5e-3 # slit-width in meter\n", + "f = 0.4 # focal-length of convex lens in meter\n", + "\n", + "#Calculation\n", + "m = 1 # for first dark fringe\n", + "x = (f * m * l) / b \n", + "n = 1 # for first secondary maxima\n", + "x_ = ((2 * n + 1) * l * f) / (2 * b) \n", + "delta_x = x_ - x # calculation for separation of dark band \n", + "\n", + "#Result\n", + "print(\"Separation of dark band = %.3e meter.\"%(delta_x))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Separation of dark band = 1.956e-05 meter.\n" + ] + } + ], + "prompt_number": 105 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22, Page 2.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.893e-7 # wavelength of light in meter\n", + "b = 5e-4 # slit-width in meter\n", + "f = 1 # focal length of convex lens in meter\n", + "\n", + "#Calculation\n", + "x = (2 * l * f) / b # calculation for Separation of dark band on either side of the cenral maximum\n", + "\n", + "#Result\n", + "print(\"Separation of dark band on either side of the central maximum = %.3e meter\"%x)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Separation of dark band on either side of the central maximum = 2.357e-03 meter\n" + ] + } + ], + "prompt_number": 106 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23, Page 2.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d = 4e-4 # separation between slits in meter\n", + "b = 8e-5 # slit-width in meter\n", + "\n", + "#Calculations\n", + "r = (b + d) / b # calculation for ratio of n with m\n", + "m1 = 1\n", + "n1 = r * m1 # calculation for Missing orders \n", + "m2 = 2\n", + "n2 = r * m2 # calculation for Missing orders \n", + "m3 = 3\n", + "n3 = r * m3 # calculation for Missing orders \n", + "\n", + "#Result\n", + "print(\"Missing orders = %d,%d,%d,......etc.\"%(n1,n2,n3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Missing orders = 6,12,18,......etc.\n" + ] + } + ], + "prompt_number": 107 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24, Page 2.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "d = 4e-4 # separation between slits in meter\n", + "b = 2e-4 # slit-width in meter\n", + "fringe_width = 2.5e-3 # fringe width in meter\n", + "D = 1.6 # distance between screen and slits\n", + "\n", + "#Calculations\n", + "l = (fringe_width * d) / D # calculation for wavelength of light\n", + "r = (b + d) / b # calculation for ratio of n with m\n", + "m1 = 1\n", + "n1 = r * m1 # calculation for missing order\n", + "m2 = 2\n", + "n2 = r * m2 # calculation for missing order\n", + "m3 = 3\n", + "n3 = r * m3 # calculation for missing order\n", + "\n", + "#Result\n", + "print(\"Wavelength of light = %.3e meter. \\nMissing order = %d,%d,%d....etc.\"%(l,n1,n2,n3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 6.250e-07 meter. \n", + "Missing order = 3,6,9....etc.\n" + ] + } + ], + "prompt_number": 109 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.25, Page 2.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sin\n", + "\n", + "# Given \n", + "N = 425000 # no. of lines in plane transmission grating per meter\n", + "theta = pi / 6 # angle at which second order spectral line is observed in radian\n", + "n = 2 # order of spectral line\n", + "\n", + "#Calculation\n", + "l = sin(theta) / (2 * N) # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print \"Wavelength of light = \",round(l/1e-10),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light = 5882.0 A\n" + ] + } + ], + "prompt_number": 115 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.26, Page 2.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sin\n", + " \n", + "# Given \n", + "N = 500000 # no. of lines in plane transmission grating per meter\n", + "theta = pi / 6 # angle at which second order spectral line is observed in radian\n", + "n = 2 # order of spectral line\n", + "\n", + "#Calculation\n", + "l = sin(theta) / (2 * N) # calculation for wavelength of light\n", + "\n", + "#Result\n", + "print \"wavelength of light = \",l/1e-10,\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of light = 5000.0 A\n" + ] + } + ], + "prompt_number": 116 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.27, Page 2.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import ceil\n", + "\n", + "# Given \n", + "lambda2 = 5.461e-7 # wavelength of light in second case in meter\n", + "n1 = 4 # no. of order in first case\n", + "n2 = 3 # no. of order in second case \n", + "\n", + "#Calculation\n", + "lambda1 = (n2 * lambda2) / n1 # calculation for Wavelength of light in first case\n", + "\n", + "#Result\n", + "print(\"Wavelength of light in first case = %d A\"%(ceil(lambda1*1e10)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light in first case = 4096 A\n" + ] + } + ], + "prompt_number": 90 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.28, Page 2.49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sin\n", + "\n", + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "theta = pi / 6 # angle at which second order spectral line is observed in radian\n", + "n = 2 # order of spectral line\n", + "\n", + "#Calculations\n", + "k = (n * l) / sin(theta) # calculation for (b+d)\n", + "N = 1 / k # calculation for no. of lines in per cm\n", + "\n", + "#Result\n", + "print(\"No. of lines per cm = %.f \"%(N / 100))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of lines per cm = 5000 \n" + ] + } + ], + "prompt_number": 117 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.29, Page 2.49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin,pi \n", + "\n", + "# Given \n", + "lambda1 = 5.048e-7 # wavelength of light in first case in meter\n", + "lambda2 = 5.016e-7 # wavelength of light in second case in meter\n", + "n = 2 # no. of order in first case\n", + "N = 15000 # no. of lines in grating per inch \n", + "\n", + "#Calculations\n", + "k = 2.54 / 1500000 # in meter\n", + "theta1 = asin(n * lambda1 / k) * (180 / pi) # calculation for angle in first case\n", + "theta2 = asin(n * lambda2 / k) * (180 / pi) # calculation for angle in second case\n", + "delta_theta = theta1 - theta2 # calculation for angle of separation\n", + "\n", + "#Result\n", + "print(\"Angle of separation = %.2f degree\"%delta_theta)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of separation = 0.27 degree\n" + ] + } + ], + "prompt_number": 118 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.30, Page 2.50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin,pi \n", + "\n", + "# Given \n", + "lambda1 = 5.89e-7 # wavelength of light in first case in meter\n", + "lambda2 = 5.896e-7 # wavelength of light in second case in meter\n", + "n = 2 # no. of order in first case\n", + "N = 600000 # no. of lines in grating per meter \n", + "\n", + "#Calculations\n", + "k = 1. / N # in meter\n", + "theta1 = asin(n * lambda1 / k) * (180 / pi) # calculation for angle in first case\n", + "theta2 = asin(n * lambda2 / k) * (180 / pi) # calculation for angle in second case\n", + "delta_theta = theta2 - theta1 # calculation for angle of separation\n", + "\n", + "#Result\n", + "print(\"Angle of separation = %.2f degree\"%delta_theta)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of separation = 0.06 degree\n" + ] + } + ], + "prompt_number": 119 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.31, Page 2.50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "lambda1 = 5.4e-7 # wavelength of light for nth order in meter\n", + "lambda2 = 4.05e-7 # wavelength of light for (n+1)th order in meter \n", + "theta = pi / 6 # angle of diffraction in radian \n", + "\n", + "#Calculations\n", + "k = (lambda1 * lambda2) / ((lambda1 - lambda2) * sin(theta)) # calculation for b+d\n", + "N = (1 / k) * (0.01) # calculation for no. of lines per cm\n", + "\n", + "#Result\n", + "print(\"No. of lines per cm = %d \"%N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of lines per cm = 3086 \n" + ] + } + ], + "prompt_number": 97 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.32, Page 2.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, cos, sin\n", + "\n", + "# Given \n", + "d_theta = 0.01 # angular separation between two wavelengths in radian \n", + "theta = pi / 6 # angle of diffraction in radian \n", + "l = 5e-7 # wavelength of light in meter\n", + "\n", + "#Calculation\n", + "d_lambda = (l * cos(theta) * d_theta) / sin(theta) # calculation for difference in two waveligth\n", + "\n", + "#Result\n", + "print \"Difference in two wavelength = \",round(d_lambda/1e-10,1),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Difference in two wavelength = 86.6 A\n" + ] + } + ], + "prompt_number": 127 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.33, Page 2.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "N = 2620 # no. of lines in plane transmission grating per inch\n", + "l = 5e-7 # wavelength of incident radiation in meter\n", + "\n", + "#Calculations\n", + "k = 2.54 / N * 1 / 100 # calculation for b+d in meter\n", + "n = k / l # calculation for order of spectrum\n", + "\n", + "#Result\n", + "print(\"Order of spectrum = %d\"%n)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Order of spectrum = 19\n" + ] + } + ], + "prompt_number": 99 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.34, Page 2.51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "N = 500000. # no. of lines in plane transmission grating per meter\n", + "l = 5e-7 # wavelength of incident radiation in meter\n", + "\n", + "#Calculations\n", + "k = 1 / N # calculation for b+d in meter\n", + "n = k / l # calculation for order of spectrum \n", + "\n", + "#Result\n", + "print \"Order of spectrum = %d\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Order of spectrum = 4\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.35, Page 2.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "N = 4000. # no. of lines in plane transmission grating per meter\n", + "lambda1 = 4.e-7 # wavelength of light in first case in meter\n", + "lambda2 = 7.e-7 # wavelength of light in second case in meter\n", + "\n", + "#Calculations\n", + "b_plus_d = (1/N)*10**-2\n", + "n1 = b_plus_d / lambda1 # calculation for Observed order in first case\n", + "n2 = b_plus_d / lambda2 # calculation for Observed order in second case\n", + "\n", + "#Result\n", + "print \"Observed order = %.2f,%.2f\"%(n1,n2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Observed order = 6.25,3.57\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.36, Page 2.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "N = 4000 # no. of lines in grating per meter\n", + "l = 5e-5 # wavelength of incident radiation in cm\n", + "n = 3 # no. of order\n", + "\n", + "#Calculation\n", + "p = (n * N) / (sqrt(1 - (N * n * l)))# dispersive power (p) = d(theta)/d(lambda)\n", + "\n", + "#Result\n", + "print \"Dispersive power = %.3e rad/m\"%p" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Dispersive power = 1.897e+04 rad/m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.37, Page 2.52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 2 # no. of order\n", + "lambda1 = 5.89e-7 # wavelength of light in first case in meter\n", + "lambda2 = 5.896e-7 # wavelength of light in second case in meter\n", + "\n", + "#Calculation\n", + "N = lambda1 / (n * (lambda2 - lambda1)) # calculation for minimum no. of lines in grating \n", + "\n", + "#Result\n", + "print \"Minimum no. of lines in grating = %.1f\"%N" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum no. of lines in grating = 490.8\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.38, Page 2.53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "n = 1 # no. of order\n", + "lambda1 = 5.89e-7 # wavelength of light in first case in meter\n", + "lambda2 = 5.896e-7 # wavelength of light in second case in meter\n", + "\n", + "#Calculation\n", + "N = lambda1 / (n * (lambda2 - lambda1)) # calculation for minimum no. of lines in grating\n", + "\n", + "#Result\n", + "print \"Minimum no. of lines in grating = %.2f\"%N" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum no. of lines in grating = 981.67\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.39, Page 2.53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi,sin\n", + "\n", + "# Given \n", + "n = 3 # no. of order\n", + "theta = pi / 6 # view angle of third order in radian\n", + "lambda1 = 5.89e-7 # min. wavelength of light in meter\n", + "lambda2 = 5.896e-7 # max.wavelength of light in meter\n", + "\n", + "#Calculations\n", + "mean_lambda = (lambda1 + lambda2) / 2 # calculation for mean wavelength\n", + "s = (n * mean_lambda) / sin(theta) # calculation for grating space b+d\n", + "N = lambda1 / (n * (lambda2 - lambda1)) # calculation for minimum no. of lines in grating\n", + "\n", + "#Result\n", + "print \"Grating space = %.3e meter. \\nTotal width of ruled surface = %.3e meter. \"%(s,s * N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Grating space = 3.536e-06 meter. \n", + "Total width of ruled surface = 1.157e-03 meter. \n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.40, Page 2.53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "a = 5 # diameter of objective lens of telescope in meter\n", + "R = 3.8e8 # distance of moon in meter\n", + "\n", + "#Calculations\n", + "theta = (1.22 * l) / a # calculation for angle \n", + "x = (R * theta) # calculation for the separation of two points on moon\n", + "\n", + "#Result\n", + "print \"The separation of two points on moon = %.3f meter\"%x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The separation of two points on moon = 50.996 meter\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.41, Page 2.54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "theta = (1e-3) * (pi / 180) # separation angle of stars in radian\n", + "\n", + "#Calculation\n", + "a = (1.22 * l) / theta # calculation for diameter of telescope objective\n", + "\n", + "#Result\n", + "print \"Diameter of telescope objective = %.5f meter\"%a" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of telescope objective = 0.03495 meter\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.42, Page 42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 6e-7 # wavelength of light in meter\n", + "theta = 2.44e-6 # separation angle of stars in radian\n", + "\n", + "#Calculation\n", + "a = (1.22 * l) / theta # calculation for diameter of telescope objective\n", + "\n", + "#Result\n", + "print \"Diameter of telescope objective = %.2f meter\"%a" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of telescope objective = 0.30 meter\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.43, Page 2.54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "a = 0.004 # diameter of objective lens of telescope in meter\n", + "x = 1.5e-3 # distance between two pin holes in meter\n", + "\n", + "#Calculations\n", + "theta = (1.22 * l) / a # calculation for angle \n", + "R = x / theta # calculation for max. distance of pin holes from microscope\n", + "\n", + "#Result\n", + "print \"Max. distance of pin holes from microscope = %.4f meter\"%R" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Max. distance of pin holes from microscope = 8.9419 meter\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.44, Page 2.55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sin\n", + "\n", + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "theta = pi / 6 # semi-angle of cone in radian\n", + "\n", + "#Calculation\n", + "d = (1.22 * l) / (2 * sin(theta)) # calculation for the resolving limit of microscope \n", + "\n", + "#Result\n", + "print \"The resolving limit of microscope = %.1e meter\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The resolving limit of microscope = 6.7e-07 meter\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.45, Page 2.55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.461e-7 # wavelength of light in meter\n", + "d = 4e-7 # separation between objects in meter\n", + "\n", + "#Calculation\n", + "NA = (1.22 * l) / (2 * d) # calculation for numerical aperture of objective \n", + "\n", + "#Result\n", + "print \"Numerical aperture of objective = %.3f\"%NA" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture of objective = 0.833\n" + ] + } + ], + "prompt_number": 41 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_20.ipynb b/Engineering_Physics/Chapter_20.ipynb new file mode 100755 index 00000000..6252eb1b --- /dev/null +++ b/Engineering_Physics/Chapter_20.ipynb @@ -0,0 +1,755 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 20: X-Ray" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.1, Page 20.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "V1 = 40e3 # voltage in first case in V\n", + "V2 = 20e3 # voltage in second case in V\n", + "V3 = 100e3 # voltage in second in V\n", + "\n", + "#Calculations\n", + "v1 = 0.593e6 * sqrt(V1)\n", + "lambda1 = 12400 / V1\n", + "v2 = 0.593e6 * sqrt(V2)\n", + "lambda2 = 12400 / V2\n", + "v3 = 0.593e6 * sqrt(V3)\n", + "lambda3 = 12400 / V3\n", + "\n", + "#Results\n", + "print \"Max. speed of electrons at %d Volts is %.3e m/sec\\nMax. speed of electrons at %d Volts is %.2e m/sec/sec\\nMax. speed of electrons at %d Volts is %.3e m/sec\\nShortest wavelength of x-ray = %.2f A\\nShortest wavelength of x-ray = %.2f A\\nShortest wavelength of x-ray = %.3f A\"%(V1,v1,V2,v2,V3,v3,lambda1,lambda2,lambda3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Max. speed of electrons at 40000 Volts is 1.186e+08 m/sec\n", + "Max. speed of electrons at 20000 Volts is 8.39e+07 m/sec/sec\n", + "Max. speed of electrons at 100000 Volts is 1.875e+08 m/sec\n", + "Shortest wavelength of x-ray = 0.31 A\n", + "Shortest wavelength of x-ray = 0.62 A\n", + "Shortest wavelength of x-ray = 0.124 A\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.2, Page 20.7\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "V = 30e3 # voltage in V\n", + "lambda_min = 0.414e-10 # shortest wavelength in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "h = (e * V * lambda_min) / c\n", + "\n", + "#Result\n", + "print \"Planck constant is %.3e J sec\"%h" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Planck constant is 6.624e-34 J sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.3, Page 20.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "V = 25e3 # voltage in V\n", + "\n", + "#Calculations\n", + "lambda_min = 12400 / V\n", + "\n", + "#Result\n", + "print \"Minimum wavelength of x-ray is %.3f A\"%lambda_min" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum wavelength of x-ray is 0.496 A\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.4, Page 20.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "V = 13.6e3 # voltage in V\n", + "\n", + "#Calculations\n", + "v = 0.593e6*sqrt(V)\n", + "\n", + "#Result\n", + "print \"Maximum speed of electron is %.2e m/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum speed of electron is 6.92e+07 m/sec\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.5, Page 20.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "V = 10e3 # voltage in V\n", + "i = 2e-3 # current in amp\n", + "\n", + "#Calculations\n", + "v = 0.593e6*sqrt(V)\n", + "\n", + "#Result\n", + "print \"Velocity of electron is %.2e m/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of electron is 5.93e+07 m/sec\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.6, Page 20.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given\n", + "V = 9.8e3 # voltage in V\n", + "i = 2e-3 # current in amp\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "lamda = 12400 / V\n", + "f = c / (lamda*10**-10)\n", + "\n", + "#Results\n", + "print \"Highest frequency is %.2e Hz\\nMinimum wavelength is %.2f A\"%(f,lamda)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Highest frequency is 2.37e+18 Hz\n", + "Minimum wavelength is 1.27 A\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.7, Page 20.9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "V = 12.4e3 # voltage in V\n", + "i = 2e-3 # current in amp\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "n = i / e\n", + "v = 0.593e6*sqrt(V)\n", + "\n", + "#Result\n", + "print \"Number of electrons striking the target per sec is %.2e\\nSpeed of electrons is %.1e m/sec\"%(n,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of electrons striking the target per sec is 1.25e+16\n", + "Speed of electrons is 6.6e+07 m/sec\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.8, Page 20.9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "V = 10e3 # voltage in V\n", + "i = 15e-3 # current in amp\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "n = i / e\n", + "lamda = 12400 / V \n", + "\n", + "#Results\n", + "print \"Number of electrons striking the anode per sec is %.2e\\nMinimum wavelength produced is %.2f A\"%(n,lamda)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of electrons striking the anode per sec is 9.38e+16\n", + "Minimum wavelength produced is 1.24 A\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.9, Page 20.9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "V = 50e3 # voltage in V\n", + "i = 1e-3 # current in amp\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "n = i / e\n", + "\n", + "#Result\n", + "print \"Number of electrons striking the anode per sec is %.2e\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of electrons striking the anode per sec is 6.25e+15\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.10, Page 20.10" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lambda1 = 40e-12 # minimum wavelength in first case in m\n", + "lambda2 = 1e-10 # minimum wavelength in second case in m\n", + "\n", + "#Calculations\n", + "V1 = 12400e-10 / lambda1\n", + "V2 = 12400e-10 / lambda2\n", + "\n", + "#Results\n", + "print \"Applied voltage to get wavelength of %.e meter is %.f KV\\nApplied voltage to get wavelength of %.e meter is %.1f KV\"%(lambda1,V1/10**3,lambda2,V2/10**3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Applied voltage to get wavelength of 4e-11 meter is 31 KV\n", + "Applied voltage to get wavelength of 1e-10 meter is 12.4 KV\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.11, Page 20.10" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "V1 = 44e3 # voltage in first case in V\n", + "V2 = 50e3 # voltage in second case in V\n", + "lambda1 = 0.284e-10 # shortest wavelength in first case in m\n", + "lambda2 = 0.248e-10 # shortest wavelength in second case in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "h1 = e * V1 * lambda1 / c\n", + "h2 = e * V2 * lambda2 / c\n", + "\n", + "#Results\n", + "print \"Planck constant is %.2e J sec if shortest wavelength is %.3e m \\nPlanck constant is %.3e Jsec if shortest wavelength is %.3e m \"%(h1,lambda1,h2,lambda2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Planck constant is 6.66e-34 J sec if shortest wavelength is 2.840e-11 m \n", + "Planck constant is 6.613e-34 Jsec if shortest wavelength is 2.480e-11 m \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.12, Page 20.10" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 1e-11 # K-absorption limit for uranium in m\n", + "\n", + "#Calculations\n", + "V = 12400e-10 / lamda\n", + "\n", + "#Result\n", + "print \"Excitation potential is %d kV\"%(V/10**3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Excitation potential is 124 kV\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.13, Page 20.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "lamda = 1.4e-11 # K-absorption edge for lead in m\n", + "V = 88.6e3 # minimum voltage required for producing k-lines in V\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "r = V * lamda / c\n", + "\n", + "#Result\n", + "print \"The value of the ratio of h/e = %.3e Jsec/C\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The value of the ratio of h/e = 4.135e-15 Jsec/C\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.14, Page 20.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 92 # atomic no. of atom\n", + "Rh = 1.1e5 # Rydberg constant in cm^-1\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "lamda = 1 / (Rh *(Z-1)**2 * (1 - (1 / 2**2)))\n", + "\n", + "#Result\n", + "print \"Wavelength of K line = %.2f A\"%(lamda*1e8)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of K line = 0.11 A\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.15, Page 20.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 42 # atomic no. of Mo\n", + "lamda = 0.71e-10 # wavelength in m\n", + "Z_ = 29 # atomic no. of Cu\n", + "\n", + "#Calculations\n", + "lambda_ = (Z-1)**2 * lamda / (Z_-1)**2\n", + "\n", + "#Result\n", + "print \"Wavelength of the corresponding radiation of Cu is %.2f A\"%(lambda_*1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of the corresponding radiation of Cu is 1.52 A\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.16, Page 20.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 79 # atomic no. of element\n", + "b = 1 # a constant\n", + "a = 2.468e15 # a constant in per sec\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "f = a * (Z - b)**2\n", + "lamda = c / f\n", + "\n", + "#Result\n", + "print \"Wavelength of x-ray is %.4f A\"%(lamda*1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of x-ray is 0.1998 A\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.17, Page 20.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 29 # atomic no. of Cu\n", + "R = 1.097e7 # Rydberg constant in m^-1\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "\n", + "#Calculations\n", + "f = 3./4 * (R * c) * (Z-1)**2\n", + "E = h * f / 1.6e-16\n", + "E_L = 0.931 # let E_L = 0.931 KeV\n", + "E_ = E + E_L\n", + "\n", + "#Result\n", + "print \"Ionization potential of K-shell electron of Cu is %.3f keV\"%E_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ionization potential of K-shell electron of Cu is 8.938 keV\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.18, Page 20.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 79 # atomic no. of anticathode\n", + "R = 1.097e7 # Rydberg constant in m^-1\n", + "c = 3e8 # speed of light in m/sec\n", + "\n", + "#Calculations\n", + "f = 3./4 * (R * c) * (Z-1)**2\n", + "\n", + "#Result\n", + "print \"Frequency of k line is %.3e Hz\"%f" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of k line is 1.502e+19 Hz\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20.19, Page 20.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "Z = 27 # atomic no. of Co\n", + "R = 1.097e7 # Rydberg constant in m^-1\n", + "c = 3e8 # speed of light in m/sec\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "\n", + "#Calculations\n", + "f = 3./4 * (R * c) * (Z-1)**2\n", + "E = h * f\n", + "lamda = c / f\n", + "\n", + "#Results\n", + "print \"Energy is %.2f keV\\nWavelength of x-ray is %.2f A\"%(E / 1.6e-16,lamda*1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy is 6.90 keV\n", + "Wavelength of x-ray is 1.80 A\n" + ] + } + ], + "prompt_number": 24 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_22.ipynb b/Engineering_Physics/Chapter_22.ipynb new file mode 100755 index 00000000..a955c292 --- /dev/null +++ b/Engineering_Physics/Chapter_22.ipynb @@ -0,0 +1,62 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 22: Nanopyhsics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 22.1, Page 22.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given \n", + "d = 12e-6 # diameter in m\n", + "d_ = 90e-9 # diameter of nanoparticle in m\n", + "\n", + "#Calculations\n", + "r = d / 2\n", + "r_ = d_ / 2\n", + "k = r / 3\n", + "k_ = r_ / 3\n", + "R = k_ / k\n", + "\n", + "#Result\n", + "print \"The ratio of the value of Nb/Ns of spherical particle and nanoparticle = %.1e\"%R" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of the value of Nb/Ns of spherical particle and nanoparticle = 7.5e-03\n" + ] + } + ], + "prompt_number": 1 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_3.ipynb b/Engineering_Physics/Chapter_3.ipynb new file mode 100755 index 00000000..1e5fdb51 --- /dev/null +++ b/Engineering_Physics/Chapter_3.ipynb @@ -0,0 +1,996 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: Polarisation" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.1, Page 3.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, atan\n", + "\n", + "# Given \n", + "mu = 1.5 # refractive index of glass\n", + "\n", + "#Calculations\n", + "Ip = atan(mu) * (180 / pi) # by brewster's law\n", + "r = 90 - Ip # calculation for angle of refraction\n", + "\n", + "#Result\n", + "print \"Brewster angle = %.f degree\\nAngle of refraction = %.f degree\"%(Ip,r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Brewster angle = 56 degree\n", + "Angle of refraction = 34 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.2, Page 3.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, atan\n", + "\n", + "# Given \n", + "mu = 1.33 # refractive index of glass\n", + "\n", + "#Calculations\n", + "Ip = atan(mu) * (180 / pi) # by Brewster's law\n", + "\n", + "#Result\n", + "print \"Angle of brewster = %.2f degree\"%Ip" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of brewster = 53.06 degree\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.3, Page 3.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, atan\n", + "\n", + "# Given \n", + "mu_w = 1.33 # refractive index of water\n", + "mu_g = 1.54 # refractive index of glass\n", + "\n", + "#Calculations\n", + "Ip_1 = atan(mu_g / mu_w) * (180 / pi)#calculation for polarizing angle for water\n", + "Ip_2 = atan(mu_w / mu_g) * (180 / pi) # calculation for polarizing angle for glass\n", + "\n", + "#Result\n", + "print \"Polarizing angle for water to glass = %.2f degree,\\n Polarizing angle for glass to water = %.2f degree\"%(Ip_1,Ip_2)\n", + "print \"So polarizing angle is greater for a beam incident from water to glass\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Polarizing angle for water to glass = 49.18 degree,\n", + " Polarizing angle for glass to water = 40.82 degree\n", + "So polarizing angle is greater for a beam incident from water to glass\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.4, Page 24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, asin, tan, sin\n", + "\n", + "# Given \n", + "Ip = pi / 3 # polarizing angle of piece of glass for green light in radian\n", + "a = pi / 3 # angle of prism in radian \n", + "\n", + "#Calculations\n", + "mu = tan(Ip) # calculation for refractive index\n", + "delta_m = 2 * (asin(mu * sin(a / 2)) - (a / 2)) * (180 / pi) # calculation for angle of minimum deviation\n", + "\n", + "#Result\n", + "print \"Angle of minimum deviation = %.f degree\"%delta_m" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of minimum deviation = 60 degree\n" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.5, Page 3.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, atan\n", + "\n", + "# Given \n", + "mu_w = 1.33 # refractive index of water\n", + "mu_g = 1.5 # refractive index of glass\n", + "\n", + "#Calculations\n", + "Ip = atan(mu_g / mu_w) * (180 / pi) # calculation for Brewster angle\n", + "\n", + "#Result\n", + "print \"Brewster angle = %.1f degree\"%Ip\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Brewster angle = 48.4 degree\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.6, Page 3.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, atan\n", + "\n", + "# Given \n", + "mu = 1.732 # refractive index of glass\n", + "\n", + "#Calculations\n", + "Ip = atan(mu) * (180 / pi) # by Brewster's law\n", + "r = 90 - Ip# calculation for angle of refraction\n", + "\n", + "#Result\n", + "print \"Angle of incidence = %.f degree\\nAngle of refraction = %.f degree\"%(Ip,r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of incidence = 60 degree\n", + "Angle of refraction = 30 degree\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.7, Page 3.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, cos\n", + "\n", + "# Given \n", + "alpha = pi / 3 # angle between polarizer and analyzer\n", + "\n", + "#Calculation\n", + "r = (cos(alpha))**2 # where r = transmitted intensity / incident intensity\n", + "\n", + "#Result\n", + "print \"Ratio between transmitted intensity to incident intensity = %.2f \"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between transmitted intensity to incident intensity = 0.25 \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.8, Page 3.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt,acos,degrees\n", + "\n", + "#Given \n", + "r1 = 1./3 #ratio of intensity of transmitted light to the intensity of transmitted beam in first case\n", + "r2 = 1./3 #ratio of intensity of transmitted light to the intensity of incident beam in second case\n", + "p = 50 #percentage reduction in intensity of unpolarized light by the sheet \n", + "\n", + "#Calculations\n", + "theta1 = degrees(acos(sqrt(r1))) #calculation for the angle between characteristics directions of the sheet in first case\n", + "theta2 = degrees(acos(sqrt(2*r2))) #calculation for the angle between characteristics directions of the sheet in second case\n", + "\n", + "#Result\n", + "print \"The angle between characteristics directions of the sheet in 1st case = %.2f degrees.\"%(theta1)\n", + "print \"The angle between characteristics directions of the sheet in 2nd case = %.2f degrees.\"%(theta2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle between characteristics directions of the sheet in 1st case = 54.74 degrees.\n", + "The angle between characteristics directions of the sheet in 2nd case = 35.26 degrees.\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.9, Page 3.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import acos, sqrt, pi\n", + "\n", + "# Given \n", + "r = 3. / 4 # ratio of intensity of transmitted light to the intensity of incident light\n", + "\n", + "#Calculation\n", + "theta = acos(sqrt(r)) * (180 / pi) # calculation for angle between the nicol prisms\n", + "\n", + "#Result\n", + "print \"Angle between the nicol prisms = %.f degree\"%theta" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle between the nicol prisms = 30 degree\n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.10, Page 3.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, cos\n", + "\n", + "# Given \n", + "theta1 = pi / 6 # angle between Nicole prisms in first case in radian\n", + "theta2 = pi / 4 # angle between Nicole prisms in second case in radian\n", + "theta3 = pi / 3 # angle between Nicole prisms in third case in radian\n", + "theta4 = pi / 2 # angle between Nicole prisms in fourth case in radian\n", + "\n", + "#Calculations\n", + "I1 = (1 - (cos(theta1))**2) * 100\n", + "I2 = (1 - (cos(theta2))**2) * 100\n", + "I3 = (1 - (cos(theta3))**2) * 100\n", + "I4 = (1 - (cos(theta4))**2) * 100\n", + "\n", + "#Result\n", + "print \"Percentage reduction in intensity of light-\\n(i)%.f %%\\n(ii)%.f %%\\n(iii)%.f %%\\n(iv)%.f %%\"%(I1,I2,I3,I4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage reduction in intensity of light-\n", + "(i)25 %\n", + "(ii)50 %\n", + "(iii)75 %\n", + "(iv)100 %\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.11, Page 3.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, acos, sqrt \n", + "\n", + "# Given \n", + "i1 = 1. / 2 # reduced intensity ratio in first case\n", + "i2 = 1. / 4 # reduced intensity ratio in second case\n", + "\n", + "#Calculations\n", + "theta1 = acos(sqrt(i1)) * (180 / pi)# calculation for angle between nicols in first case \n", + "theta2 = acos(sqrt(i2)) * (180 / pi)# calculation for angle between nicols in second case\n", + "\n", + "#Result\n", + "print \"Angle between the Nicols in first case = %.f degree\\nAnd in second case = %.f degree\"%(theta1,theta2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle between the Nicols in first case = 45 degree\n", + "And in second case = 60 degree\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.12, Page 3.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "mu_e = 1.553 # refractive index for extraordinary light\n", + "mu_o = 1.544 # refractive index for ordinary light\n", + "\n", + "#Calculations\n", + "t = l / (2 * (mu_e - mu_o)) # calculation for thickness of half-wave plate of quartz\n", + "\n", + "#Result\n", + "print \"Thickness of half-wave plate of quartz = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of half-wave plate of quartz = 2.78e-05 meter\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.13, Page 3.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.893e-7 # wavelength of light in meter\n", + "mu_e = 1.533 # refractive index for extraordinary light\n", + "mu_o = 1.554 # refractive index for ordinary light\n", + "\n", + "#Calculation\n", + "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate\n", + "\n", + "#Result\n", + "print \"Thickness of quartz plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of quartz plate = 7.02e-06 meter\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.14, Page 3.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "mu_e1 = 1.5 # refractive index for extraordinary light in first case\n", + "mu_o1 = 1.55 # refractive index for ordinary light in first case\n", + "mu_e2 = 1.57 # refractive index for extraordinary light in second case\n", + "mu_o2 = 1.55 # refractive index for ordinary light in second case\n", + "\n", + "#Calculations\n", + "t1 = l / (4 * (mu_o1 - mu_e1))\n", + "t2 = l / (4 * (mu_e2 - mu_o2))\n", + " # calculation for thickness of plate of quartz\n", + "\n", + "#Result\n", + "print \"Thickness of plate of quartz in first case = %.3e meter,\\nAnd thickness of plate of quartz in second case = %.2e meter\"%(t1,t2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of plate of quartz in first case = 2.945e-06 meter,\n", + "And thickness of plate of quartz in second case = 7.36e-06 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.15, Page 3.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "mu_e = 1.486 # refractive index for extraordinary light\n", + "mu_o = 1.658 # refractive index for ordinary light\n", + "\n", + "#Calculation\n", + "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of calcite plate \n", + "\n", + "#Result\n", + "print \"Thickness of calcite plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of calcite plate = 8.56e-07 meter\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.16, Page 3.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5e-7 # wavelength of light in meter\n", + "mu_e = 1.5533 # refractive index for extraordinary light\n", + "mu_o = 1.5442 # refractive index for ordinary light\n", + "\n", + "#Calculation\n", + "t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate\n", + "\n", + "#Result\n", + "print \"Thickness of quartz plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of quartz plate = 1.37e-05 meter\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.17, Page 3.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "mu_e = 1.54 # refractive index for extraordinary light\n", + "mu_o = 1.55 # refractive index for ordinary light\n", + "\n", + "#Calculation\n", + "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate\n", + "\n", + "#Result\n", + "print \"Thickness of quartz plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of quartz plate = 1.47e-05 meter\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.18, Page 3.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "l = 5.89e-7 # wavelength of light in meter\n", + "mu_e = 1.553 # refractive index for extraordinary light\n", + "mu_o = 1.544 # refractive index for ordinary light\n", + "\n", + "#Calculation\n", + "t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate\n", + "\n", + "#Result\n", + "print \"Thickness of quartz plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of quartz plate = 1.64e-05 meter\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.19, Page 3.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "mu_e = 1.5442 # refractive index for extraordinary light\n", + "mu_o = 1.5533 # refractive index for ordinary light\n", + "l = 5e-7 # wavelength of plane polarized light in meter\n", + "\n", + "#Calculation\n", + "t = l / (2 * (mu_o - mu_e))# calculation for thickness of quartz plate\n", + "\n", + "#Result\n", + "print \"Thickness of quartz plate = %.2e meter\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of quartz plate = 2.75e-05 meter\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.20, Page 3.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 10 # rotation of plane of polarization in degree\n", + "s = 60 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", + "l = 2.5 # length of Polari meter in decimeter\n", + "\n", + "#Calculation\n", + "c = theta / (s * l) # calculation for concentration of sugar solution\n", + "\n", + "#Result\n", + "print \"Concentration of sugar solution = %.3f gm/cc\"%c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Concentration of sugar solution = 0.067 gm/cc\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.21, Page 3.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 26.4 # rotation of plane of polarization in degree\n", + "c = 0.2 # concentration of sugar solution in gm/cc\n", + "l = 2 # length of polarizing tube in decimeter\n", + "\n", + "#Calculation\n", + "s = theta / (l * c)# calculation for specific rotation of sugar solution\n", + "\n", + "#Result\n", + "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Specific rotation of sugar solution = 66 degree/(dm-cc)\n" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.22, Page 3.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 6.5 # rotation of plane of polarization in degree\n", + "c = 0.05 # concentration of sugar solution in gm/cc\n", + "l = 2 # length of polarizing tube in decimeter\n", + "\n", + "#Calculation\n", + "s = theta / (l * c) # calculation for specific rotation of sugar solution\n", + "\n", + "#Result\n", + "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Specific rotation of sugar solution = 65 degree/(dm-cc)\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.23, Page 3.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "w = 80 # weight of impure sugar in gm\n", + "theta = 9.9 # rotation of plane of polarization in degree\n", + "s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", + "l = 2 # length of Polari meter in decimeter\n", + "\n", + "#Calculations\n", + "c = theta / (s * l) * (1000) # in gm/l\n", + "per_c = (c * 100) / w # calculation for concentration of sugar solution\n", + "\n", + "#Result\n", + "print \"Concentration of sugar solution = %.2f percent\"%per_c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Concentration of sugar solution = 93.75 percent\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.24, Page 3.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 11. # rotation of plane of polarization in degree\n", + "s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", + "l = 2 # length of Polari meter in decimeter\n", + "\n", + "#Calculation\n", + "c = theta / (s * l) # calculation for concentration of sugar solution\n", + "\n", + "#Result\n", + "print \"Concentration of sugar solution = %.4f gm/cc\"%c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Concentration of sugar solution = 0.0833 gm/cc\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.25, Page 3.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 26.4 # rotation of plane of polarization in degree\n", + "c = 0.2 # concentration of sugar solution in gm/cc\n", + "l = 2 # length of polarizing tube in decimeter\n", + "\n", + "#calculation\n", + "s = theta / (l * c) # calculation for specific rotation of sugar solution\n", + "\n", + "#Result\n", + "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Specific rotation of sugar solution = 66 degree/(dm-cc)\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.26, Page 3.30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "theta = 13 # rotation of plane of polarization in degree\n", + "r = (1. / 3) # ratio of the final concentration to the initial solution\n", + "l = 2 # length of Polari meter in decimeter\n", + "l_ = 3 # length of second polarizing tube in decimeter \n", + "\n", + "#Calculation\n", + "theta_ = (l_ * r * theta) / l# calculation for optical rotation of diluted solution\n", + "\n", + "#Result\n", + "print \"Optical rotation of diluted solution = %.1f degree\"%theta_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Optical rotation of diluted solution = 6.5 degree\n" + ] + } + ], + "prompt_number": 39 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_4.ipynb b/Engineering_Physics/Chapter_4.ipynb new file mode 100755 index 00000000..981a3d82 --- /dev/null +++ b/Engineering_Physics/Chapter_4.ipynb @@ -0,0 +1,311 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Lasers and Holography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1, Page 4.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import exp\n", + "\n", + "# Given \n", + "l = 5.5e-7 # wavelength of light in meter\n", + "c = 3e+8 # speed of light in m/sec\n", + "h = 6.63e-34 # Planck constant in j/sec\n", + "e = 1.6e-19 # charge on electron in coulomb \n", + "k = 8.62e-5 # Boltzmann constant in eV/K\n", + "T = 300 # temperature in kelvin\n", + "\n", + "#Calculations\n", + "delta_E = (h * c) / (l * e) # calculation for energy difference \n", + "r = exp(-delta_E / (k * T)) # calculation for ratio of population of upper level to the lower energy level\n", + "T_ = (delta_E / (k * 0.693)) # calculation for temperature for the second condition\n", + "\n", + "#Result\n", + "print \"Ratio of population of upper level to the lower energy level = %.1e. \\nTemperature for the second condition = %.f K. \"%(r,T_)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of population of upper level to the lower energy level = 1.1e-38. \n", + "Temperature for the second condition = 37837 K. \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.2, Page 4.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "lambda1 = 6.328e-7 # wavelength of light in first case in meter\n", + "lambda2 =2e-7 # wavelength of light in second case in meter\n", + "r1 = 2.3e-4 # the radius of internal beam of laser in first case in meter\n", + "r2 = 2.4e-3 # the radius of internal beam of laser in second case in meter\n", + "\n", + "#Calculations\n", + "theta1 = lambda1 / (pi * r1) # calculation for beam divergence angle in first case\n", + "theta2 = lambda2 / (pi * r2) # calculation for beam divergence angle in second case\n", + "\n", + "#Result\n", + "print \"Beam divergence angle in first case = %.2e radian. \\nBeam divergence angle in second case = %.2e radian. \"%(theta1,theta2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Beam divergence angle in first case = 8.76e-04 radian. \n", + "Beam divergence angle in second case = 2.65e-05 radian. \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3, Page 4.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi,ceil\n", + "\n", + "# Given \n", + "l = 6.0*10**-2 # length of laser in meter\n", + "D = 1.0*10**-2 # diameter of laser in meter\n", + "L = 6.944e-7 # wavelength of light in meter\n", + "d = 3700 # density of aluminium oxide in kg/meter cube\n", + "Na = 6e+23 # Avogadro number\n", + "M = 0.102 # molar mass of aluminium oxide in kg/meter cube\n", + "h = 4.1e-15 # Planck constant in eV-sec\n", + "c = 3e+8 # speed of light in meter/sec\n", + "\n", + "#Calculations\n", + "v = (pi * (D**2) * l) / 4 # calculation for volume \n", + "N = (2 * Na * d * v) / M # calculation for no. of aluminium ions\n", + "N_ = N / 3500 # calculation for the no. of chromium ions\n", + "E = (h * c) / L # calculation for the energy of stimulated emission photon \n", + "Et = N_ * E * (1.6e-19) # calculation for total energy\n", + "\n", + "#Result\n", + "print \"Total energy = %.f J\"%(ceil(Et))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total energy = 17 J\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4, Page 4.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "p = 4e-3 # energy of laser pulse in meter\n", + "r = 1.5e-5 # radius of spot in meter\n", + "t = 1e-9 # pulse length in time in sec\n", + "\n", + "#Calculations\n", + "p_ = p / t# calculation for power in watt\n", + "I = p_ / (pi * r**2)# calculation for power per unit area delivered by the laser\n", + "\n", + "#Result\n", + "print \"Power per unit area delivered by the laser = %.1e watt/square meter\"%I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power per unit area delivered by the laser = 5.7e+15 watt/square meter\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.5, Page 4.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "D = 5e-3 # diameter of laser in meter\n", + "l = 7.2e-7 # wavelength of light in meter\n", + "d = 4e8 # distance at moon from earth in meter\n", + "\n", + "#Calculations\n", + "r = (D / 2) # calculation for radius\n", + "theta = (0.637 * l) / r # calculation for angular spread\n", + "areal_spread = (d * theta)**2 # calculation for areal spread\n", + "\n", + "#Result\n", + "print \"Angular spread = %.3e radian ,\\nAreal spread = %.2e square meter\"%(theta,areal_spread)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular spread = 1.835e-04 radian ,\n", + "Areal spread = 5.38e+09 square meter\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.6, Page 4.27\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "D = 5.0e-3 # diameter of laser in meter\n", + "l = 6.943e-7 # wavelength of light in meter\n", + "f =0.1 # focal length in meter\n", + "P = 0.1 # power of laser in watt\n", + "\n", + "#Calculations\n", + "r = (D / 2)# calculation for \n", + "theta = (0.637 * l) / r# calculation for angular spread\n", + "areal_spread = (f * theta)**2# calculation for areal spread\n", + "I = P / areal_spread# calculation for intensity\n", + "\n", + "#Result\n", + "print \"Areal spread = %.3e square meter,\\nIntensity = %.3e watt/square meter\"%(areal_spread,I)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Areal spread = 3.130e-10 square meter,\n", + "Intensity = 3.195e+08 watt/square meter\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.7, Page 4.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "tou = 1e-10 # coherence time in sec\n", + "l = 5.4e-7 # wavelength of light in meter\n", + "\n", + "#Calculations\n", + "delta_v = 1 / tou \n", + "v_ = (3e+8) / l # calculation for frequency\n", + "d = delta_v / v_ # calculation for degree of non-monochromaticity\n", + "\n", + "#Result\n", + "print \"Degree of non-monochromaticity = %f \"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Degree of non-monochromaticity = 0.000018 \n" + ] + } + ], + "prompt_number": 9 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_5.ipynb b/Engineering_Physics/Chapter_5.ipynb new file mode 100755 index 00000000..e9ebdd41 --- /dev/null +++ b/Engineering_Physics/Chapter_5.ipynb @@ -0,0 +1,549 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5: Fibre Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1, Page 5.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + "\n", + "# Given \n", + "mu1 = 1.52 # refractive index for core\n", + "mu2 = 1.41 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "theta_c = asin(mu2 / mu1) * (180 / pi)\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Result\n", + "print \"Critical angle = %.2f degree \\nNumerical aperture = %.3f\\nMaximum incidence angle = %.1f degree\"%(theta_c,NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical angle = 68.07 degree \n", + "Numerical aperture = 0.568\n", + "Maximum incidence angle = 34.6 degree\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2, Page 5.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + "\n", + "# Given \n", + "mu1 = 1.6 # refractive index for core\n", + "mu2 = 1.5 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "theta_0 = asin(NA) * (180 / pi)#calculation for maximum incidence angle\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.3f\\nMaximum incidence angle = %.2f degree\"%(NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.557\n", + "Maximum incidence angle = 33.83 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3, Page 5.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + " \n", + "# Given \n", + "mu_0 = 1 # refractive index of air\n", + "mu1 = 1.5 # refractive index for core\n", + "mu2 = 1.48 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "theta_c = asin(mu2 / mu1) * (180 / pi)\n", + "delta_mu = (mu1 - mu2) / mu1\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Result\n", + "print \"Critical angle = %.2f degrees \\nNumerical aperture = %.3f \\nAcceptance angle = %.2f degrees\\nFractional refractive index = %.2f %%\"%(theta_c,NA,theta_0,delta_mu*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical angle = 80.63 degrees \n", + "Numerical aperture = 0.244 \n", + "Acceptance angle = 14.13 degrees\n", + "Fractional refractive index = 1.33 %\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import * \n", + "# Given \n", + "mu1 = 1.62 # refractive index for core\n", + "mu2 = 1.52 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Results\n", + "print \"Numerical aperture = %.2f \\nMaximum incidence angle = %.1f degrees\"%(NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.56 \n", + "Maximum incidence angle = 34.1 degrees\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "NA = 0.22 # numerical aperture\n", + "delta_mu = 0.012 # fractional refractive index\n", + "\n", + "#Calculations\n", + "mu1 = sqrt(NA**2 / (1 - (1 - delta_mu)**2))\n", + "mu2 = (1 - delta_mu) * mu1\n", + "\n", + "#Result\n", + "print \"Refractive index for core = %.3f\\nRefractive index for cladding = %.2f\"%(mu1,mu2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index for core = 1.424\n", + "Refractive index for cladding = 1.41\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin, sin\n", + "\n", + "# Given \n", + "d = 0.0064 # diameter of fiber in cm\n", + "mu1 = 1.53 # refractive index for core\n", + "mu2 = 1.39 # refractive index for clad\n", + "L = 90 # length of fiber in cm\n", + "mu_0 = 1 # refractive index of air\n", + "\n", + "#calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "N1 = L / (d * sqrt((mu1 / (mu_0 * sin(theta_0 * (pi / 180))))**2 - 1))\n", + "N2 = L / (d * sqrt((mu1 / (mu_0 * sin(theta_0 * (pi / 360))))**2 - 1))\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.2f\\nAcceptance angle = %.1f degrees \\nNumber of reflections at maximum incidence = %.f \\nNumber of reflections in second case = %.f \"%(NA,theta_0,N1,N2)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.64\n", + "Acceptance angle = 39.7 degrees \n", + "Number of reflections at maximum incidence = 6468 \n", + "Number of reflections in second case = 3204 \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7, Page 5.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "d = 0.05 # diameter of fiber in mm\n", + "NA = 0.22 # numerical aperture\n", + "l = 8.5e-4 # wavelength of light in mm\n", + "\n", + "#calculations\n", + "Vn = (pi * d * NA) / l\n", + "Mm = 0.5 * (Vn)**2\n", + "\n", + "#Result\n", + "print \"The normalized frequency = %.2f\\nNumber of guided in the core = %d\"%(Vn,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The normalized frequency = 40.66\n", + "Number of guided in the core = 826\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.8, Page 5.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 1.25e-6 #wavelength of light in meter\n", + "mu1 = 1.465 # refractive index for core\n", + "mu2 = 1.460 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "k = (2.4 * l) / ( pi * NA)\n", + "Mm = 0.5 * ((pi * 50e-6 * NA) / l)**2\n", + "\n", + "#Result\n", + "print \"Diameter of core < %.1e meter,\\n number of modes = %d\"%(k,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of core < 7.9e-06 meter,\n", + " number of modes = 115\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9, Page 5.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 0.85e-6 #wavelength of light in meter\n", + "mu1 = 1.461 # refractive index for core\n", + "mu2 = 1.456 # refractive index for clad\n", + "d = 4e-5 # diameter of core in meter\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "Mm = 0.5 * ((pi * d * NA) / l)**2\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.3f\\n Number of modes = %d \"%(NA,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.121\n", + " Number of modes = 159 \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10, Page 5.19\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given\n", + "mu1 = 3.6 # refractive index for core\n", + "mu2 = 3.55 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "Mm1 = 0.5 * (pi * 5 * NA)**2#calculation for no. of modes in first case\n", + "Mm2 = 0.5 * (pi * 50 * NA)**2#calculation for no. of modes in second case\n", + "\n", + "#Result\n", + "print \"Number of modes in first case = %d \\nNumber of modes in second case = %d\"%(Mm1,Mm2)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of modes in first case = 44 \n", + "Number of modes in second case = 4410\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.11, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 1.25e-6 #wavelength of light in meter\n", + "mu1 = 1.46 # refractive index for core\n", + "mu2 = 1.457 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "k = (2.4 * l) / ( pi * NA)\n", + "\n", + "#Result\n", + "print \"Maximum diameter of core = %.2f micro meter\"%(k*1e6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum diameter of core = 10.21 micro meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.12, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log10\n", + "\n", + "# Given \n", + "L = 0.1 # length of fiber in km\n", + "p = 5e-6 # power of signal in watt\n", + "p_ = 1e-6 # power of signal inside the fiber in watt\n", + "\n", + "#Calculation\n", + "alpha = (10 * log10(p / p_)) / L#calculation for absorption coefficient\n", + "\n", + "#Result\n", + "print \"Absorption coefficient = %d dB/km \"%alpha" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Absorption coefficient = 69 dB/km \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.13, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import exp\n", + "\n", + "# Given \n", + "L = 3 # length of optical fiber in km\n", + "l = 6 # losses in dB\n", + "p = 5e-3 # input power in watt \n", + "\n", + "#calculations\n", + "alpha = (l * 3) / L\n", + "p_ = p / (exp((2.303 * alpha * L) / 10))\n", + "\n", + "#Result\n", + "print \"Output power = %.3f mW \"%(p_*1e3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Output power = 0.079 mW \n" + ] + } + ], + "prompt_number": 19 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_6.ipynb b/Engineering_Physics/Chapter_6.ipynb new file mode 100755 index 00000000..76ec5aef --- /dev/null +++ b/Engineering_Physics/Chapter_6.ipynb @@ -0,0 +1,399 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6: Electron Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.1, Page 6.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "V = 500 # voltage across the electrode in eV\n", + "m = 9e-31 # mass of electron in kg\n", + "e = 1.6e-19 # charge on an electron in coulomb\n", + "\n", + "#Calculations\n", + "E = e * V\n", + "v = sqrt((2 * e * V) / m)\n", + "p = m * v\n", + "\n", + "#Result\n", + "print \"Energy gained by electron = %.e J\\nSpeed of electron = %.2e meter/sec\\nMomentum of electron = %.2e kg-meter/sec\"%(E,v,p)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy gained by electron = 8e-17 J\n", + "Speed of electron = 1.33e+07 meter/sec\n", + "Momentum of electron = 1.20e-23 kg-meter/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.2, Page 6.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "v = 2.5e6 # speed of electron in meter/sec\n", + "B = 2e-4 # magnetic field in tesla\n", + "r = 1.76e11 # ratio of charge on electron to the mass of electron in C/kg\n", + "\n", + "#Calculations\n", + "a = (B * r * v)\n", + "\n", + "#Result\n", + "print \"Momentum of acceleration = %.2e meter/square sec.\"%a" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Momentum of acceleration = 8.80e+13 meter/square sec.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4, Page 6.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given that\n", + "v = 5.2e6 # speed of electron in meter/sec\n", + "B = 1.3e-4 # magnetic field in tesla\n", + "r = 1.76e11 # ratio of charge on electron to the mass of electron in C/kg\n", + "E = 3.2e-12 # energy of the electron beam in J\n", + "M = 9e-31 # mass of an electron in kg\n", + "\n", + "R = v / (r * B)\n", + "v_ = sqrt((2 * E) / M )\n", + "\n", + "print \"Radius of circle traced by the beam = %.1f cm. \\nSpeed of beam in second case = %.2e meter/sec\"%(R*100,v_)\n", + "print \"Speed of beam in second case is greater than speed of light so we cannot use above formula.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of circle traced by the beam = 22.7 cm. \n", + "Speed of beam in second case = 2.67e+09 meter/sec\n", + "Speed of beam in second case is greater than speed of light so we cannot use above formula.\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5, Page 6.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "V = 2.500e3 # voltage across the electrode in V\n", + "E = 3.6e4 # strength of electric field in V/m\n", + "B = 1.2e-3 # magnetic field in tesla\n", + "\n", + "#Calculation\n", + "r = (E / B)**2 / (2 * V)#calculation for ratio of the charge on an electron to the mass of an electron\n", + "\n", + "#Result\n", + "print \"Ratio of the charge on an electron to the mass of an electron = %.1e C/kg.\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of the charge on an electron to the mass of an electron = 1.8e+11 C/kg.\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.6, Page 6.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "M = 9.1e-31 # mass of electron in kg\n", + "E = 1.6e-15 # energy of electron in J\n", + "B = 5e-5 # magnetic field in tesla\n", + "e = 1.6e-19 # charge on an electron in coulomb\n", + "\n", + "#Calculations\n", + "v = sqrt((2 * E) / M)\n", + "r = (M * v) / (e * B)\n", + "\n", + "#Result\n", + "print \"Larmoure radius = %.2f meter\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Larmoure radius = 6.75 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.7, Page 6.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "Mp = 1.67e-27 # mass of proton in kg\n", + "v = 3e5 # speed of proton in meter/sec\n", + "B = 5e-9 # magnetic field in tesla\n", + "e = 1.6e-19 # charge on a proton in coulomb\n", + "\n", + "#Calculation\n", + "r = (Mp * v) / (e * B)#calculation for Larmour radius\n", + "\n", + "#Result\n", + "print \"Larmour radius = %.2e meter\"%r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Larmour radius = 6.26e+05 meter\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8, Page 6.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "M = 6.68e-27 # mass of helium ion in kg\n", + "E = 1.6e-16 # energy of helium ion in J\n", + "B = 5e-2 # magnetic field in tesla\n", + "e = 1.6e-19 # charge on helium ion in coulomb\n", + "\n", + "#calculations\n", + "v = sqrt((2 * E) / M)#calculation for velocity\n", + "r = (M * v) / (e * B)#calculation for Larmour radius\n", + "A = pi * r**2#calculation for area traced by the trajectory of helium ion\n", + "\n", + "#Result\n", + "print \"Area traced by the trajectory of helium ion = %.3f square meter\"%A" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Area traced by the trajectory of helium ion = 0.105 square meter\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.9, Page 6.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 100 # strength of electric field in V/m\n", + "B = 1e-3 # magnetic field in tesla\n", + "\n", + "#Calculation\n", + "v = E / B\n", + "\n", + "#Result\n", + "print \"The drift of the guiding center = %.e m/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The drift of the guiding center = 1e+05 m/sec\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.10, Page 6.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "v = 1e6 # velocity of ion beam in m/sec\n", + "B = 1 # magnetic field in tesla\n", + "\n", + "#Calculation\n", + "E = B * v\n", + "\n", + "#Result\n", + "print \"Internal electric field = %.e V/m\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Internal electric field = 1e+06 V/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.12, Page 6.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "r = 1.1 # ratio of new number of turns to the initial number of turns\n", + "\n", + "#Calculation\n", + "r_ = (1 / r)**2\n", + "\n", + "#Result\n", + "print \"Ratio of the new focus length to the initial focus length = %.3f \"%r_" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of the new focus length to the initial focus length = 0.826 \n" + ] + } + ], + "prompt_number": 11 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_7.ipynb b/Engineering_Physics/Chapter_7.ipynb new file mode 100755 index 00000000..6762cbc5 --- /dev/null +++ b/Engineering_Physics/Chapter_7.ipynb @@ -0,0 +1,569 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7: Waves and Oscillations" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1, Page 7.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sin, sqrt\n", + "\n", + "# Given \n", + "E = 1.024e-3 # total energy of particle in J\n", + "T = 2 * pi # time period of S.H.M. in sec\n", + "x = 0.08 * sqrt(2) # distance of partile in meter\n", + "t = pi / 4 # time in second\n", + "\n", + "#Calculations\n", + "A = x / sin((2 * pi * t) / T)\n", + "M = (E * T**2) / (2 * pi**2 * A**2)\n", + "\n", + "#Result\n", + "print \"Amplitude = %.2f meter\\nMass of particle = %.f g\"%(A,M/1e-3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Amplitude = 0.16 meter\n", + "Mass of particle = 80 g\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2, Page 7.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "A = 0.05 # amplitude in meter\n", + "T = 10 # time period of S.H.M. in sec\n", + "\n", + "#Calculations\n", + "v = (A * 2 * pi) / T\n", + "\n", + "#Result\n", + "print \"Maximum amplitude of velocity = %.4f meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum amplitude of velocity = 0.0314 meter/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3, Page 7.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt\n", + "\n", + "# Given \n", + "E = 9 # total energy of particle in J\n", + "U = 5 # potential energy in J\n", + "A = 1 # amplitude in meter\n", + "m = 2. # mass of harmonic oscillator in kg\n", + "\n", + "#Calculations\n", + "kE = E - U# calculation for kinetic energy\n", + "k = (2 * kE) / A**2# calculation for force constant\n", + "T = (2 * pi) * sqrt(m / k)# calculation for time period\n", + "\n", + "#Result\n", + "print \"Force constant = %.f J/m\\nTime period = %.2f sec\"%(k,T)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force constant = 8 J/m\n", + "Time period = 3.14 sec\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4, Page 7.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import asin, sin, pi\n", + "\n", + "# Given \n", + "A = 0.06 # amplitude in meter\n", + "T = 6 # time period of S.H.M. in sec\n", + "x = 0.03 # position of particle in meter\n", + "\n", + "#Calculations\n", + "delta = asin(1) # by the formula x=Asin(wt+delta) and (at t = 0,x=A) \n", + "t = x / (A * sin(((2 * pi) / T) + delta))\n", + "\n", + "#Result\n", + "print \"Time taken by the particle = %.f sec\"%t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time taken by the particle = 1 sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5, Page 7.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "A = 0.05# amplitude in meter\n", + "T = 10 * pi # time period of s.h.m. in sec\n", + "\n", + "#Calculations\n", + "v = A * (2 * pi / T)\n", + "a = A * (2 * pi / T)**2\n", + "\n", + "#Result\n", + "print \"Maximum velocity = %.e meter/sec\\nacceleration = %.e m/sec^2\"%(v,a)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum velocity = 1e-02 meter/sec\n", + "acceleration = 2e-03 m/sec^2\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6, Page 7.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "A = 0.06# amplitude in meter\n", + "T = 10 * pi # time period of s.h.m. in sec\n", + "\n", + "#Calculation\n", + "v = A * (2 * pi / T)\n", + "\n", + "#Result\n", + "print \"Maximum velocity = %.1e meter/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum velocity = 1.2e-02 meter/sec\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7, Page 7.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "k = 16 # stiffness constant of spring n/m\n", + "m = 1 # mass of particle in kg\n", + "\n", + "#Calculations\n", + "n = sqrt(k / m) / (2 * pi)\n", + "\n", + "#Result\n", + "print \"natural frequency = %.2f Hz\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "natural frequency = 0.64 Hz\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.8, Page 7.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 1 # length of pendulum in meter\n", + "m = 2 # mass of particle in kg\n", + "g = 9.8 # acceleration due to gravity in m/sec^2\n", + "\n", + "#Calculation\n", + "T = 2 * pi * sqrt(l / g)\n", + "\n", + "#Result\n", + "print \"The time period of pendulum = %.f sec\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The time period of pendulum = 2 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.9, Page 7.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "m = 100. # mass of particle in gm\n", + "\n", + "#Calculation\n", + "n = (1 / (2 * pi)) * sqrt(10 / m) # by using given formula \n", + "\n", + "#Result\n", + "print \"Frequency = %.2f Hz\"%n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 0.05 Hz\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.10, Page 7.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "f = 3 # acceleration of pendulum in m/sec^2\n", + "l = 1 # length of pendulum in meter\n", + "g = 9.8 # acceleration due to gravity in m/sec^2\n", + "\n", + "#calculatiom\n", + "T = 2 * pi * sqrt(l / (g + f))\n", + "\n", + "#Result\n", + "print \"Time period of pendulum = %.2f sec\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time period of pendulum = 1.76 sec\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.11, Page 7.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "x = 0.3 # stretch in spring in meter\n", + "m1 = 6 # mass of first body in kg\n", + "m2 = 1 # mass of second body in kg\n", + "g = 9.8 # gravitational acceleration of earth in m/sec^2\n", + "\n", + "#Calculations\n", + "k = (m1 * g) / x\n", + "T = (2 * pi) * sqrt(m2 / k)\n", + "\n", + "#Result\n", + "print \"Time period of motion = %.2f sec \"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time period of motion = 0.45 sec \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.12, Page 7.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "x = 0.1 # compression in spring in m\n", + "F = 10 # restoring force in N\n", + "m = 4 # mass of body in kg\n", + "g = 9.8 # acceleration due to gravity in m/sec^2\n", + "\n", + "#Calculations\n", + "k = F / x\n", + "F_ = m * g\n", + "x_ = F_ / k\n", + "T = (2 * pi) * sqrt(m / k)\n", + "\n", + "#Result\n", + "print \"Time period of motion = %.2f sec \\nCompression of the spring due to the weight of the body = %.3f m \"%(T,x_)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time period of motion = 1.26 sec \n", + "Compression of the spring due to the weight of the body = 0.392 m \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.13, Page 7.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import exp\n", + "\n", + "# Given \n", + "t = 50. # relaxation time in sec\n", + "r = 1 / exp(1) # falls in amplitude and energy\n", + "\n", + "#Calculations\n", + "s = 1 / (2 * t)\n", + "T = 1 / s # by using formula A=A_exp(-st) and using r=A/A_\n", + "\n", + "#Result\n", + "print \"Time = %.f sec\"%T\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time = 100 sec\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.14, Page 7.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, exp\n", + "\n", + "# Given \n", + "n = 260 # frequency in Hz\n", + "Q = 2000 # quality factor\n", + "r = 1 / (exp(1)**2) # decrease in amplitude \n", + "\n", + "#Calculations\n", + "tou = Q / (2 * pi * n)\n", + "t = 2 * tou # by using formula A=A_exp(-st) and using r=A/A_\n", + "\n", + "#Result\n", + "print \"Time = %.3f sec\"%t\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time = 2.449 sec\n" + ] + } + ], + "prompt_number": 17 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_8.ipynb b/Engineering_Physics/Chapter_8.ipynb new file mode 100755 index 00000000..60f3ed3a --- /dev/null +++ b/Engineering_Physics/Chapter_8.ipynb @@ -0,0 +1,413 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 8: Sound Waves and Acoustics of Buildings \n" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.1, Page 8.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "v = 34500 # speed of sound in cm/sec\n", + "f = 20 # lower limit of frequency for human hearing ear in Hz\n", + "f_ = 20000 # upper limit of frequency for human hearing ear in Hz\n", + "\n", + "#Clculations\n", + "l1 = v / f\n", + "l2 = v / f_\n", + "\n", + "#Results\n", + "print \"Wavelength range of the sound wave is %.f cm to %.f cm.\"%(l1,l2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength range of the sound wave is 1725 cm to 1 cm.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.2, Page 8.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "T = 373. # temperature in kelvin\n", + "d = 1.293e-3 # density of air at S.T.P. in gm/cm^3\n", + "d_ = 13.6 # density of mercury in gm/cm^3\n", + "Cp = 0.2417 # specific heat of air at constant pressure \n", + "Cv = 0.1715 # specific heat of air at constant volume\n", + "g = 980 # gravitational constant i dynes/cm^3\n", + "\n", + "#calculations\n", + "p = 76 * d_ * g\n", + "gama = Cp / Cv\n", + "v = sqrt(gama * (p / d))\n", + "v_ = v * sqrt(T / 273)\n", + "\n", + "#Result\n", + "print \"Velocity of sound in the air in %.f cm/sec.\"%v_\n", + "#Incorrect answer in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of sound in the air in 38839 cm/sec.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.3, Page 8.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + " \n", + "# Given that\n", + "n = 512. # frequency of tuning fork in Hz \n", + "T = 290. # temperature in kelvin\n", + "l = 66.5 # wavelength of the gas emitted by tuning fork in cm\n", + "d = 1.293e-3 # density of air at S.T.P. in gm/cm^3\n", + "d_ = 13.6 # density of mercury in gm/cm^3\n", + "g = 980 # gravitational constant i dynes/cm^3\n", + "\n", + "#Calculations\n", + "p = 76 * d_ * g# calculation for pressure\n", + "v_ = n * l# calculation for velocity of sound in air at temperature 17 c \n", + "v = v_ * sqrt(273 / T)# calculation for velocity of sound in air at temp 0 c\n", + "gama = v**2 * (d / p)# calculation for ratio of two specific heat\n", + "\n", + "#Result\n", + "print \"Ratio of two principal specific heats of air is %.2f\"%gama" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of two principal specific heats of air is 1.39\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.4, Page 8.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "A = 15 * 30 # area of the floor in square meter\n", + "h = 6 # height of hall in meter\n", + "N = 500 # no. of people\n", + "t = 1.36 # optimum time for orchestral music in sec\n", + "k = 0.44 # absorption coefficient per person\n", + "\n", + "#Calculations\n", + "aS = 0.161 * ((A * h) / t)\n", + "a = N * k\n", + "a_ = aS - a\n", + "w = a_ + (N / 2) * k + (N / 2) * 0.02\n", + "t = (0.161 * (A * h)) / w\n", + "\n", + "#Results\n", + "print \"Coefficient of absorption to be provided by the walls, floor and ceiling when the hall is fully occupied is %.f SI unit.\"%a_\n", + "print \"Reverberation time if only half upholstered seats are occupied is %.2f sec.\"%t\n", + "#Answer varies due to rounding-off " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "319.632352941\n", + "Coefficient of absorption to be provided by the walls, floor and ceiling when the hall is fully occupied is 100 SI unit.\n", + "Reverberation time if only half upholstered seats are occupied is 2.03 sec.\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.5, Page 8.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given\n", + "V = 8000 # volume of hall in meter^3\n", + "t = 1.8 # reverberation time in sec\n", + "\n", + "#Calculation\n", + "aS = (0.161 * V) / t# calculation for the total absorption constant\n", + "\n", + "#Result\n", + "print \"The total absorption constant = %.3f O.W.U.\"%aS\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total absorption constant = 715.556 O.W.U.\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.6, Page 8.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "V = 1700 # volume in meter^3\n", + "a1 = 98 # area of plastered wall in m^2\n", + "a2 = 144 # area of plastered ceiling in m^2\n", + "a3 = 15 # area of wooden door in m^2\n", + "a4 = 88 # area of cushioned chairs in m^2\n", + "a5 = 150 # area of audience (each person) in m^2\n", + "k1 = 0.03 # coefficient of absorption for plastered wall in O.W.U.\n", + "k2 = 0.04 # coefficient of absorption for plastered ceiling in O.W.U.\n", + "k3 = 0.06 # coefficient of absorption for wooden door in O.W.U.\n", + "k4 = 1 # coefficient of absorption for cushioned chair in O.W.U.\n", + "k5 = 4.7 # coefficient of absorption for audience (each person) in O.W.U.\n", + "\n", + "#Calculations\n", + "A1 = a1 * k1# calculation for the absorption by the plaster wall\n", + "A2 = a2 * k2# calculation for the absorption by the plastered ceiling\n", + "A3 = a3 * k3# calculation for wooden door\n", + "A4 = a4 * k4# calculation for cushioned chairs \n", + "A = A1 + A2 + A3 + A4# calculation for total absorption\n", + "T = 0.161 * (V / A)# calculation for reverberation time\n", + "\n", + "#Result\n", + "print \"Reverberation time is %.2f sec\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time is 2.80 sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.7, Page 8.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "V = 1400 # volume of hall in meter^3\n", + "C = 110 # seating capacity of hall \n", + "a1 = 98 # area of plastered wall in m^2\n", + "a2 = 144 # area of plastered ceiling in m^2\n", + "a3 = 15 # area of wooden door in m^2\n", + "a4 = 88 # area of cushioned chairs in m^2\n", + "a5 = 150 # area of audience (each person) in m^2\n", + "k1 = 0.03 # coefficient of absorption for plastered wall in O.W.U.\n", + "k2 = 0.04 # coefficient of absorption for plastered ceiling in O.W.U.\n", + "k3 = 0.06 # coefficient of absorption for wooden door in O.W.U.\n", + "k4 = 1 # coefficient of absorption for cushioned chair in O.W.U.\n", + "k5 = 4.7 # coefficient of absorption for audience (each person) in O.W.U.\n", + "\n", + "#Calculations\n", + "A1 = a1 * k1# calculation for the absorption by the plaster wall\n", + "A2 = a2 * k2# calculation for the absorption by the plastered ceiling\n", + "A3 = a3 * k3# calculation for wooden door\n", + "A4 = a4 * k4# calculation for cushioned chairs \n", + "A5 = C*k5 # the absorption due to persons\n", + "A = A1 + A2 + A3 + A4 + A5 # calculation for total absorption\n", + "T = (0.161 * V) / A# calculation for the reverberation time\n", + "\n", + "#Result\n", + "print \"Reverberation time is %.3f sec\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time is 0.367 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8, Page 8.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "V = 980 # volume in meter^3\n", + "a1 = 150 # area of wall in m^2\n", + "a2 = 95 # area of ceiling in m^2\n", + "a3 = 90 # area of floor in m^2\n", + "k1 = 0.03 # coefficient of absorption for wall in O.W.U.\n", + "k2 = 0.80 # coefficient of absorption for ceiling in O.W.U.\n", + "k3 = 0.06 # coefficient of absorption for floor in O.W.U.\n", + "\n", + "#calculations\n", + "A1 = a1 * k1\n", + "A2 = a2 * k2\n", + "A3 = a3 * k3\n", + "A = A1 + A2 + A3\n", + "T = 0.161 * (V / A)\n", + "\n", + "#Result\n", + "print \"Reverberation time = %.2f sec\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time = 1.84 sec\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.9, Page 8.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "V = 980 # volume in meter^3\n", + "a = 1.58 # area of window in m^2\n", + "I_ = 1e-12 # standard intensity level of sound wave in W/m^2\n", + "l = 60 # intensity level in dB\n", + "\n", + "#calculations\n", + "I = I_ * 10**(l / 10)# calculation for intensity\n", + "AP = I * a# calculation for acoustic power\n", + "\n", + "#Result\n", + "print \"Acoustic power = %.2e watt\"%AP" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Acoustic power = 1.58e-06 watt\n" + ] + } + ], + "prompt_number": 14 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter_9.ipynb b/Engineering_Physics/Chapter_9.ipynb new file mode 100755 index 00000000..a43c0fed --- /dev/null +++ b/Engineering_Physics/Chapter_9.ipynb @@ -0,0 +1,254 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9: Dielectrics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1, Page 9.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 10**6 # electric field inside the plates in V/m\n", + "d = 0.02 # distance between the plates in meter\n", + "k = 3 # dielectric constant of slab\n", + "e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2\n", + "\n", + "#Calculations\n", + "D = e_*k*E\n", + "P = D-e_*E\n", + "\n", + "#Result\n", + "print \"Polarization vector is %.2e C/m^2 \\nDisplacement vector is %.3e C/m^2\"%(P,D)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Polarization vector is 1.77e-05 C/m^2 \n", + "Displacement vector is 2.655e-05 C/m^2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2, Page 9.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "E1 = 3*10**5 # electric intensity when space between plates evacuated in V/m\n", + "E2 = 1*10**5 # electric intensity when space between plates is filled with dielectric in V/m\n", + "e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2\n", + "\n", + "#calculation\n", + "sigma = e_*(E1 - E2)\n", + "\n", + "#result\n", + "print \"The included charge density on the surface of the dielectric is %.2e C/m^2\"%sigma" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The included charge density on the surface of the dielectric is 1.77e-06 C/m^2\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3, Page 9.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 1*10**5 # electric field strength inside the plates in V/m\n", + "d = 6. # distance between the plates in mm\n", + "k = 2.8 # dielectric constant of slab\n", + "e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2\n", + "\n", + "#Calculations\n", + "P = e_*(k-1)*E\n", + "D = e_*k*E\n", + "energy_density = 1./2 * k*e_*E**2\n", + "\n", + "#Result\n", + "print \"Polarization vector is %.1e C/m^2 \\nDisplacement vector is %.1eC/m^2 \\nEnergy density is %.3f J/m^3\"%(P,D,energy_density )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Polarization vector is 1.6e-06 C/m^2 \n", + "Displacement vector is 2.5e-06C/m^2 \n", + "Energy density is 0.124 J/m^3\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4, Page 9.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "D = 5e-4 # electric displacement vector in C/m^2\n", + "P = 4e-4 # electric polarization vector in C/m^2\n", + "v = 0.5 # volume of the slab in m^3\n", + "e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2\n", + "\n", + "#Calculations\n", + "E= (D-P)/ e_\n", + "k = D/(e_*E)\n", + "p = P*v\n", + "energy_density = 1./2 * k*e_*E**2\n", + "\n", + "#Result\n", + "print \"Value of relative permittivity is %d \\nTotal dipole moment of the slab is %.e C-m\"%(k,p) " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Value of relative permittivity is 5 \n", + "Total dipole moment of the slab is 2e-04 C-m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5, Page .12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given that\n", + "E = 3e4 # external field in V/m\n", + "k = 1.00074 # dielectric constant of gas at N.T.P.\n", + "e_ = 8.85e-12 # electric permittivity of air in C^2/Nm^2\n", + "\n", + "#Calculations\n", + "x = k-1\n", + "P = x*e_*E\n", + "N = 6.023e23/22.4e-3\n", + "p = P/N\n", + "\n", + "#Result\n", + "print \"Induce dipole moment of each is %.2e C-m\"%p" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induce dipole moment of each is 7.31e-36 C-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6, Page .13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given \n", + "E = 3e4 # external field in V/m\n", + "k = 1.000041 # dielectric constant of gas at 0 degree centigrate\n", + "\n", + "#calculation\n", + "x = k-1\n", + "\n", + "#Result\n", + "print \"Electric susceptibility at 0 degree centigrate is %.1e\"%x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electric susceptibility at 0 degree centigrate is 4.1e-05\n" + ] + } + ], + "prompt_number": 8 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/README.txt b/Engineering_Physics/README.txt index bd7c4bfa..85c741ca 100755 --- a/Engineering_Physics/README.txt +++ b/Engineering_Physics/README.txt @@ -1,10 +1,10 @@ -Contributed By: KRISHNA CHAITANYA -Course: btech -College/Institute/Organization: JNTUH -Department/Designation: Computer Science +Contributed By: Muktesh Chaudhary +Course: be +College/Institute/Organization: Anglo Eastern ship management india Pvt. Ltd +Department/Designation: Electrical & Electronics Officer Book Title: Engineering Physics -Author: D. K. Bhattacharya & A. Bhaskaran -Publisher: Oxford University Press, New Delhi -Year of publication: 2013 -Isbn: 9780198065425 -Edition: 1
\ No newline at end of file +Author: H. K. Malik & A. Singh +Publisher: Tata McGraw Hill, New Delhi +Year of publication: 2010 +Isbn: 9780070671539 +Edition: 1st
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