diff options
Diffstat (limited to 'Engineering_Physics')
27 files changed, 2698 insertions, 2994 deletions
diff --git a/Engineering_Physics/Chapter1.ipynb b/Engineering_Physics/Chapter1.ipynb new file mode 100755 index 00000000..a3614569 --- /dev/null +++ b/Engineering_Physics/Chapter1.ipynb @@ -0,0 +1,357 @@ +{ + "metadata": { + "name": "Chapter1", + "signature": "sha256:e55f587b2da98ead68f73bb2b4d29bef91aa67eb577c460fb9dcaab92acc4339" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "1: Ultrasonics" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.1, Page number 20" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.33; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",d1, \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 237.6 m\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.2, Page number 21" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 40; #length of iron rod(mm)\nE = 115*10**9; #Young's modulus(N/m**2)\nrho = 7.25*10**3; #density of pure iron(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"depth of the submerged submarine is\",new, \"kHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 49.785 kHz\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.3, Page number 21" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 1; #length of quartz crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"fundamental frequency of crystal is\",new, \"*10**6 Hz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "fundamental frequency of crystal is 2.73 *10**6 Hz\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.4, Page number 22" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 0.55; #distance between 2 constructive antinodes(mm)\nnew = 1.5; #frequency of crystal(MHz)\n \n#Calculation\nnew = new*10**6; #frequency of crystal(Hz)\nd = d*10**-3; #distance between 2 constructive antinodes(m)\n#distance between 2 antinodes is given by lamda/2\nlamda = 2*d; #wavelength of ultrasonic waves(m)\nv = new*lamda; #velocity of waves(m/s)\n\n#Result\nprint \"velocity of waves is\",int(v), \"m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "velocity of waves is 1650 m/s\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.5, Page number 22" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 50; #length of rod(mm)\nE = 11.5*10**10; #Young's modulus(N/m**2)\nrho = 7250; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew = math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"natural frequency of rod is\",new, \"kHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "natural frequency of rod is 39.83 kHz\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.6, Page number 22" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 2; #length of crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; #natural frequency of the rod(MHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"MHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "frequency of crystal is 1.365 MHz\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.7, Page number 23" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 3; #length of crystal(mm)\nE = 8*10**10; #Young's modulus(N/m**2)\nrho = 2500; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz) \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"kHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "frequency of crystal is 942.81 kHz\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.8, Page number 23" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 1.5; #length of crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; #natural frequency of the rod(MHz) \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"MHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "frequency of crystal is 1.82 MHz\n" + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.9, Page number 24" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.95; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of sea(m)\n\n#Result\nprint \"depth of the submerged submarine is\",int(d1), \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 684 m\n" + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.10, Page number 24" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.83; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",d1, \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 597.6 m\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.11, Page number 24" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\naS = 1050; #total absorption inside hall(Sabine)\nV = 9000; #volume of cinema hall(m**3)\n\n#Calculation\nT = 0.165*V/aS; #reverberation time of hall(s)\nT = math.ceil(T*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"reverberation time of the hall is\",T, \"s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "reverberation time of the hall is 1.4143 s\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.12, Page number 25" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 0.65; #average absorption coefficient(Sabine/m**2)\nV = 13500; #volume of auditorium(m**3)\nT = 1.2; #reverberation time of hall(s)\n\n#Calculation\nS = 0.165*V/(a*T); #reverberation time of hall(s)\nS = math.ceil(S*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"total area of interior surface is\",S, \"m**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "total area of interior surface is 2855.8 m**2\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.13, Page number 25" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nV = 15000; #volume of cinema hall(m**3)\nT1 = 1.3; #initial reverberation time of hall(s)\na1S1 = 300; #number of chairs placed\n\n#Calculation\naS = 0.165*V/T1; #total absorption of hall\nT2 = (0.165*V)/(aS+a1S1); #reverberation time of hall after adding chairs(s)\nT2 = math.ceil(T2*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"reverberation time of the hall after adding chairs is\",T2, \"s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "reverberation time of the hall after adding chairs is 1.1231 s\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.14, Page number 26" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.5; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",int(d1), \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 360 m\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.15, Page number 26" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 0.4; #distance between 2 constructive antinodes(mm)\nnew = 1.5; #frequency of crystal(MHz)\n \n#Calculation\nnew = new*10**6; #frequency of crystal(Hz)\nd = d*10**-3; #distance between 2 constructive antinodes(m)\n#distance between 2 antinodes is given by lamda/2\nlamda = 2*d; #wavelength of ultrasonic waves(m)\nv = new*lamda; #velocity of waves(m/s)\n\n#Result\nprint \"velocity of waves is\",int(v), \"m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "velocity of waves is 1200 m/s\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.16, Page number 26" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 40; #length of iron rod(mm)\nE = 11.5*10**10; #Young's modulus(N/m**2)\nrho = 7250; #density of pure iron(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"depth of the submerged submarine is\",new, \"kHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 49.785 kHz\n" + } + ], + "prompt_number": 18 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter10.ipynb b/Engineering_Physics/Chapter10.ipynb new file mode 100755 index 00000000..051ee9c1 --- /dev/null +++ b/Engineering_Physics/Chapter10.ipynb @@ -0,0 +1,62 @@ +{ + "metadata": { + "name": "Chapter10" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "10: Dielectric Materials" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 10.1, Page number 289" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nepsilon_r = 1.0000684; #dielectric constant\nN = 2.7*10**25; #number of atoms(per m**3)\nepsilon0 = 8.85*10**-12; #permittivity of free space\n\n#Calculation\nalpha_e = epsilon0*(epsilon_r-1)/N; #electronic polarizability(Fm**2)\n\n#Result\nprint \"electronic polarizability is\",alpha_e,\"Fm**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electronic polarizability is 2.242e-41 Fm**2\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 10.2, Page number 290" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nepsilon_r = 1.0024; #relative permittivity\nN = 2.7*10**25; #number of atoms(per m**3)\nepsilon0 = 8.85*10**-12; #permittivity of free space\n\n#Calculation\nalpha_e = epsilon0*(epsilon_r-1)/N; #electronic polarizability(Fm**2)\n\n#Result\nprint \"electronic polarizability is\",alpha_e,\"Fm**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electronic polarizability is 7.86666666667e-40 Fm**2\n" + } + ], + "prompt_number": 2 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter10_1.ipynb b/Engineering_Physics/Chapter10_1.ipynb index b2bd25cb..051ee9c1 100755 --- a/Engineering_Physics/Chapter10_1.ipynb +++ b/Engineering_Physics/Chapter10_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:4b61028c3be5c168cde4c3aa75ae23500168dbc119942b73de7c79e4a037fd53" + "name": "Chapter10" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,52 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "10: Statistical Mechanics" - ] + "source": "10: Dielectric Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 10.1, Page number 222" - ] + "source": "Example number 10.1, Page number 289" }, { "cell_type": "code", "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "g1 = 2; #The degeneracy of ground state\n", - "g2 = 8; #The degeneracy of excited state\n", - "delta_E = 10.2; #Energy of excited state above the ground state(eV)\n", - "T = 6000; #Temperature of the state(K)\n", - "\n", - "#Calculation\n", - "D_ratio = g2/g1; #Ratio of degeneracy of states\n", - "x = k*T/e;\n", - "N_ratio = D_ratio*math.exp(-delta_E/x); #Ratio of occupancy of the excited to the ground state\n", - "\n", - "#Result\n", - "print \"The ratio of occupancy of the excited to the ground state is\",N_ratio" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nepsilon_r = 1.0000684; #dielectric constant\nN = 2.7*10**25; #number of atoms(per m**3)\nepsilon0 = 8.85*10**-12; #permittivity of free space\n\n#Calculation\nalpha_e = epsilon0*(epsilon_r-1)/N; #electronic polarizability(Fm**2)\n\n#Result\nprint \"electronic polarizability is\",alpha_e,\"Fm**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The ratio of occupancy of the excited to the ground state is 1.10167326887e-08\n" - ] + "text": "electronic polarizability is 2.242e-41 Fm**2\n" } ], "prompt_number": 1 @@ -66,229 +38,22 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 10.2, Page number 222" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "a = 10/2;\n", - "#enegy of 10 bosons is E = (10*pi**2*h**2)/(2*m*a**2) = (5*pi**2*h**2)/(m*a**2)\n", - "\n", - "#Result\n", - "print \"enegy of 10 bosons is E = \",int(a),\"(pi**2*h**2)/(m*a**2)\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "enegy of 10 bosons is E = 5 (pi**2*h**2)/(m*a**2)\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 10.3, Page number 223" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "n1=1; #1st level\n", - "n2=2; #2nd level\n", - "n3=3; #3rd level\n", - "n4=4; #4th level\n", - "n5=5; #5th level\n", - "\n", - "#Calculation\n", - "#an energy level can accomodate only 2 fermions. hence there will be 2 fermions in each level\n", - "#thus total ground state energy will be E = (2*E1)+(2*E2)+(2*E3)+(2*E4)+E5\n", - "#let X = ((pi**2)*(h**2)/(2*m*a**2)). E = X*((2*n1**2)+(2*n2**2)+(2*n3**2)+(2*n4**2)+(n5**2))\n", - "A = (2*n1**2)+(2*n2**2)+(2*n3**2)+(2*n4**2)+(n5**2);\n", - "#thus E = A*X\n", - "\n", - "#Result\n", - "print \"the ground state energy of the system is\",A,\"(pi**2)*(h**2)/(2*m*a**2)\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "the ground state energy of the system is 85 (pi**2)*(h**2)/(2*m*a**2)\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 10.4, Page number 223" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "N_A = 6.02*10**23; #Avogadro's number\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "me = 9.1*10**-31; #Mass of electron(kg)\n", - "rho = 10.5; #Density of silver(g/cm)\n", - "m = 108; #Molecular mass of silver(g/mol)\n", - "\n", - "#Calculation\n", - "N_D = rho*N_A/m; #Number density of conduction electrons(per cm**3)\n", - "N_D = N_D*10**6; #Number density of conduction electrons(per m**3)\n", - "E_F = ((h**2)/(8*me))*(3/math.pi*N_D)**(2/3); #fermi energy(J)\n", - "E_F = E_F/e; #fermi energy(eV)\n", - "E_F = math.ceil(E_F*10**2)/10**2; #rounding off the value of E_F to 2 decimals\n", - "\n", - "#Result\n", - "print \"The number density of conduction electrons is\",N_D, \"per metre cube\"\n", - "print \"The Fermi energy of silver is\",E_F, \"eV\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The number density of conduction electrons is 5.85277777778e+28 per metre cube\n", - "The Fermi energy of silver is 5.51 eV\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 10.5, Page number 224" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "N_A = 6.02*10**23; #Avogadro's number\n", - "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", - "T = 293; #Temperature of sodium(K)\n", - "E_F = 3.24; #Fermi energy of sodium(eV)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "\n", - "#Calculation\n", - "C_v = math.pi**2*N_A*k**2*T/(2*E_F*e); #Molar specific heat of sodium(per mole)\n", - "C_v = math.ceil(C_v*10**2)/10**2; #rounding off the value of C_v to 2 decimals\n", - "\n", - "#Result\n", - "print \"The electronic contribution to molar specific heat of sodium is\",C_v, \"per mole\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The electronic contribution to molar specific heat of sodium is 0.32 per mole\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 10.6, Page number 224" - ] + "source": "Example number 10.2, Page number 290" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "m = 9.1*10**-31; #Mass of the electron(kg)\n", - "N_D = 18.1*10**28; #Number density of conduction electrons in Al(per metre cube)\n", - "\n", - "#Calculation\n", - "E_F = h**2/(8*m)*(3/math.pi*N_D)**(2/3); #N_D = N/V. Fermi energy of aluminium(J)\n", - "E_F = E_F/e; #Fermi energy of aluminium(eV)\n", - "E_F = math.ceil(E_F*10**3)/10**3; #rounding off the value of E_F to 3 decimals\n", - "Em_0 = 3/5*E_F; #Mean energy of the electron at 0K(eV)\n", - "Em_0 = math.ceil(Em_0*10**3)/10**3; #rounding off the value of Em_0 to 3 decimals\n", - "\n", - "#Result\n", - "print \"The Fermi energy of aluminium is\",E_F, \"eV\"\n", - "print \"The mean energy of the electron is\",Em_0, \"eV\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nepsilon_r = 1.0024; #relative permittivity\nN = 2.7*10**25; #number of atoms(per m**3)\nepsilon0 = 8.85*10**-12; #permittivity of free space\n\n#Calculation\nalpha_e = epsilon0*(epsilon_r-1)/N; #electronic polarizability(Fm**2)\n\n#Result\nprint \"electronic polarizability is\",alpha_e,\"Fm**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The Fermi energy of aluminium is 11.696 eV\n", - "The mean energy of the electron is 7.018 eV\n" - ] + "text": "electronic polarizability is 7.86666666667e-40 Fm**2\n" } ], - "prompt_number": 9 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 2 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter1_1.ipynb b/Engineering_Physics/Chapter1_1.ipynb index 9c835441..a3614569 100755 --- a/Engineering_Physics/Chapter1_1.ipynb +++ b/Engineering_Physics/Chapter1_1.ipynb @@ -1,7 +1,7 @@ { "metadata": { - "name": "", - "signature": "sha256:078983e30b4c728fb3bac2d9363145a8f1fffb1522bc3df76d2595e630af4298" + "name": "Chapter1", + "signature": "sha256:e55f587b2da98ead68f73bb2b4d29bef91aa67eb577c460fb9dcaab92acc4339" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,51 +12,46 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "1: Oscillations and Waves" - ] + "source": "1: Ultrasonics" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.1, Page number 23" - ] + "source": "Example number 1.1, Page number 20" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "S=4; #SHM described by a particle(cm)\n", - "x=0; #mean position\n", - "v=12; #velocity at mean position(cm/s)\n", - "\n", - "#Calculation\n", - "A=S/2; #amplitude of motion(cm)\n", - "omega=v/A; #angular frequency(sec-1)\n", - "T=(2*math.pi)/omega; #time period(sec)\n", - "T=math.ceil(T*10**3)/10**3; #rounding off to 3 decimals\n", - "\n", - "#Result\n", - "print \"time period of motion is\",T, \"sec\"\n", - "print \"time period of motion is pi/3 sec\"" + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.33; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",d1, \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 237.6 m\n" + } ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.2, Page number 21" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 40; #length of iron rod(mm)\nE = 115*10**9; #Young's modulus(N/m**2)\nrho = 7.25*10**3; #density of pure iron(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"depth of the submerged submarine is\",new, \"kHz\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "time period of motion is 1.048 sec\n", - "time period of motion is pi/3 sec\n" - ] + "text": "depth of the submerged submarine is 49.785 kHz\n" } ], "prompt_number": 2 @@ -65,47 +60,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.2, Page number 23" - ] + "source": "Example number 1.3, Page number 21" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "T=0.1; #time period(sec)\n", - "A=4; #amplitude of motion(cm)\n", - "x=0.2; #distance from mean position(cm)\n", - "\n", - "#Calculation\n", - "omega=(2*math.pi)/T; #angular frequency(sec-1)\n", - "a=(omega**2)*x; #acceleration(cm/sec^2)\n", - "a=math.ceil(a*10**2)/10**2; #rounding off to 2 decimals\n", - "#maximum velocity is when particle is in the mean position\n", - "v_max=omega*A; #maximum velocity(cm/sec)\n", - "v_max=math.ceil(v_max*10**2)/10**2; #rounding off to 2 decimals\n", - "\n", - "#Result\n", - "print \"acceleration is\",a, \"cm/sec^2\"\n", - "print \"maximum velocity is\",v_max, \"cm/sec\"\n", - "\n", - "#answers given in the book are wrong" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 1; #length of quartz crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"fundamental frequency of crystal is\",new, \"*10**6 Hz\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "acceleration is 789.57 cm/sec^2\n", - "maximum velocity is 251.33 cm/sec\n" - ] + "text": "fundamental frequency of crystal is 2.73 *10**6 Hz\n" } ], "prompt_number": 3 @@ -114,146 +81,82 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.3, Page number 24" - ] + "source": "Example number 1.4, Page number 22" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "import numpy as np\n", - "\n", - "#Variable declaration\n", - "A1 = 40; #First amplitude of oscillation(cm)\n", - "An_plus_1 = 4; #Amplitude after 100 oscillations(cm)\n", - "n = 100; #Number of oscillations\n", - "T = 2.5; #Time period of oscillations(s)\n", - "\n", - "#Calculation\n", - "t = T/4; #Time taken to reach the first amplitude from the mean position(s)\n", - "#Now A1 = x0*math.exp(-lambda*t) and An_plus_1 = x0*math.exp(-lambda*(t+nT))\n", - "#A1/An_plus_1 = math.exp(n*lambda*T)\n", - "x=A1/An_plus_1;\n", - "lamda=np.log(x)/(n*T); #Damping constant(per sec)\n", - "lamda=lamda*10**2;\n", - "lamda=math.ceil(lamda*10**3)/10**3; #rounding off to 3 decimals\n", - "\n", - "#Result\n", - "print \"Damping constant is\",lamda,\"*10**-2 per sec\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 0.55; #distance between 2 constructive antinodes(mm)\nnew = 1.5; #frequency of crystal(MHz)\n \n#Calculation\nnew = new*10**6; #frequency of crystal(Hz)\nd = d*10**-3; #distance between 2 constructive antinodes(m)\n#distance between 2 antinodes is given by lamda/2\nlamda = 2*d; #wavelength of ultrasonic waves(m)\nv = new*lamda; #velocity of waves(m/s)\n\n#Result\nprint \"velocity of waves is\",int(v), \"m/s\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "Damping constant is 0.922 *10**-2 per sec\n" - ] + "text": "velocity of waves is 1650 m/s\n" } ], - "prompt_number": 6 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.4, Page number 24" - ] + "source": "Example number 1.5, Page number 22" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "x1 = 3; #First position of the particle(cm)\n", - "x2 = 4; #Second position of the particle(cm)\n", - "v1 = 16; #Velocity of particle executing SHM at 1st position(cm/s)\n", - "v2 = 12; #Velocity of particle executing SHM at 2nd position (cm/s)\n", - "\n", - "#Calculation\n", - "#As v = omega*sqrt(A**2 - x**2) so\n", - "#(v1/v2)**2=(A**2 - x1**2)/(A**2 - x2**2)\n", - "#RHS gives (A**2-9)/(A**2-16)\n", - "#(v2**2)*(A**2 - x1**2)=(v1**2)*(A**2 - x2**2), on solving we get\n", - "A=math.sqrt((((v1**2)*(x2**2))-((v2**2)*(x1**2)))/((v1**2)-(v2**2))); #amplitude in cm\n", - "omega=v1/math.sqrt(A**2-x1**2); #Angular speed of the particle(per sec)\n", - "T=2*math.pi/omega; #Time period of oscillation(sec)\n", - "T=math.ceil(T*10**3)/10**3; #rounding off to 3 decimals\n", - "\n", - "#Result\n", - "print \"The amplitude of SHM is\",A, \"cm\"\n", - "print \"The time period of oscillation is\",T, \"sec\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 50; #length of rod(mm)\nE = 11.5*10**10; #Young's modulus(N/m**2)\nrho = 7250; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew = math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"natural frequency of rod is\",new, \"kHz\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The amplitude of SHM is 5.0 cm\n", - "The time period of oscillation is 1.571 sec\n" - ] + "text": "natural frequency of rod is 39.83 kHz\n" } ], - "prompt_number": 7 + "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.5, Page number 25" - ] + "source": "Example number 1.6, Page number 22" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "m = 0.3; #Mass attached to the string(kg)\n", - "g = 9.8; #Acceleration due to gravity(m/sec**2)\n", - "x = 0.15; #Stretchness produced in the spring(m)\n", - "s = 0.1; #spring is stretched and released(m)\n", - "\n", - "#Calculation\n", - "F = m*g; #Restoring force acting on the mass(N)\n", - "k = F/x; #Spring constant(N/m)\n", - "A = s; #amplitude equals to the spring stretched and released\n", - "omega = math.sqrt(k/m); #Angular frequency of oscillation(rad per sec)\n", - "v0 = omega*A; #Maximum velocity during the oscillations(m/s)\n", - "v0=math.ceil(v0*100)/100; #rounding off to 2 decimals\n", - "\n", - "#Result\n", - "print \"The spring constant is\",k, \"N/m\"\n", - "print \"The amplitude of oscillation is\",A, \"m\"\n", - "print \"The maximum velocity during oscillations is\",v0, \"m/s\"" + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 2; #length of crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; #natural frequency of the rod(MHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"MHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "frequency of crystal is 1.365 MHz\n" + } ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.7, Page number 23" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 3; #length of crystal(mm)\nE = 8*10**10; #Young's modulus(N/m**2)\nrho = 2500; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz) \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"kHz\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The spring constant is 19.6 N/m\n", - "The amplitude of oscillation is 0.1 m\n", - "The maximum velocity during oscillations is 0.81 m/s\n" - ] + "text": "frequency of crystal is 942.81 kHz\n" } ], "prompt_number": 8 @@ -262,96 +165,61 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.6, Page number 25" - ] + "source": "Example number 1.8, Page number 23" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lambda1 = 400; #Lower limit of wavelength of visible region(nm)\n", - "lambda2 = 700; #Upper limit of wavelength of visible region(nm)\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "\n", - "#Calculation\n", - "lambda1 = lambda1*10**-9 #Lower limit of wavelength(m) \n", - "lambda2 = lambda2*10**-9 #upper limit of wavelength(m) \n", - "new_1 = c/lambda1; #Upper limit of frequency of visible region(m)\n", - "new_2 = c/lambda2; #Lower limit of frequency of visible region(m)\n", - "\n", - "#Result\n", - "print \"The frequency equivalent of 400 nm is\",new_1, \"Hz\"\n", - "print \"The frequency equivalent of 700 nm is\",new_2, \"Hz\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 1.5; #length of crystal(mm)\nE = 7.9*10**10; #Young's modulus(N/m**2)\nrho = 2650; #density(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-6; #natural frequency of the rod(MHz) \nnew=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"frequency of crystal is\",new, \"MHz\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The frequency equivalent of 400 nm is 7.5e+14 Hz\n", - "The frequency equivalent of 700 nm is 4.28571428571e+14 Hz\n" - ] + "text": "frequency of crystal is 1.82 MHz\n" } ], - "prompt_number": 9 + "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.7, Page number 26" - ] + "source": "Example number 1.9, Page number 24" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "#Comparing the standard equation u(x,t) = A*sin(2*%pi(x/lambda-t/T)) with the given equation, we get\n", - "A = 1.5*10**-3; #Amplitude of the sound wave(m)\n", - "lamda = 8; #Wavelength of the sound wave(m)\n", - "T = 1/40; #Time period of the sound wave(s)\n", - "\n", - "#Calculation\n", - "A = A*10**3;\n", - "new = 1/T; #Frequency of the sound wave(Hz)\n", - "v = new*lamda; #Velocity of the sound wave(m/s)\n", - "T=math.ceil(T*100)/100; #rounding off to 2 decimals\n", - "\n", - "#Result\n", - "print \"The amplitude of the sound wave is\",A,\"*10**-3 m\"\n", - "print \"The wavelength of the sound wave is\",lamda, \"m\"\n", - "print \"The time period of the sound wave is\",T, \"s\"\n", - "print \"The frequency of the sound wave is\",new, \"Hz\"\n", - "print \"The velocity of the sound wave is\",v, \"m/s\"" + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.95; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of sea(m)\n\n#Result\nprint \"depth of the submerged submarine is\",int(d1), \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 684 m\n" + } ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.10, Page number 24" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.83; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",d1, \"m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The amplitude of the sound wave is 1.5 *10**-3 m\n", - "The wavelength of the sound wave is 8 m\n", - "The time period of the sound wave is 0.03 s\n", - "The frequency of the sound wave is 40.0 Hz\n", - "The velocity of the sound wave is 320.0 m/s\n" - ] + "text": "depth of the submerged submarine is 597.6 m\n" } ], "prompt_number": 12 @@ -360,47 +228,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.8, Page number 26" - ] + "source": "Example number 1.11, Page number 24" }, { "cell_type": "code", "collapsed": false, - "input": [ - "\n", - "\n", - "#import modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "A = 2; #Amplitude of the wave(cm)\n", - "T = 0.5; #Time period of the wave(sec)\n", - "v = 200; #Wave velocity(cm/s)\n", - "\n", - "#Calculation\n", - "f = 1/T; #Frequency of the wave(Hz)\n", - "lamda = v/f; #Wavelength of the wave(cm)\n", - "\n", - "#Result\n", - "print \"frequency of wave is\",f, \"Hz\"\n", - "print \"wavelength of wave is\",lamda, \"cm\"\n", - "print \"The Equation of the wave moving along X-axis :\"\n", - "print \"u = \",A,\"*sin*2*math.pi*(x/\",lamda,\"- t/\",T,\")\" #x and y are in cm and t is in sec" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\naS = 1050; #total absorption inside hall(Sabine)\nV = 9000; #volume of cinema hall(m**3)\n\n#Calculation\nT = 0.165*V/aS; #reverberation time of hall(s)\nT = math.ceil(T*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"reverberation time of the hall is\",T, \"s\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "frequency of wave is 2.0 Hz\n", - "wavelength of wave is 100.0 cm\n", - "The Equation of the wave moving along X-axis :\n", - "u = 2 *sin*2*math.pi*(x/ 100.0 - t/ 0.5 )\n" - ] + "text": "reverberation time of the hall is 1.4143 s\n" } ], "prompt_number": 13 @@ -409,59 +249,106 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 1.9, Page number 27" - ] + "source": "Example number 1.12, Page number 25" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#import modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "T = 1000; #Tension in the wire(N)\n", - "M=15; #mass of the wire(kg)\n", - "l=300; #length of the wire(m)\n", - "lamda = 0.30; #Wavelength of wave along wire(m)\n", - "\n", - "#Calculation\n", - "m = M/l; #Mass per unit length of the wire(kg/m)\n", - "v = math.sqrt(T/m); #Velocity of wave through wire(m/s)\n", - "v=math.ceil(v*100)/100; #rounding off to 2 decimals\n", - "new = v/lamda; #Frequency of wave through string(Hz)\n", - "new=math.ceil(new*100)/100; #rounding off to 2 decimals\n", - "\n", - "#Result\n", - "print \"The velocity of the wave through wire is\",v, \"m/s\"\n", - "print \"The frequency of the wave through wire is\",new, \"Hz\"\n", - "\n", - "#answer for frequency of the wave is wrong in the textbook" + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 0.65; #average absorption coefficient(Sabine/m**2)\nV = 13500; #volume of auditorium(m**3)\nT = 1.2; #reverberation time of hall(s)\n\n#Calculation\nS = 0.165*V/(a*T); #reverberation time of hall(s)\nS = math.ceil(S*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"total area of interior surface is\",S, \"m**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "total area of interior surface is 2855.8 m**2\n" + } ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.13, Page number 25" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nV = 15000; #volume of cinema hall(m**3)\nT1 = 1.3; #initial reverberation time of hall(s)\na1S1 = 300; #number of chairs placed\n\n#Calculation\naS = 0.165*V/T1; #total absorption of hall\nT2 = (0.165*V)/(aS+a1S1); #reverberation time of hall after adding chairs(s)\nT2 = math.ceil(T2*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"reverberation time of the hall after adding chairs is\",T2, \"s\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The velocity of the wave through wire is 141.43 m/s\n", - "The frequency of the wave through wire is 471.44 Hz\n" - ] + "text": "reverberation time of the hall after adding chairs is 1.1231 s\n" } ], "prompt_number": 15 }, { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.14, Page number 26" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Variable declaration\nv = 1440; #velocity of ultrasonic waves(m/s)\nt = 0.5; #time elapsed(s)\n\n#Calculation\nd = v*t; #distance travelled(m)\nd1 = d/2; #depth of submarine(m)\n\n#Result\nprint \"depth of the submerged submarine is\",int(d1), \"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 360 m\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.15, Page number 26" + }, + { "cell_type": "code", "collapsed": false, - "input": [], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 0.4; #distance between 2 constructive antinodes(mm)\nnew = 1.5; #frequency of crystal(MHz)\n \n#Calculation\nnew = new*10**6; #frequency of crystal(Hz)\nd = d*10**-3; #distance between 2 constructive antinodes(m)\n#distance between 2 antinodes is given by lamda/2\nlamda = 2*d; #wavelength of ultrasonic waves(m)\nv = new*lamda; #velocity of waves(m/s)\n\n#Result\nprint \"velocity of waves is\",int(v), \"m/s\"", "language": "python", "metadata": {}, - "outputs": [] + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "velocity of waves is 1200 m/s\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 1.16, Page number 26" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nl = 40; #length of iron rod(mm)\nE = 11.5*10**10; #Young's modulus(N/m**2)\nrho = 7250; #density of pure iron(kg/m**3)\n\n#Calculation\nl = l*10**-3; #length of iron rod(m)\nnew = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\nnew = new*10**-3; #natural frequency of the rod(kHz)\nnew=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"depth of the submerged submarine is\",new, \"kHz\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "depth of the submerged submarine is 49.785 kHz\n" + } + ], + "prompt_number": 18 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter2.ipynb b/Engineering_Physics/Chapter2.ipynb new file mode 100755 index 00000000..fff10b22 --- /dev/null +++ b/Engineering_Physics/Chapter2.ipynb @@ -0,0 +1,84 @@ +{ + "metadata": { + "name": "Chapter2", + "signature": "sha256:ac80f9dfe1725f11a5d4ce0fbda5ffed825d99c680f116629e5e3fcb8b69c198" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "2: Lasers" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 2.1, Page number 52" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 590; #wavelength(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\nk = 1.38*10**-23; #boltzmann's constant\nT = 523; #temperature(Kelvin)\n\n#Calculation\nlamda = lamda*10**-9; #wavelength(m) \n#n1byn2 = math.exp(-(E2-E1)/(k*T))\n#but E2-E1 = h*new and new = c/lamda\n#therefore n1byn2 = math.exp(-h*c/(lamda*k*T))\nn1byn2 = math.exp(-h*c/(lamda*k*T));\n\n#Result\nprint \"relative population of Na atoms is\",n1byn2", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "relative population of Na atoms is 5.36748316686e-21\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 2.2, Page number 53" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 590; #wavelength(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\nk = 1.38*10**-23; #boltzmann's constant\nT = 523; #temperature(Kelvin)\n\n#Calculation\nlamda = lamda*10**-9; #wavelength(m) \n#n21dashbyn21 = 1/(math.exp(h*new/(k*T))-1)\n#but new = c/lamda\n#therefore n21dashbyn21 = 1/(math.exp(h*c/(lamda*k*T))-1)\nA = math.exp(h*c/(lamda*k*T))-1;\nn21dashbyn21 = 1/A; \n\n#Result\nprint \"ratio of stimulated to spontaneous emission is\",n21dashbyn21\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "ratio of stimulated to spontaneous emission is 5.36748316686e-21\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 2.3, Page number 53" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 632.8; #wavelength of laser(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\np = 3.147; #output power(mW)\n\n#Calculation\np = p*10**-3; #output power(W)\nlamda = lamda*10**-9; #wavelength(m) \nnew = c/lamda; #frequency(Hz)\nE = h*new; #energy of each photon(J)\nEm = p*60; #energy emitted per minute(J/min)\nN = Em/E; #number of photons emitted per second\n\n#Result\nprint \"number of photons emitted per second is\",N", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "number of photons emitted per second is 6.01183879245e+17\n" + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter2_1.ipynb b/Engineering_Physics/Chapter2_1.ipynb index 3d6c503f..fff10b22 100755 --- a/Engineering_Physics/Chapter2_1.ipynb +++ b/Engineering_Physics/Chapter2_1.ipynb @@ -1,7 +1,7 @@ { "metadata": { - "name": "", - "signature": "sha256:2693d83b10c8e62fc8d3ef78c9959c4d8327c36ed1f7884372585d33796bcbc3" + "name": "Chapter2", + "signature": "sha256:ac80f9dfe1725f11a5d4ce0fbda5ffed825d99c680f116629e5e3fcb8b69c198" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,231 +12,70 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "2: Electromagnetic Theory" - ] + "source": "2: Lasers" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 2.1, Page number 46" - ] + "source": "Example number 2.1, Page number 52" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "from sympy import *\n", - "import math\n", - "\n", - "#Variable declaration\n", - "C = 10; #Capacitance of the capacitor(pF)\n", - "#given V=0.2*sin(120*math.pi*t) in volts\n", - "\n", - "#Calculation\n", - "C=C*10**-12; #Capacitance of the capacitor(F)\n", - "x, y, z, t = symbols('x y z t')\n", - "k, m, n = symbols('k m n', integer=True)\n", - "f, g, h = symbols('f g h', cls=Function)\n", - "#I = C*dV/dt\n", - "#let dV/dt be a\n", - "a=diff(0.2*sin(120*math.pi*t),t) #dV/dt\n", - "#value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n", - "#for cosine function peak value occurs when 120*math.pi*t = 0\n", - "#therefore value of dV/dt becomes d = 75.398223686155\n", - "d = 75.398223686155; #value of dV/dt \n", - "I=C*d; #displacement current(A)\n", - "\n", - "#Result\n", - "print \"value of dV/dt is\",a\n", - "print \"displacement current is\",I, \"A\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n", - "displacement current is 7.53982236862e-10 A\n" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 2.2, Page number 46" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "from sympy import *\n", - "import math\n", - "\n", - "#Variable declaration\n", - "epsilon_r = 1; #Relative electrical permittivity of free space\n", - "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", - "#given E=sin(120*math.pi*t) in volts\n", - "\n", - "#Calculation\n", - "x, y, z, t = symbols('x y z t')\n", - "k, m, n = symbols('k m n', integer=True)\n", - "f, g, h = symbols('f g h', cls=Function)\n", - "#J2 = epsilon*dE/dt\n", - "epsilon=epsilon_0*epsilon_r;\n", - "#let dE/dt be a\n", - "a=diff(sin(120*math.pi*t),t) #dE/dt\n", - "#value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n", - "#for cosine function peak value occurs when 120*math.pi*t = 0\n", - "#therefore value of dE/dt becomes d = 376.991118430775\n", - "d = 376.991118430775; #value of dE/dt\n", - "J2=epsilon*d; #displacement current density(A/m**2)\n", - "\n", - "#Result\n", - "print \"value of dE/dt is\",a\n", - "print \"The peak value of displacement current density is\",J2, \"A/m**2\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 590; #wavelength(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\nk = 1.38*10**-23; #boltzmann's constant\nT = 523; #temperature(Kelvin)\n\n#Calculation\nlamda = lamda*10**-9; #wavelength(m) \n#n1byn2 = math.exp(-(E2-E1)/(k*T))\n#but E2-E1 = h*new and new = c/lamda\n#therefore n1byn2 = math.exp(-h*c/(lamda*k*T))\nn1byn2 = math.exp(-h*c/(lamda*k*T));\n\n#Result\nprint \"relative population of Na atoms is\",n1byn2", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n", - "The peak value of displacement current density is 3.33787936259e-09 A/m**2\n" - ] + "text": "relative population of Na atoms is 5.36748316686e-21\n" } ], - "prompt_number": 3 + "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 2.3, Page number 47 (Theoritical proof)" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 2.4, Page number 47" - ] + "source": "Example number 2.2, Page number 53" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "p = 60; #Power rating of bulb(W)\n", - "d = 0.5; #Distance from the bulb(m)\n", - "\n", - "#Calculation\n", - "A=4*math.pi*d**2; #area(m**2)\n", - "P = p/A; #Value of Poynting vector(W/m**2)\n", - "P = math.ceil(P*100)/100; #rounding off value of P to 1 decimal\n", - "\n", - "#Result\n", - "print \"The value of Poynting vector is\",P, \"W/m**2\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 590; #wavelength(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\nk = 1.38*10**-23; #boltzmann's constant\nT = 523; #temperature(Kelvin)\n\n#Calculation\nlamda = lamda*10**-9; #wavelength(m) \n#n21dashbyn21 = 1/(math.exp(h*new/(k*T))-1)\n#but new = c/lamda\n#therefore n21dashbyn21 = 1/(math.exp(h*c/(lamda*k*T))-1)\nA = math.exp(h*c/(lamda*k*T))-1;\nn21dashbyn21 = 1/A; \n\n#Result\nprint \"ratio of stimulated to spontaneous emission is\",n21dashbyn21\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The value of Poynting vector is 19.1 W/m**2\n" - ] + "text": "ratio of stimulated to spontaneous emission is 5.36748316686e-21\nanswer given in the book is wrong\n" } ], - "prompt_number": 4 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 2.5, Page number 47" - ] + "source": "Example number 2.3, Page number 53" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "E_peak = 6; #Peak value of electric field intensity(V/m)\n", - "c = 3*10**8; #Speed of electromagnetic wave in free space(m/s)\n", - "mew_0 = 4*math.pi*10**-7; #Absolute permeability of free space(Tm/A)\n", - "epsilon_0 = 8.854*10**-12; #Absolute permittivity of free space(F/m)\n", - "mew_r = 1; #Relative permeability of medium\n", - "epsilon_r = 3; #Relative permittivity of the medium\n", - "\n", - "#Calculation\n", - "v = c/math.sqrt(mew_r*epsilon_r); #Wave velocity(m/s)\n", - "v = v/10**8;\n", - "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "eta = math.sqrt((mew_0/epsilon_0)*(mew_r/epsilon_r)); #Intrinsic impedance of the medium(ohm)\n", - "eta = math.ceil(eta*10)/10; #rounding off the value of v to 1 decimal\n", - "H_P = E_peak/eta; #Peak value of the magnetic intensity(A/m)\n", - "H_P = H_P*10**2;\n", - "H_P = math.ceil(H_P*10**2)/10**2; #rounding off the value of v to 2 decimals\n", - "\n", - "#Result\n", - "print \"The wave velocity is\",v,\"*10**8 m/s\"\n", - "print \"The intrinsic impedance of the medium is\",eta, \"ohm\"\n", - "print \"The peak value of the magnetic intensity is\",H_P,\"*10**-2 A/m\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 632.8; #wavelength of laser(nm)\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/s)\np = 3.147; #output power(mW)\n\n#Calculation\np = p*10**-3; #output power(W)\nlamda = lamda*10**-9; #wavelength(m) \nnew = c/lamda; #frequency(Hz)\nE = h*new; #energy of each photon(J)\nEm = p*60; #energy emitted per minute(J/min)\nN = Em/E; #number of photons emitted per second\n\n#Result\nprint \"number of photons emitted per second is\",N", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The wave velocity is 1.7321 *10**8 m/s\n", - "The intrinsic impedance of the medium is 217.6 ohm\n", - "The peak value of the magnetic intensity is 2.76 *10**-2 A/m\n" - ] + "text": "number of photons emitted per second is 6.01183879245e+17\n" } ], - "prompt_number": 11 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 3 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter3.ipynb b/Engineering_Physics/Chapter3.ipynb new file mode 100755 index 00000000..9e2d3109 --- /dev/null +++ b/Engineering_Physics/Chapter3.ipynb @@ -0,0 +1,83 @@ +{ + "metadata": { + "name": "Chapter3" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "3: Fibre Optics and Applications" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 3.1, Page number 84" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nn0 = 1; #refractive index of air\na = 180/math.pi; #conversion factor of radian to degree\n\n#Calculation\nNA = math.sqrt((n1**2)-(n2**2)); #numerical aperture\nNA=math.ceil(NA*10)/10; #rounding off to 1 decimal\nalpha_m = math.asin(NA/n0); #acceptance angle(radian)\nalpha_m = alpha_m*a; #acceptance angle(degrees)\nalpha_m=math.ceil(alpha_m*10**2)/10**2; #rounding off to 2 decimals\nphi_m = math.asin(NA/n1); #phase angle(radian)\nphi_m = phi_m*a; #phase angle(degrees)\nphi_m=math.ceil(phi_m*10**2)/10**2; #rounding off to 2 decimals\ntheta_c = math.asin(n2/n1); #critical angle(radian)\ntheta_c = theta_c*a; #critical angle(degrees)\ntheta_c=math.ceil(theta_c*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"numerical aperture is\",NA\nprint \"acceptance angle is\",alpha_m,\"degrees\"\nprint \"phase angle is\",phi_m,\"degrees\"\nprint \"critical angle is\",theta_c,\"degrees\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "numerical aperture is 0.3\nacceptance angle is 17.46 degrees\nphase angle is 11.54 degrees\ncritical angle is 78.522 degrees\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 3.2, Page number 85" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nc = 3*10**8; #velocity of light(m/sec)\n\n#Calculation\ndeltatbyL = (n1/n2)*((n1-n2)/c);\n\n#Result\nprint \"pulse broadening per unit length is\",deltatbyL,\"s/m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "pulse broadening per unit length is 1.02040816327e-10 s/m\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 3.3, Page number 85" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nphi_m = 11.54; #phase angle(degrees)\na = 0.5*10**-4;\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi_m = phi_m*x; #phase angle(radian)\nL = a/math.tan(phi_m); #length(m)\nn = 1/(2*L); #total number of internal reflections(m-1)\n\n#Result\nprint \"alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\"\nprint \"alpha = alpha_m rays have\",int(n),\"m-1 internal reflections\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\nalpha = alpha_m rays have 2041 m-1 internal reflections\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter3_1.ipynb b/Engineering_Physics/Chapter3_1.ipynb index 7f02f8be..9e2d3109 100755 --- a/Engineering_Physics/Chapter3_1.ipynb +++ b/Engineering_Physics/Chapter3_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:366ab969956cd234404db0091b17960805856ec3ff44007e36b0efdbe1414f5e" + "name": "Chapter3" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,452 +11,70 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "3: Interference" - ] + "source": "3: Fibre Optics and Applications" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.1, Page number 71" - ] + "source": "Example number 3.1, Page number 84" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "beta = 0.51; #Fringe width(mm)\n", - "d = 2.2; #Distance between the slits(mm)\n", - "D = 2; #Distance between the slits and the screen(m)\n", - "\n", - "#Calculation\n", - "beta = beta*10**-1; #Fringe width(cm)\n", - "d = d*10**-1; #Distance between the slits(cm)\n", - "D=D*10**2; #Distance between the slits and the screen(cm)\n", - "lamda = beta*d/D; #Wavelength of light(cm)\n", - "lamda = lamda*10**8; #Wavelength of light(A)\n", - "\n", - "#Result\n", - "print \"The wavelength of light is\",lamda, \"angstrom\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The wavelength of light is 5610.0 angstrom\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.2, Page number 71" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lambda1 = 4250; #First wavelength emitted by source of light(A)\n", - "lambda2 = 5050; #Second wavelength emitted by source of light(A)\n", - "D = 1.5; #Distance between the source and the screen(m)\n", - "d = 0.025; #Distance between the slits(mm)\n", - "n = 3; #Number of fringe from the centre\n", - "\n", - "#Calculation\n", - "lambda1 = lambda1*10**-10; #First wavelength emitted(m)\n", - "lambda2 = lambda2*10**-10; #Second wavelength emitted(m)\n", - "d = d*10**-3; #Distance between the slits(m)\n", - "x3 = n*lambda1*D/d; #Position of third bright fringe due to lambda1(m)\n", - "x3_prime = n*lambda2*D/d; #Position of third bright fringe due to lambda2(m)\n", - "x = x3_prime-x3; #separation between the third bright fringe(m)\n", - "x = x*10**2; #separation between the third bright fringe(cm)\n", - "\n", - "#Result\n", - "print \"The separation between the third bright fringe due to the two wavelengths is\",x, \"cm\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nn0 = 1; #refractive index of air\na = 180/math.pi; #conversion factor of radian to degree\n\n#Calculation\nNA = math.sqrt((n1**2)-(n2**2)); #numerical aperture\nNA=math.ceil(NA*10)/10; #rounding off to 1 decimal\nalpha_m = math.asin(NA/n0); #acceptance angle(radian)\nalpha_m = alpha_m*a; #acceptance angle(degrees)\nalpha_m=math.ceil(alpha_m*10**2)/10**2; #rounding off to 2 decimals\nphi_m = math.asin(NA/n1); #phase angle(radian)\nphi_m = phi_m*a; #phase angle(degrees)\nphi_m=math.ceil(phi_m*10**2)/10**2; #rounding off to 2 decimals\ntheta_c = math.asin(n2/n1); #critical angle(radian)\ntheta_c = theta_c*a; #critical angle(degrees)\ntheta_c=math.ceil(theta_c*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"numerical aperture is\",NA\nprint \"acceptance angle is\",alpha_m,\"degrees\"\nprint \"phase angle is\",phi_m,\"degrees\"\nprint \"critical angle is\",theta_c,\"degrees\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The separation between the third bright fringe due to the two wavelengths is 1.44 cm\n" - ] + "text": "numerical aperture is 0.3\nacceptance angle is 17.46 degrees\nphase angle is 11.54 degrees\ncritical angle is 78.522 degrees\n" } ], - "prompt_number": 5 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.3, Page number 71" - ] + "source": "Example number 3.2, Page number 85" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 5.5*10**-5; #Wavelength emitted by source of light(cm)\n", - "n = 4; #Number of fringes shifted\n", - "t = 3.9*10**-4; #Thickness of the thin glass sheet(cm)\n", - "\n", - "#Calculation\n", - "mew = (n*lamda/t)+1; #Refractive index of the sheet of glass\n", - "mew = math.ceil(mew*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "\n", - "#Result\n", - "print \"The refractive index of the sheet of glass is\",mew" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nc = 3*10**8; #velocity of light(m/sec)\n\n#Calculation\ndeltatbyL = (n1/n2)*((n1-n2)/c);\n\n#Result\nprint \"pulse broadening per unit length is\",deltatbyL,\"s/m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The refractive index of the sheet of glass is 1.5642\n" - ] + "text": "pulse broadening per unit length is 1.02040816327e-10 s/m\n" } ], - "prompt_number": 6 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.4, Page number 72" - ] + "source": "Example number 3.3, Page number 85" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 5893; #Wavelength of monochromatic lihgt used(A)\n", - "n = 1; #Number of fringe for the least thickness of the film\n", - "cosr = 1; #for normal incidence\n", - "mew = 1.42; #refractive index of the soap film\n", - "\n", - "#Calculation\n", - "#As for constructive interference, \n", - "#2*mew*t*cos(r) = (2*n-1)*lambda/2, solving for t\n", - "t = (2*n-1)*lamda/(4*mew*cosr); #Thickness of the film that appears bright(A)\n", - "#As for destructive interference, \n", - "#2*mu*t*cos(r) = n*lambda, solving for t\n", - "t1 = n*lamda/(2*mew*cosr); #Thickness of the film that appears bright(A)\n", - "\n", - "#Result\n", - "print \"The thickness of the film that appears bright is\",t, \"angstrom\"\n", - "print \"The thickness of the film that appears dark is\",t1, \"angstrom\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nphi_m = 11.54; #phase angle(degrees)\na = 0.5*10**-4;\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi_m = phi_m*x; #phase angle(radian)\nL = a/math.tan(phi_m); #length(m)\nn = 1/(2*L); #total number of internal reflections(m-1)\n\n#Result\nprint \"alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\"\nprint \"alpha = alpha_m rays have\",int(n),\"m-1 internal reflections\"\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The thickness of the film that appears bright is 1037.5 angstrom\n", - "The thickness of the film that appears dark is 2075.0 angstrom\n" - ] + "text": "alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\nalpha = alpha_m rays have 2041 m-1 internal reflections\nanswer given in the book is wrong\n" } ], "prompt_number": 7 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.5, Page number 72" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 5893; #Wavelength of monochromatic lihgt used(A)\n", - "n = 10; #Number of fringe that are found \n", - "d = 1; #Distance of 10 fringes(cm)\n", - "\n", - "#Calculation\n", - "beta = d/n; #Fringe width(cm)\n", - "lamda = lamda*10**-8; #Wavelength of monochromatic lihgt used(cm)\n", - "theta = lamda/(2*beta); #Angle of the wedge(rad)\n", - "theta = theta*10**4;\n", - "theta = math.ceil(theta*10**4)/10**4; #rounding off the value of theta to 4 decimals\n", - "\n", - "#Result\n", - "print \"The angle of the wedge is\",theta,\"*10**-4 rad\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The angle of the wedge is 2.9465 *10**-4 rad\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.6, Page number 72" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 5900; #Wavelength of monochromatic lihgt used(A)\n", - "t = 0.010; #Spacer thickness(mm)\n", - "l = 10; #Wedge length(cm)\n", - "\n", - "#Calculation\n", - "t = t*10**-1; #Spacer thickness(cm)\n", - "theta = t/l; #Angle of the wedge(rad)\n", - "lamda = lamda*10**-8; #Wavelength of monochromatic lihgt used(cm)\n", - "beta = lamda/(2*theta); #Fringe width(cm)\n", - "\n", - "#Result\n", - "print \"The separation between consecutive bright fringes is\",beta, \"cm\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The separation between consecutive bright fringes is 0.295 cm\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.7, Page number 72" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "import math\n", - "\n", - "#Variable declaration\n", - "D4 = 0.4; #Diameter of 4th dark ring(cm)\n", - "D12 = 0.7; #Diameter of 12th dark ring(cm)\n", - "\n", - "#Calculation\n", - "#We have (dn_plus_k**2)-Dn**2 = 4*k*R*lamda\n", - "#D12**2-D4**2 = 32*R*lamda and D20**2-D12**2 = 32*R*lamda for k = 8\n", - "#since RHS are equal, by equating the LHS we get D12**2-D4**2 = D20**2-D12**2\n", - "D20 = math.sqrt((2*D12**2)-D4**2); #Diameter of 20th dark ring(cm)\n", - "D20 = math.ceil(D20*10**4)/10**4; #rounding off the value of D20 to 4 decimals\n", - "\n", - "#Result\n", - "print \"The diameter of 20th dark ring is\",D20, \"cm\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The diameter of 20th dark ring is 0.9056 cm\n" - ] - } - ], - "prompt_number": 14 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.8, Page number 73" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "Dn = 0.30; #Diameter of nth dark ring with air film(cm)\n", - "dn = 0.25; #Diameter of nth dark ring with liquid film(cm)\n", - "\n", - "#Calculation\n", - "mew = (Dn/dn)**2; #Refractive index of the liquid\n", - "\n", - "#Result\n", - "print \"The refractive index of the liquid is\", mew\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The refractive index of the liquid is 1.44\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.9, Page number 73" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "x = 0.002945; #Distance through which movable mirror is shifted(cm)\n", - "N = 100; #Number of fringes shifted\n", - "\n", - "#Calculation\n", - "x = x*10**-2; #Distance through which movable mirror is shifted(m)\n", - "lamda = 2*x/N; #Wavelength of light(m)\n", - "lamda = lamda*10**10; #Wavelength of light(A)\n", - "\n", - "#Result\n", - "print \"The wavelength of light is\",lamda, \"angstrom\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The wavelength of light is 5890.0 angstrom\n" - ] - } - ], - "prompt_number": 16 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 3.10, Page number 73" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "import math\n", - "\n", - "#Variable declaration\n", - "lambda1 = 5896; #Wavelength of D1 line of sodium(A)\n", - "lambda2 = 5890; #Wavelength of D2 line of sodium(A)\n", - "\n", - "#Calculation\n", - "lamda = (lambda1+lambda2)/2;\n", - "x = (lamda**2)/(2*(lambda1-lambda2)); #Shift in movable mirror of Michelson Interferometer(A)\n", - "x = x*10**-7; #Shift in movable mirror of Michelson Interferometer(mm)\n", - "x = math.ceil(x*10**4)/10**4; #rounding off the value of D20 to 4 decimals\n", - "\n", - "#Result\n", - "print \"The shift in movable mirror is\",x, \"mm\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The shift in movable mirror is 0.2894 mm\n" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] } ], "metadata": {} diff --git a/Engineering_Physics/Chapter4.ipynb b/Engineering_Physics/Chapter4.ipynb new file mode 100755 index 00000000..5651b165 --- /dev/null +++ b/Engineering_Physics/Chapter4.ipynb @@ -0,0 +1,209 @@ +{ + "metadata": { + "name": "Chapter4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "4: Quantum Physics" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.1, Page number 117" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.62*10**-34; #planck's constant\nlamda = 1.2; #wavelength of photon(Angstrom)\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = (h*c)/(lamda*e); #energy of photon(eV)\nE=math.ceil(E*10)/10; #rounding off to 1 decimal\np = h/lamda; #momentum of photon(kg m/s)\n\n#Result\nprint \"energy of the photon is\",E,\"eV\"\nprint \"momentum of the photon is\",p,\"kg m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "energy of the photon is 10343.8 eV\nmomentum of the photon is 5.51666666667e-24 kg m/s\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.2, Page number 117" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nnew = 900; #frequency(kHz)\nE1 = 10; #power radiated(kW)\n\n#Calculation\nE1 = E1*10**3; #power radiated(W)\nnew = new*10**3; #frequency(Hz)\nE = h*new; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "number of photons emitted per second is 1.67714884696e+31\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.3, Page number 118" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.63*10**-34; #planck's constant\nlamda = 5893; #wavelength of photon(Angstrom)\nE1 = 100; #power of lamp(W) \n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = h*c/lamda; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "number of photons emitted per second is 2.96279537456e+20\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.4, Page number 118" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.6*10**-34; #planck's constant\nm0 = 9.1*10**-31; #mass of photon(kg)\ntheta = 30; #viewing angle(degrees)\nlamda = 2.8*10**-10; #wavelength of photon(m)\n\n#Calculation\nx = math.pi/180; #conversion factor from degrees to radians\ntheta = theta*x; #viewing angle(radian) \nlamda_dash = (2*h*(math.sin(theta/2))**2/(m0*c))+lamda; #wavelength of scattered radiation(m)\nlamda_dash = lamda_dash*10**10; #wavelength of scattered radiation(Angstrom)\nlamda_dash=math.ceil(lamda_dash*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint \"wavelength of scattered radiation is\",lamda_dash,\"Angstrom\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "wavelength of scattered radiation is 2.80324 Angstrom\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.5, Page number 119" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.6*10**-34; #planck's constant\nm = 0.040; #mass of bullet(kg)\nv = 1; #speed of bullet(km/s)\n\n#Calculation\nv = v*10**3; #speed of bullet(m/s)\np = m*v; #momemtun of bullet(kg m/s)\nlamda = h/p; #deBroglie wavelength(m)\nlamda = lamda*10**10; #deBroglie wavelength(Angstrom)\n\n#Result\nprint \"deBroglie wavelength is\",lamda,\"Angstrom\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "deBroglie wavelength is 1.65e-25 Angstrom\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.6, Page number 119" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of particle(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy of particle is\",E,\"J or\",E_eV,\"eV\" ", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "energy of particle is 6.02231407794e-18 J or 37.6 eV\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.7, Page number 120" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 4; #width of well(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.6025*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"minimum energy of electron is\",E,\"J or\",E_eV,\"eV\" ", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "minimum energy of electron is 3.76394629871e-21 J or 0.0235 eV\n" + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.8, Page number 120" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1; #lowest energy state\nn2 = 6; #for 6th excited state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE1 = (n1**2)*(h**2)/(8*m*(a**2)); #energy of electron in ground state(J)\nE6 = (n2**2)*(h**2)/(8*m*(a**2)); #energy of electron in excited state(J)\nE = E6-E1; #energy required to excite the electron(J)\nE_eV = E/e; #energy required to excite the electron(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy required to excite the electron is\",E,\"J or\",E_eV,\"eV\" \nprint \"answer for energy in eV given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "energy required to excite the electron is 2.10780992728e-16 J or 1315.8 eV\nanswer for energy in eV given in the book is wrong\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 4.9, Page number 121" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/sec)\nm0 = 9.11*10**-31; #rest mass of electron(kg)\nphi = 90; #angle of scattering(degrees)\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi = phi*x; ##angle of scattering(radian)\ndelta_lamda = h*(1-math.cos(phi))/(m0*c); #change in wavelength(m)\n\n#Result\nprint \"change in wavelength of X-ray photon is\",delta_lamda,\"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "change in wavelength of X-ray photon is 2.42407610684e-12 m\n" + } + ], + "prompt_number": 9 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter4_1.ipynb b/Engineering_Physics/Chapter4_1.ipynb index c2e7944f..5651b165 100755 --- a/Engineering_Physics/Chapter4_1.ipynb +++ b/Engineering_Physics/Chapter4_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:bd975238ecc341317a545ed613e73ea0b105f0af115e6d7857237510924e96a0" + "name": "Chapter4" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,61 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "4: Diffraction" - ] + "source": "4: Quantum Physics" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.1, Page number 91" - ] + "source": "Example number 4.1, Page number 117" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "D = 50; #Distance between source and the screen(cm)\n", - "lamda = 6563; #Wavelength of light of parallel rays(A)\n", - "d = 0.385; #Width of the slit(mm)\n", - "n1 = 1; #Order of diffraction for first minimum\n", - "n2 = 5; #Order of diffraction for fifth minimum\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of light of parallel rays(cm)\n", - "d = d*10**-1; #Width of the slit(cm)\n", - "#As sin(theta1) = n*lambda/d = x1/D, solving for x1\n", - "x1 = n1*lamda*D/d; #Distance from the centre of the principal maximum to the first minimum(cm)\n", - "x1 = x1*10; #Distance from the centre of the principal maximum to the first minimum(mm)\n", - "x1 = math.ceil(x1*10**3)/10**3; #rounding off the value of x1 to 3 decimals\n", - "x2 = n2*lamda*D/d; #Distance from the centre of the principal maximum to the fifth minimum(cm)\n", - "x2 = x2*10; #Distance from the centre of the principal maximum to the fifth minimum(mm)\n", - "x2 = math.ceil(x2*10**3)/10**3; #rounding off the value of x2 to 3 decimals\n", - "\n", - "#Result\n", - "print \"The Distance from the centre of the principal maximum to the first minimum is\",x1, \"mm\"\n", - "print \"The Distance from the centre of the principal maximum to the fifth minimum is\",x2, \"mm\"\n", - "\n", - "#answer for x2 given in the book is wrong" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.62*10**-34; #planck's constant\nlamda = 1.2; #wavelength of photon(Angstrom)\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = (h*c)/(lamda*e); #energy of photon(eV)\nE=math.ceil(E*10)/10; #rounding off to 1 decimal\np = h/lamda; #momentum of photon(kg m/s)\n\n#Result\nprint \"energy of the photon is\",E,\"eV\"\nprint \"momentum of the photon is\",p,\"kg m/s\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The Distance from the centre of the principal maximum to the first minimum is 0.853 mm\n", - "The Distance from the centre of the principal maximum to the fifth minimum is 4.262 mm\n" - ] + "text": "energy of the photon is 10343.8 eV\nmomentum of the photon is 5.51666666667e-24 kg m/s\n" } ], "prompt_number": 1 @@ -75,405 +38,169 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.2, Page number 91" - ] + "source": "Example number 4.2, Page number 117" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "D = 0.04; #Diameter of circular aperture(cm)\n", - "f = 20; #Focal length of convex lens(cm)\n", - "lamda = 6000; #Wavelength of light used(A)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of light used(cm)\n", - "#We have sin(theta) = 1.22*lambda/D = theta, for small theta\n", - "#For first dark ring\n", - "theta = 1.22*lamda/D; #The half angular width at central maximum(rad)\n", - "r1 = theta*f; #The half width of central maximum for first dark ring(cm)\n", - "r1 = r1*10**2;\n", - "#We have sin(theta) = 5.136*lambda/(%pi*D) = theta, for small theta\n", - "#For second dark ring\n", - "theta = 5.136*lamda/(math.pi*D); #The half angular width at central maximum(rad)\n", - "r2 = theta*f; #The half width of central maximum for second dark ring(cm)\n", - "r2 = r2*10**2;\n", - "r2 = math.ceil(r2*100)/100; #rounding off the value of r2 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The radius of first dark ring is\",r1,\"*10**-2 cm\"\n", - "print \"The radius of second dark ring is\",r2,\"*10**-2 cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nnew = 900; #frequency(kHz)\nE1 = 10; #power radiated(kW)\n\n#Calculation\nE1 = E1*10**3; #power radiated(W)\nnew = new*10**3; #frequency(Hz)\nE = h*new; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The radius of first dark ring is 3.66 *10**-2 cm\n", - "The radius of second dark ring is 4.91 *10**-2 cm\n" - ] + "text": "number of photons emitted per second is 1.67714884696e+31\n" } ], - "prompt_number": 6 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.3, Page number 92" - ] + "source": "Example number 4.3, Page number 118" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "n = 2; #Order of diffraction\n", - "lamda = 650; #Wavelength of light used(nm)\n", - "d = 1.2*10**-3; #Distance between two consecutive slits of grating(cm)\n", - "\n", - "#Calculation\n", - "#We have sin(theta) = n*N*lambda = n*lambda/d, solving for theta\n", - "lamda = lamda*10**-9; #Wavelength of light used(m)\n", - "d = d*10**-2; #Distance between two consecutive slits of grating(m)\n", - "a=n*lamda/d;\n", - "theta = math.asin(a); #Angle at which the 650 nm light produces a second order maximum(rad)\n", - "theta = theta*57.2957795; #angle in degrees\n", - "theta = math.ceil(theta*10**2)/10**2; #rounding off the value of theta to 2 decimals\n", - "\n", - "#Result\n", - "print \"The angle at which the light produces a second order maximum is\",theta, \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.63*10**-34; #planck's constant\nlamda = 5893; #wavelength of photon(Angstrom)\nE1 = 100; #power of lamp(W) \n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = h*c/lamda; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The angle at which the light produces a second order maximum is 6.22 degrees\n" - ] + "text": "number of photons emitted per second is 2.96279537456e+20\nanswer given in the book is wrong\n" } ], - "prompt_number": 7 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.4, Page number 92" - ] + "source": "Example number 4.4, Page number 118" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 650; #Wavelength of light used(nm)\n", - "N = 6000; #Number of lines per cm on grating\n", - "theta = 90; #Angle at which the highest spectral order is obtained(degrees)\n", - "\n", - "#Calculation\n", - "theta = theta*0.0174532925; #Angle at which the highest spectral order is obtained(rad)\n", - "#We have sin(theta) = n*N*lambda, solving for n\n", - "lamda = lamda*10**-9; #Wavelength of light used(m)\n", - "N = N*10**2; #Number of lines per m on grating\n", - "n = math.sin(theta)/(N*lamda); #The highest order of spectra with diffraction grating\n", - "n = math.ceil(n*10**3)/10**3; #rounding off the value of theta to 3 decimals\n", - "i,d = divmod(n, 1); #divides the value of n into integer and decimal parts where i is integer\n", - "\n", - "#Result\n", - "print \"value of n is\",n\n", - "print \"The highest order of spectra obtained with diffraction grating is\",i\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.6*10**-34; #planck's constant\nm0 = 9.1*10**-31; #mass of photon(kg)\ntheta = 30; #viewing angle(degrees)\nlamda = 2.8*10**-10; #wavelength of photon(m)\n\n#Calculation\nx = math.pi/180; #conversion factor from degrees to radians\ntheta = theta*x; #viewing angle(radian) \nlamda_dash = (2*h*(math.sin(theta/2))**2/(m0*c))+lamda; #wavelength of scattered radiation(m)\nlamda_dash = lamda_dash*10**10; #wavelength of scattered radiation(Angstrom)\nlamda_dash=math.ceil(lamda_dash*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint \"wavelength of scattered radiation is\",lamda_dash,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "value of n is 2.565\n", - "The highest order of spectra obtained with diffraction grating is 2.0\n" - ] + "text": "wavelength of scattered radiation is 2.80324 Angstrom\n" } ], - "prompt_number": 8 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.5, Page number 92" - ] + "source": "Example number 4.5, Page number 119" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "N = 4000; #Number of lines per cm on grating\n", - "#For Blue Line\n", - "lamda1 = 450; #Wavelength of blue light(nm)\n", - "n1 = 3; #Order of diffraction spectrum\n", - "#For Red Line\n", - "lamda2 = 700; #Wavelength of red light(nm)\n", - "n2 = 2; #Order of diffraction spectrum\n", - "\n", - "#Calculation\n", - "N = N*10**2; #Number of lines per m on grating\n", - "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", - "lamda2 = lamda2*10**-9; #Wavelength of red light(m)\n", - "#We have sin(theta) = n*N*lambda, solving for sin(theta)\n", - "sin_theta_3 = n1*N*lamda1; #Sine of angle at third order diffraction \n", - "sin_theta_2 = n2*N*lamda2; #Sine of angle at second order diffraction\n", - "\n", - "#Result\n", - "print \"Sine of angle at third order diffraction is\",sin_theta_3\n", - "print \"Sine of angle at second order diffraction is\",sin_theta_2 \n", - "#Check for overlapping\n", - "if (sin_theta_2-sin_theta_3)<0.05:\n", - " print \"The two orders overlap\"\n", - "else:\n", - " print \"The two orders do not overlap\" " - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.6*10**-34; #planck's constant\nm = 0.040; #mass of bullet(kg)\nv = 1; #speed of bullet(km/s)\n\n#Calculation\nv = v*10**3; #speed of bullet(m/s)\np = m*v; #momemtun of bullet(kg m/s)\nlamda = h/p; #deBroglie wavelength(m)\nlamda = lamda*10**10; #deBroglie wavelength(Angstrom)\n\n#Result\nprint \"deBroglie wavelength is\",lamda,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "Sine of angle at third order diffraction is 0.54\n", - "Sine of angle at second order diffraction is 0.56\n", - "The two orders overlap\n" - ] + "text": "deBroglie wavelength is 1.65e-25 Angstrom\n" } ], - "prompt_number": 9 + "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.6, Page number 93" - ] + "source": "Example number 4.6, Page number 119" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "n = 1; #Order of diffraction spectrum\n", - "N = 6000; #Number of lines per cm on diffraction grating\n", - "D = 2; #Distance of screen from the source(m)\n", - "lamda1 = 400; #Wavelength of blue light(nm)\n", - "lamda2 = 750; #Wavelength of blue light(nm)\n", - "\n", - "#Calculation\n", - "N = N*10**2; #Number of lines per m on grating\n", - "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", - "lamda2 = lamda2*10**-9; #Wavelength of blue light(m)\n", - "#We have sin(theta1) = n*N*lamda1, solving for theta1\n", - "theta1 = math.asin(n*N*lamda1); #Angle at first order diffraction for Blue light(rad)\n", - "theta1_d = theta1*57.2957795; #Angle at first order diffraction for Blue light(degrees)\n", - "theta2 = math.asin(n*N*lamda2); #Angle at first order diffraction for Red light(rad)\n", - "theta2_d = theta2*57.2957795; #Angle at first order diffraction for Red light(degrees)\n", - "x1 = D*math.tan(theta1); #Half width position at central maximum for blue color(m)\n", - "x2 = D*math.tan(theta2); #Half width position at central maximum for red color(m)\n", - "x = x2-x1; #width of first order spectrum on the screen(m)\n", - "x = x*10**2; #width of first order spectrum on the screen(cm)\n", - "x = math.ceil(x*10**2)/10**2; #rounding off the value of x to 2 decimals\n", - "\n", - "#Result\n", - "print \"The width of first order spectrum on the screen is\",x, \"cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of particle(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy of particle is\",E,\"J or\",E_eV,\"eV\" ", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The width of first order spectrum on the screen is 51.34 cm\n" - ] + "text": "energy of particle is 6.02231407794e-18 J or 37.6 eV\n" } ], - "prompt_number": 10 + "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.7, Page number 93" - ] + "source": "Example number 4.7, Page number 120" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "w = 5; #Width of the grating(cm)\n", - "N = 32; #Number of lines per mm on grating\n", - "lamda = 640; #Wavelength of light(nm)\n", - "n = 2; #Order of diffraction\n", - "\n", - "#Calculation\n", - "N= N*10; #Number of lines per cm on grating\n", - "N0 = w*N; #Total number of lines on the grating\n", - "d_lambda = lamda/(n*N0); #Separation between wavelengths(nm)\n", - "\n", - "#Result\n", - "print \"The separation between wavelengths which the grating can just resolve is\",d_lambda, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 4; #width of well(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.6025*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"minimum energy of electron is\",E,\"J or\",E_eV,\"eV\" ", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The separation between wavelengths which the grating can just resolve is 0.2 nm\n" - ] + "text": "minimum energy of electron is 3.76394629871e-21 J or 0.0235 eV\n" } ], - "prompt_number": 11 + "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.8, Page number 93" - ] + "source": "Example number 4.8, Page number 120" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 550; #Wavelength of light(nm)\n", - "D = 3.2; #Diameter of circular lens(cm)\n", - "f = 24; #Focal length of the lens(cm) \n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of light(m)\n", - "D = D*10**-2; #Diameter of circular lens(m)\n", - "theta_min = 1.22*lamda/D; #Minimum angle of resolution provided by the lens(rad)\n", - "#As delta_x/f = theta_min, solving for delta_x\n", - "f = f*10**-2; #Focal length of the lens(m) \n", - "delta_x = theta_min*f; #Separation of the centres of the images in the focal plane of lens(m)\n", - "delta_x = delta_x*10**6; #Separation of the centres of the images in the focal plane of lens(micro m)\n", - " \n", - "#Result\n", - "print \"The separation of the centres of the images in the focal plane is\",round(delta_x), \"micro-metre\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1; #lowest energy state\nn2 = 6; #for 6th excited state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE1 = (n1**2)*(h**2)/(8*m*(a**2)); #energy of electron in ground state(J)\nE6 = (n2**2)*(h**2)/(8*m*(a**2)); #energy of electron in excited state(J)\nE = E6-E1; #energy required to excite the electron(J)\nE_eV = E/e; #energy required to excite the electron(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy required to excite the electron is\",E,\"J or\",E_eV,\"eV\" \nprint \"answer for energy in eV given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The separation of the centres of the images in the focal plane is 5.0 micro-metre\n" - ] + "text": "energy required to excite the electron is 2.10780992728e-16 J or 1315.8 eV\nanswer for energy in eV given in the book is wrong\n" } ], - "prompt_number": 12 + "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.9, Page number 94" - ] + "source": "Example number 4.9, Page number 121" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 550; #Wavelength of light(nm)\n", - "D = 20; #Diameter of objective of telescope(cm)\n", - "d = 6; #Distance of two points from the objective of telescope(km)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of light(m)\n", - "D = D*10**-2; #Diameter of objective of telescope(m)\n", - "d = d*10**3; #Distance of two points from the objective of telescope(m)\n", - "theta = 1.22*lamda/D; #Angular separation between two points(rad)\n", - "x = theta*d; #Linear separation between two points(m)\n", - "x = x*10**3; #Linear separation between two points(mm)\n", - "\n", - "#Result\n", - "print \"The linear separation between two points is\",x, \"mm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/sec)\nm0 = 9.11*10**-31; #rest mass of electron(kg)\nphi = 90; #angle of scattering(degrees)\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi = phi*x; ##angle of scattering(radian)\ndelta_lamda = h*(1-math.cos(phi))/(m0*c); #change in wavelength(m)\n\n#Result\nprint \"change in wavelength of X-ray photon is\",delta_lamda,\"m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The linear separation between two points is 20.13 mm\n" - ] + "text": "change in wavelength of X-ray photon is 2.42407610684e-12 m\n" } ], - "prompt_number": 13 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 9 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter5.ipynb b/Engineering_Physics/Chapter5.ipynb new file mode 100755 index 00000000..ba6e0e69 --- /dev/null +++ b/Engineering_Physics/Chapter5.ipynb @@ -0,0 +1,152 @@ +{ + "metadata": { + "name": "Chapter5" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "5: Crystal Physics" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.1, Page number 149, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.2, Page number 150" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 8; #number of atoms per cell\na = 5.43*10**-8; #lattice constant(cm)\nw = 28.1; #atomic weight(gm)\nN = 6.02*10**23; #avagadro number\n\n#Calculation\nac = n/(a**3); #atomic concentration(atoms/cm**3)\nd = ac*w/N; #density of Si(g/cm**3)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"density of Si is\",d,\"g/cm**3\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "density of Si is 2.333 g/cm**3\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.3, Page number 151" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\na = 5; #lattice constant(Angstrom)\n\n#Calculation\na = a*10**-10; #lattice constant(m)\n#to calculate the planar concentration, only equilateral triangular region is considered of length a*math.sqrt(2) and height a*math.sqrt(3/2)\nl = a*math.sqrt(2); #length of face diagonal(m)\nh = a*math.sqrt(3/2); #height of triangle(m)\nA = l*h/2; #area of shaded portion(m**2)\n#every atom at the corner contributes 1/6 to this area.\nn111 = (3/6)*(1/A); #planar concentration(atoms/m**2)\n\n#Result\nprint \"surface density of atoms is\",n111,\"atoms/m**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "surface density of atoms is 2.30940107676e+18 atoms/m**2\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.4, Page number 152" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 4.049; #lattice constant(Angstrom)\nh = 2;\nk = 2;\nl = 0; #miller indices of(2 2 0)\n\n#Calculation\nd = a/math.sqrt(h**2+k**2+l**2); #spacing of planes(Angstrom)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"spacing of planes is\",d,\"Angstrom\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "spacing of planes is 1.432 Angstrom\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.5, Page number 152" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nd110 = 2.03; #distance between planes(Angstrom)\nh = 1;\nk = 1;\nl = 0; #miller indices of(1 1 0)\n\n#Calculation\na = d110*math.sqrt(h**2+k**2+l**2); #size of unit cell(Angstrom)\na=math.ceil(a*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"size of unit cell is\",a,\"Angstrom\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "size of unit cell is 2.871 Angstrom\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.6, Page number 152" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 5.64; #lattice constant(Angstrom)\nh1 = 1;\nk1 = 0;\nl1 = 0; #miller indices of(1 0 0)\nh2 = 1;\nk2 = 1;\nl2 = 0; #miller indices of(1 1 0)\nh3 = 1;\nk3 = 1;\nl3 = 1; #miller indices of(1 1 1)\n\n#Calculation\nd100 = a/math.sqrt(h1**2+k1**2+l1**2); #spacing of planes[100](Angstrom)\nd110 = a/math.sqrt(h2**2+k2**2+l2**2); #spacing of planes[110](Angstrom)\nd111 = a/math.sqrt(h3**2+k3**2+l3**2); #spacing of planes[111](Angstrom)\nd111=math.ceil(d111*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"spacing of plane [100] is\",d100,\"Angstrom\"\nprint \"spacing of plane [110] is\",round(d110),\"Angstrom\"\nprint \"spacing of plane [111] is\",d111,\"Angstrom\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "spacing of plane [100] is 5.64 Angstrom\nspacing of plane [110] is 4.0 Angstrom\nspacing of plane [111] is 3.26 Angstrom\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.7, Page number 153" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 1.605; #radius of atom(Angstrom)\n\n\n#Calculation\nr = r*10**-10; #radius of atom(m)\na = 2*r; #size of unit cell(m)\nc = a*math.sqrt(8/3);\nV = 3*math.sqrt(3)*a**2*c/2; #volume of unit cell(m**3)\n\n#Result\nprint \"volume of unit cell is\",V,\"m**3\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "volume of unit cell is 1.40330266432e-28 m**3\n" + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter5_1.ipynb b/Engineering_Physics/Chapter5_1.ipynb index 86db7d36..ba6e0e69 100755 --- a/Engineering_Physics/Chapter5_1.ipynb +++ b/Engineering_Physics/Chapter5_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:7539e2f35ea93dc5f143cbd45df18f4d6a1bee4d35a1729fab5d759b4b27d8ff" + "name": "Chapter5" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,281 +11,139 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "5: Polarization" - ] + "source": "5: Crystal Physics" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.1, Page number 113" - ] + "source": "Example number 5.1, Page number 149, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.2, Page number 150" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "mew_g = 1.72; #Refractive index of glass\n", - "mew_w = 4/3; #Refractive index of water\n", - "\n", - "#Calculation\n", - "#For polarization to occur on flint glass, tan(i) = mew_g/mew_w\n", - "#Solving for i\n", - "i_g = math.atan(mew_g/mew_w); #angle of incidence for complete polarization for flint glass(rad)\n", - "a = 180/math.pi; #conversion factor from radians to degrees\n", - "i_g = i_g*a; #angle of incidence(degrees)\n", - "i_g = math.ceil(i_g*10**2)/10**2; #rounding off the value of i_g to 2 decimals\n", - "#For polarization to occur on water, tan(i) = mew_w/mew_g\n", - "#Solving for i\n", - "i_w = math.atan(mew_w/mew_g); #angle of incidence for complete polarization for water(rad)\n", - "i_w = i_w*a; #angle of incidence(degrees)\n", - "i_w = math.ceil(i_w*10**3)/10**3; #rounding off the value of i_w to 3 decimals\n", - "\n", - "#Result\n", - "print \"The angle of incidence for complete polarization to occur on flint glass is\",i_g, \"degrees\"\n", - "print \"The angle of incidence for complete polarization to occur on water is\",i_w, \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 8; #number of atoms per cell\na = 5.43*10**-8; #lattice constant(cm)\nw = 28.1; #atomic weight(gm)\nN = 6.02*10**23; #avagadro number\n\n#Calculation\nac = n/(a**3); #atomic concentration(atoms/cm**3)\nd = ac*w/N; #density of Si(g/cm**3)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"density of Si is\",d,\"g/cm**3\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The angle of incidence for complete polarization to occur on flint glass is 52.22 degrees\n", - "The angle of incidence for complete polarization to occur on water is 37.783 degrees\n" - ] + "text": "density of Si is 2.333 g/cm**3\n" } ], - "prompt_number": 5 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.2, Page number 113" - ] + "source": "Example number 5.3, Page number 151" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "I0 = 1; #For simplicity, we assume the intensity of light falling on the second Nicol prism to be unity(W/m**2)\n", - "theta = 30; #Angle through which the crossed Nicol is rotated(degrees)\n", - "\n", - "#Calculation\n", - "theeta = 90-theta; #angle between the planes of transmission after rotating through 30 degrees\n", - "a = math.pi/180; #conversion factor from degrees to radians\n", - "theeta = theeta*a; ##angle between the planes of transmission(rad)\n", - "I = I0*math.cos(theeta)**2; #Intensity of the emerging light from second Nicol(W/m**2)\n", - "T = (I/(2*I0))*100; #Percentage transmission of incident light\n", - "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", - "\n", - "#Result\n", - "print \"The percentage transmission of incident light after emerging through the Nicol prism is\",T, \"%\"" - ], + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\na = 5; #lattice constant(Angstrom)\n\n#Calculation\na = a*10**-10; #lattice constant(m)\n#to calculate the planar concentration, only equilateral triangular region is considered of length a*math.sqrt(2) and height a*math.sqrt(3/2)\nl = a*math.sqrt(2); #length of face diagonal(m)\nh = a*math.sqrt(3/2); #height of triangle(m)\nA = l*h/2; #area of shaded portion(m**2)\n#every atom at the corner contributes 1/6 to this area.\nn111 = (3/6)*(1/A); #planar concentration(atoms/m**2)\n\n#Result\nprint \"surface density of atoms is\",n111,\"atoms/m**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The percentage transmission of incident light after emerging through the Nicol prism is 12.51 %\n" - ] + "text": "surface density of atoms is 2.30940107676e+18 atoms/m**2\n" } ], - "prompt_number": 6 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.3, Page number 113" - ] + "source": "Example number 5.4, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 6000; #Wavelength of incident light(A)\n", - "mew_e = 1.55; #Refractive index of extraordinary ray\n", - "mew_o = 1.54; #Refractive index of ordinary ray\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of incident light(cm)\n", - "t = lamda/(4*(mew_e-mew_o)); #Thickness of Quarter Wave plate of positive crystal(cm)\n", - "\n", - "#Result\n", - "print \"The thickness of Quarter Wave plate is\",t, \"cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 4.049; #lattice constant(Angstrom)\nh = 2;\nk = 2;\nl = 0; #miller indices of(2 2 0)\n\n#Calculation\nd = a/math.sqrt(h**2+k**2+l**2); #spacing of planes(Angstrom)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"spacing of planes is\",d,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The thickness of Quarter Wave plate is 0.0015 cm\n" - ] + "text": "spacing of planes is 1.432 Angstrom\n" } ], - "prompt_number": 7 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.4, Page number 114" - ] + "source": "Example number 5.5, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#Calculation\n", - "#the thickness of a half wave plate of calcite for wavelength lamda is\n", - "#t = lamda/(2*(mew_e - mew_o)) = (2*lamda)/(4*(mew_e - mew_o))\n", - "\n", - "#Result\n", - "print \"The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd110 = 2.03; #distance between planes(Angstrom)\nh = 1;\nk = 1;\nl = 0; #miller indices of(1 1 0)\n\n#Calculation\na = d110*math.sqrt(h**2+k**2+l**2); #size of unit cell(Angstrom)\na=math.ceil(a*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"size of unit cell is\",a,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\n" - ] + "text": "size of unit cell is 2.871 Angstrom\n" } ], - "prompt_number": 8 + "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.5, Page number 114" - ] + "source": "Example number 5.6, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "\n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 500; #Wavelength of incident light(nm)\n", - "mew_e = 1.5508; #Refractive index of extraordinary ray\n", - "mew_o = 1.5418; #Refractive index of ordinary ray\n", - "t = 0.032; #Thickness of quartz plate(mm)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of incident light(m)\n", - "t = t*10**-3; #Thickness of quartz plate(m)\n", - "dx = (mew_e - mew_o)*t; #Path difference between E-ray and O-ray(m)\n", - "dphi = (2*math.pi)/lamda*dx; #Phase retardation for quartz for given wavelength(rad)\n", - "dphi = dphi/math.pi;\n", - "\n", - "#Result\n", - "print \"The phase retardation for quartz for given wavelength is\",dphi, \"pi rad\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 5.64; #lattice constant(Angstrom)\nh1 = 1;\nk1 = 0;\nl1 = 0; #miller indices of(1 0 0)\nh2 = 1;\nk2 = 1;\nl2 = 0; #miller indices of(1 1 0)\nh3 = 1;\nk3 = 1;\nl3 = 1; #miller indices of(1 1 1)\n\n#Calculation\nd100 = a/math.sqrt(h1**2+k1**2+l1**2); #spacing of planes[100](Angstrom)\nd110 = a/math.sqrt(h2**2+k2**2+l2**2); #spacing of planes[110](Angstrom)\nd111 = a/math.sqrt(h3**2+k3**2+l3**2); #spacing of planes[111](Angstrom)\nd111=math.ceil(d111*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"spacing of plane [100] is\",d100,\"Angstrom\"\nprint \"spacing of plane [110] is\",round(d110),\"Angstrom\"\nprint \"spacing of plane [111] is\",d111,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The phase retardation for quartz for given wavelength is 1.152 pi rad\n" - ] + "text": "spacing of plane [100] is 5.64 Angstrom\nspacing of plane [110] is 4.0 Angstrom\nspacing of plane [111] is 3.26 Angstrom\n" } ], - "prompt_number": 9 + "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.6, Page number 114" - ] + "source": "Example number 5.7, Page number 153" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "C = 52; #Critical angle for total internal reflection(degrees)\n", - "\n", - "#Calculation\n", - "a = math.pi/180; #conversion factor from degrees to radians\n", - "C = C*a; #Critical angle for total internal reflection(rad)\n", - "#From Brewster's law, math.tan(i_B) = 1_mew_2\n", - "#Also math.sin(C) = 1_mew_2, so that math.tan(i_B) = math.sin(C), solving for i_B\n", - "i_B = math.atan(math.sin(C)); #Brewster angle at the boundary(rad)\n", - "b = 180/math.pi; #conversion factor from radians to degrees\n", - "i_B = i_B*b; #Brewster angle at the boundary(degrees)\n", - "\n", - "#Result\n", - "print \"The Brewster angle at the boundary between two materials is\",int(i_B), \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 1.605; #radius of atom(Angstrom)\n\n\n#Calculation\nr = r*10**-10; #radius of atom(m)\na = 2*r; #size of unit cell(m)\nc = a*math.sqrt(8/3);\nV = 3*math.sqrt(3)*a**2*c/2; #volume of unit cell(m**3)\n\n#Result\nprint \"volume of unit cell is\",V,\"m**3\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The Brewster angle at the boundary between two materials is 38 degrees\n" - ] + "text": "volume of unit cell is 1.40330266432e-28 m**3\n" } ], - "prompt_number": 13 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 + "prompt_number": 7 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter6.ipynb b/Engineering_Physics/Chapter6.ipynb new file mode 100755 index 00000000..768ed817 --- /dev/null +++ b/Engineering_Physics/Chapter6.ipynb @@ -0,0 +1,356 @@ +{ + "metadata": { + "name": "Chapter6" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "6: Conducting Materials" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.1, Page number 170" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nm = 9.1*10**-31; #mass of electron\nvf = 1*10**6; #Fermi velocity(m/s)\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nEF = m*(vf**2)/(2*e); #Fermi energy(eV)\nEF=math.ceil(EF*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi energy is 2.85 eV\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.2, Page number 170" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nEF0 = 7.04; #Fermi energy at 0K(eV)\nT = 300; #temperature(K)\nk = 1.38*10**-23; #boltzmann constant\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nEF = EF0*(1-(((math.pi**2)/12)*(k*T/(EF0*e))**2)); #Fermi energy(eV)\nEF=math.ceil(EF*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi energy is 7.03993 eV\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.3, Page number 171" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 2.7*10**3; #density of Al(kg/m**3)\nMat = 27; #atomic weight of Al\ntow = 10**-14; #relaxation time(sec)\nNa = 6.022*10**23; #avagadro constant\na = 3*10**3; #number of free electrons per atom\ne = 1.6*10**-19; #charge of electron\nme = 9.1*10**-31; #mass of electron\n\n#Calculation\nn = d*Na*a/Mat; #concentration of atoms(per m**3)\nsigma = n*e**2*tow/me; #conductivity(ohm m)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"conductivity of Al is\",sigma,\"*10**7 ohm m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "conductivity of Al is 5.0824 *10**7 ohm m\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.4, Page number 171" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nsigma = 5.87*10**7; #electrical conductivity(per ohm m)\nK = 390; #thermal conductivity(W/mK)\nT = 20; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"Lorentz number is\",L,\"W ohm/K**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Lorentz number is 2.26756051189e-08 W ohm/K**2\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.5, Page number 172" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 8900; #density of Cu(kg/m**3)\nMat = 63.5; #atomic weight of Cu\ntow = 10**-14; #relaxation time(sec)\nNa = 6.022*10**23; #avagadro constant\na = 1*10**3; #number of free electrons per atom\ne = 1.6*10**-19; #charge of electron\nme = 9.1*10**-31; #mass of electron\n\n#Calculation\nn = d*Na*a/Mat; #concentration of atoms(per m**3)\nsigma = n*e**2*tow/me; #electrical conductivity(ohm m)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**7 ohm m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 2.3745 *10**7 ohm m\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.6, Page number 172" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.54*10**-8; #resistivity(ohm m)\nEF = 5.5; #fermi energy(eV)\nme = 9.1*10**-31; #mass of electron\nepsilon = 100;\ne = 1.6*10**-19; #charge of electron\nn = 5.8*10**28; #concentration of electrons(per m**3)\n\n#Calculation\ntow = me/(rho*n*e**2); #relaxation time(sec)\nmew = e*tow/me; #mobility of electrons(m**2/Vs)\nmew = mew*10**3;\nvd = e*tow*epsilon/me; #drift velocity(m/s)\nvd=math.ceil(vd*10)/10; #rounding off to 1 decimal\nEF = EF*e; #fermi energy((J)\nvF = math.sqrt(2*EF/me); #fermi velocity(m/s)\nvf = vF*10**-6;\nvf=math.ceil(vf*10**3)/10**3; #rounding off to 3 decimals\nlamda_m = vF*tow; #mean free path(m)\n\n#Result\nprint \"relaxation time of electrons is\",tow,\"sec\"\nprint \"mobility of electrons is\",mew,\"*10**-3 m**2/Vs\"\nprint \"drift velocity of electrons is\",vd,\"m/s\"\nprint \"drift velocity given in the book is wrong\"\nprint \"fermi velocity of electrons is\",vf,\"*10**6 m/s\"\nprint \"mean free path is\",lamda_m,\"m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "relaxation time of electrons is 3.97972178683e-14 sec\nmobility of electrons is 6.9973130318 *10**-3 m**2/Vs\ndrift velocity of electrons is 0.7 m/s\ndrift velocity given in the book is wrong\nfermi velocity of electrons is 1.391 *10**6 m/s\nmean free path is 5.53462691011e-08 m\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.7, Page number 174" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.72*10**-8; #electrical resistivity(ohm m)\nL = 2.26*10**-8; #Lorentz number(ohm W/K**2)\nT = 27; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nK = L*T/rho; #thermal conductivity(W/mK)\n\n#Result\nprint \"thermal conductivity is\",int(K),\"W/mK\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "thermal conductivity is 394 W/mK\n" + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.8, Page number 174" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nsigma = 5.87*10**7; #electrical conductivity(per ohm m)\nK = 390; #thermal conductivity(W/mK)\nT = 20; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"Lorentz number is\",L,\"W ohm/K**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Lorentz number is 2.26756051189e-08 W ohm/K**2\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.9, Page number 174" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nE_EF = 0.01; #energy(eV)\ne = 1.6*10**-19; #conversion factor from eV to J\nT = 200; #temperature(K)\nk = 1.38*10**-23; #boltzmann constant(J/K)\n\n#Calculation\nE_EF = E_EF*e; #energy(J)\nA = E_EF/(k*T);\nFofE = 1/(1+(math.exp(A))); #value of F(E)\nFofE=math.ceil(FofE*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"value of F(E) is\",FofE", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "value of F(E) is 0.36\n" + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.10, Page number 175" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 4*10**-8; #mean free path(m)\nn = 8.4*10**28; #density(per m**3)\nvthbar = 1.6*10**6; #average thermal velocity(m/s)\ne = 1.6*10**-19; #charge of electron(c)\nm = 9.11*10**-31; #mass of electron\n\n#Calculation\nsigma = n*e**2*lamda/(m*vthbar); #electrical conductivity(ohm-1 m-1)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**7 ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 5.91 *10**7 ohm-1 m-1\n" + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.11, Page number 176" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ntow = 10**-14; #relaxation time(sec)\nT = 300; #temperature(K)\nn = 6*10**28; #electron concentration(per m**3)\ne = 1.6*10**-19; #charge of electron(c)\nme = 9.1*10**-31; #mass of electron\nk = 1.38*10**-23; #boltzmann constant(J/K)\n\n#Calculation\nsigma = n*e**2*tow/me; #electrical conductivity(ohm-1 m-1)\nsigmaa = sigma*10**-7;\nsigmaa=math.ceil(sigmaa*100)/100; #rounding off to 2 decimals\nK = 3*n*(k**2)*tow*T/(2*me); #thermal conductivity(W/mK)\nK=math.ceil(K*10)/10; #rounding off to 1 decimal\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"electrical conductivity is\",sigmaa,\"*10**7 ohm-1 m-1\"\nprint \"thermal conductivity is\",K,\"W/mK\"\nprint \"Lorentz number is\",L,\"W ohm/K**2\"\nprint \"answer for thermal conductivity and Lorentz number given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 1.69 *10**7 ohm-1 m-1\nthermal conductivity is 56.6 W/mK\nLorentz number is 1.11775173611e-08 W ohm/K**2\nanswer for thermal conductivity and Lorentz number given in the book are wrong\n" + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.12, Page number 177" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 5.8*10**28; #electron concentration(per m**3)\ne = 1.6*10**-19; #charge of electron(c)\nm = 9.1*10**-31; #mass of electron\nrho = 1.54*10**-8; #resistivity of metal(ohm m)\n\n#Calculation\ntow = m/(n*rho*e**2); #relaxation time(sec)\n\n#Result\nprint \"relaxation time is\",tow,\"sec\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "relaxation time is 3.97972178683e-14 sec\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.13, Page number 177" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.54*10**-8; #resistivity(ohm m)\nE = 1; #electric field(V/cm)\nme = 9.1*10**-31; #mass of electron\ne = 1.6*10**-19; #charge of electron\nn = 5.8*10**28; #concentration of electrons(per m**3)\n\n#Calculation\nE = E*10**2; #electric field(V/m)\ntow = me/(rho*n*e**2); #relaxation time(sec)\nvd = e*E*tow/me; #drift velocity(m/s)\nvd=math.ceil(vd*10)/10; #rounding off to 1 decimal\nmew = vd/E; #mobility of electrons(m**2/Vs)\nmew = mew*10**2;\n\n#Result\nprint \"relaxation time of electrons is\",tow,\"sec\"\nprint \"drift velocity of electrons is\",vd,\"m/s\"\nprint \"mobility of electrons is\",mew,\"*10**-2 m**2/Vs\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "relaxation time of electrons is 3.97972178683e-14 sec\ndrift velocity of electrons is 0.7 m/s\nmobility of electrons is 0.7 *10**-2 m**2/Vs\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.14, Page number 178" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nT = 300; #temperature(K)\nl = 2; #length of wire(m)\nR = 0.02; #resistance(ohm)\nI = 15; #current(amp)\nmew = 4.3*10**-3; #mobility(m**2/Vs)\n\n#Calculation\nV = I*R; #voltage drop(V)\nE = V/l; #electric field(V/m)\nvd = mew*E; #drift velocity(m/s)\nvd = vd*10**3;\nvd=math.ceil(vd*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"drift velocity of electrons is\",vd,\"*10**-3 m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "drift velocity of electrons is 0.65 *10**-3 m/s\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.15, Page number 179" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nvf = 0.86*10**6; #fermi velocity(m/s)\nm = 9.1*10**-31; #mass of electron(kg)\ne = 1.6*10**-19; #charge of electron(C)\nk = 1.38*10**-23; #boltzmann constant\n\n#Calculation\nEF = m*vf**2/(2*e); #fermi energy(eV)\nEF=math.ceil(EF*100)/100; #rounding off to 2 decimals\nTF = EF*e/k; #fermi temperature(K)\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"\nprint \"Fermi temperature is\",int(TF),\"K\"\nprint \"answer for fermi temperature given in the book is wrong due to rounding off the value of EF\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi energy is 2.11 eV\nFermi temperature is 24463 K\nanswer for fermi temperature given in the book is wrong due to rounding off the value of EF\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.16, Page number 179" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nTF = 2460; #fermi temperature(K)\nm = 9.11*10**-31; #mass of electron(kg)\nk = 1.38*10**-23; #boltzmann constant\n\n#Calculation\nvF = math.sqrt(2*k*TF/m); #fermi velocity(m/s)\nvF = vF*10**-5;\nvF=math.ceil(vF*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"Fermi velocity is\",vF,\"*10**5 m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi velocity is 2.731 *10**5 m/s\n" + } + ], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter6_1.ipynb b/Engineering_Physics/Chapter6_1.ipynb index 63de6fa0..768ed817 100755 --- a/Engineering_Physics/Chapter6_1.ipynb +++ b/Engineering_Physics/Chapter6_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:761cc333c24ab0bff41cc769407ab239595ed8749ad7bd7c5ee14e4e733b1604" + "name": "Chapter6" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,50 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "6: Crystallography" - ] + "source": "6: Conducting Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.1, Page number 134" - ] + "source": "Example number 6.1, Page number 170" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "M = 23+35.5; #Molecular weight of NaCl(kg/k-mole)\n", - "d = 2.18*10**3; #Density of rock salt(kg/m**3)\n", - "n = 4; #Number of atoms per unit cell for an fcc lattice of NaCl crystal\n", - "N = 6.02*10**26; #Avogadro's No., atoms/k-mol\n", - "\n", - "#Calculation\n", - "a = (n*M/(d*N))**(1/3); #Lattice constant of unit cell of NaCl(m)\n", - "a = a*10**9; ##Lattice constant of unit cell of NaCl(nm)\n", - "a = math.ceil(a*10**3)/10**3; #rounding off the value of a to 3 decimals\n", - "\n", - "#Result\n", - "print \"Lattice parameter for the NaCl crystal is\",a, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nm = 9.1*10**-31; #mass of electron\nvf = 1*10**6; #Fermi velocity(m/s)\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nEF = m*(vf**2)/(2*e); #Fermi energy(eV)\nEF=math.ceil(EF*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "Lattice parameter for the NaCl crystal is 0.563 nm\n" - ] + "text": "Fermi energy is 2.85 eV\n" } ], "prompt_number": 1 @@ -64,39 +38,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.2, Page number 134" - ] + "source": "Example number 6.2, Page number 170" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "m = 3;\n", - "n = 2; \n", - "p = 1; #Coefficients of intercepts along three axes\n", - "\n", - "#Calculation\n", - "#reciprocals of the intercepts are 1/m, 1/n, 1/p i.e 1/3, 1/2, 1\n", - "#multiplying by LCM the reciprocals become 2, 3, 6\n", - "\n", - "#Result\n", - "print \"The required miller indices are : (2, 3, 6)\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nEF0 = 7.04; #Fermi energy at 0K(eV)\nT = 300; #temperature(K)\nk = 1.38*10**-23; #boltzmann constant\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nEF = EF0*(1-(((math.pi**2)/12)*(k*T/(EF0*e))**2)); #Fermi energy(eV)\nEF=math.ceil(EF*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The required miller indices are : (2, 3, 6)\n" - ] + "text": "Fermi energy is 7.03993 eV\n" } ], "prompt_number": 2 @@ -105,38 +59,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.3, Page number 135" - ] + "source": "Example number 6.3, Page number 171" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "import math\n", - "\n", - "#Variable declaration\n", - "m = 2; #Coefficient of intercept along x-axis\n", - "#n = infinite Coefficient of intercept along y-axis\n", - "p = 3/2; #Coefficient of intercept along z-axis\n", - "\n", - "#Calculation\n", - "#reciprocals of the intercepts are 1/m, 1/n, 1/p i.e 1/2, 0, 2/3\n", - "#multiplying by LCM the reciprocals become 3, 0, 4\n", - "\n", - "#Result\n", - "print \"The required miller indices are : (3, 0, 4)\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 2.7*10**3; #density of Al(kg/m**3)\nMat = 27; #atomic weight of Al\ntow = 10**-14; #relaxation time(sec)\nNa = 6.022*10**23; #avagadro constant\na = 3*10**3; #number of free electrons per atom\ne = 1.6*10**-19; #charge of electron\nme = 9.1*10**-31; #mass of electron\n\n#Calculation\nn = d*Na*a/Mat; #concentration of atoms(per m**3)\nsigma = n*e**2*tow/me; #conductivity(ohm m)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"conductivity of Al is\",sigma,\"*10**7 ohm m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The required miller indices are : (3, 0, 4)\n" - ] + "text": "conductivity of Al is 5.0824 *10**7 ohm m\n" } ], "prompt_number": 3 @@ -145,59 +80,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.4, Sketching not possible" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 6.5, Page number 136" - ] + "source": "Example number 6.4, Page number 171" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "#For (110) planes\n", - "h1 = 1;\n", - "k1 = 1;\n", - "l1 = 0; #Miller Indices for planes in a cubic crystal\n", - "a1 = 0.43; #Interatomic spacing(nm)\n", - "#For (212) planes\n", - "h2 = 2; \n", - "k2 = 1;\n", - "l2 = 2; #Miller Indices for planes in a cubic crystal\n", - "a2 = 0.43; #Interatomic spacing(nm)\n", - "\n", - "#Calculation\n", - "d1 = a1/(h1**2+k1**2+l1**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", - "d1 = math.ceil(d1*10**4)/10**4; #rounding off the value of d1 to 4 decimals\n", - "d2 = a2/(h2**2+k2**2+l2**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", - "d2 = math.ceil(d2*10**4)/10**4; #rounding off the value of d2 to 4 decimals\n", - "\n", - "#Result\n", - "print \"The interplanar spacing between consecutive (110) planes is\",d1, \"nm\";\n", - "print \"The interplanar spacing between consecutive (212) planes is\",d2, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nsigma = 5.87*10**7; #electrical conductivity(per ohm m)\nK = 390; #thermal conductivity(W/mK)\nT = 20; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"Lorentz number is\",L,\"W ohm/K**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The interplanar spacing between consecutive (110) planes is 0.3041 nm\n", - "The interplanar spacing between consecutive (212) planes is 0.1434 nm\n" - ] + "text": "Lorentz number is 2.26756051189e-08 W ohm/K**2\n" } ], "prompt_number": 4 @@ -206,42 +101,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.6, Page number 136" - ] + "source": "Example number 6.5, Page number 172" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "h = 2;\n", - "k = 3;\n", - "l = 1; #Miller Indices for planes in a cubic crystal\n", - "r = 0.175; #Atomic radius of fcc lattice(nm)\n", - "\n", - "#Calculation\n", - "a = 2*math.sqrt(2)*r; #Interatomic spacing of fcc lattice(nm)\n", - "d = a/(h**2+k**2+l**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", - "d = math.ceil(d*10**4)/10**4; #rounding off the value of d to 4 decimals\n", - "\n", - "#Result\n", - "print \"The interplanar spacing between consecutive (231) planes is\",d, \"nm\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd = 8900; #density of Cu(kg/m**3)\nMat = 63.5; #atomic weight of Cu\ntow = 10**-14; #relaxation time(sec)\nNa = 6.022*10**23; #avagadro constant\na = 1*10**3; #number of free electrons per atom\ne = 1.6*10**-19; #charge of electron\nme = 9.1*10**-31; #mass of electron\n\n#Calculation\nn = d*Na*a/Mat; #concentration of atoms(per m**3)\nsigma = n*e**2*tow/me; #electrical conductivity(ohm m)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**7 ohm m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The interplanar spacing between consecutive (231) planes is 0.1323 nm\n" - ] + "text": "electrical conductivity is 2.3745 *10**7 ohm m\n" } ], "prompt_number": 5 @@ -250,47 +122,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.7, Page number 136" - ] + "source": "Example number 6.6, Page number 172" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 1.44; #Wavelength of X-rays(A)\n", - "d = 2.8; #Interplanar spacing of rocksalt crystal(A)\n", - "n1 = 1; #For 1st Order diffraction\n", - "n2 = 2; #For 2nd Order diffraction\n", - "\n", - "#Calculation\n", - "theta1 = math.asin(n1*lamda/(2*d)); #Angle of diffraction(radians)\n", - "theeta1 = theta1*57.2957795; #Angle of diffraction(degrees)\n", - "theeta1 = math.ceil(theeta1*10**2)/10**2; #rounding off the value of theeta1 to 2 decimals\n", - "theta2 = math.asin(n2*lamda/(2*d)); #Angle of diffraction(radians)\n", - "theeta2 = theta2*57.2957795; #Angle of diffraction(degrees)\n", - "theeta2 = math.ceil(theeta2*10**2)/10**2; #rounding off the value of theeta2 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The angle of diffraction for first order maxima is\",theeta1, \"degrees\"\n", - "print \"The angle of diffraction for second order maxima is\",theeta2, \"degrees\"\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.54*10**-8; #resistivity(ohm m)\nEF = 5.5; #fermi energy(eV)\nme = 9.1*10**-31; #mass of electron\nepsilon = 100;\ne = 1.6*10**-19; #charge of electron\nn = 5.8*10**28; #concentration of electrons(per m**3)\n\n#Calculation\ntow = me/(rho*n*e**2); #relaxation time(sec)\nmew = e*tow/me; #mobility of electrons(m**2/Vs)\nmew = mew*10**3;\nvd = e*tow*epsilon/me; #drift velocity(m/s)\nvd=math.ceil(vd*10)/10; #rounding off to 1 decimal\nEF = EF*e; #fermi energy((J)\nvF = math.sqrt(2*EF/me); #fermi velocity(m/s)\nvf = vF*10**-6;\nvf=math.ceil(vf*10**3)/10**3; #rounding off to 3 decimals\nlamda_m = vF*tow; #mean free path(m)\n\n#Result\nprint \"relaxation time of electrons is\",tow,\"sec\"\nprint \"mobility of electrons is\",mew,\"*10**-3 m**2/Vs\"\nprint \"drift velocity of electrons is\",vd,\"m/s\"\nprint \"drift velocity given in the book is wrong\"\nprint \"fermi velocity of electrons is\",vf,\"*10**6 m/s\"\nprint \"mean free path is\",lamda_m,\"m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The angle of diffraction for first order maxima is 14.91 degrees\n", - "The angle of diffraction for second order maxima is 30.95 degrees\n" - ] + "text": "relaxation time of electrons is 3.97972178683e-14 sec\nmobility of electrons is 6.9973130318 *10**-3 m**2/Vs\ndrift velocity of electrons is 0.7 m/s\ndrift velocity given in the book is wrong\nfermi velocity of electrons is 1.391 *10**6 m/s\nmean free path is 5.53462691011e-08 m\n" } ], "prompt_number": 6 @@ -299,42 +143,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.8, Page number 136" - ] + "source": "Example number 6.7, Page number 174" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "a = 1; #For convenience, assume interatomic spacing to be unity(m)\n", - "\n", - "#Calculation\n", - "N = 8*(1/8) + 6*(1/2); #total number of spheres in a unit cell\n", - "r = a/(2*math.sqrt(2)); #The atomic radius(m)\n", - "V_atom = N*(4/3)*math.pi*r**3; #Volume of atoms(m**3)\n", - "V_uc = a**3; #Volume of unit cell(m**3)\n", - "PV = (V_atom/V_uc)*100; #percentage of actual volume\n", - "PV = math.ceil(PV*10)/10; #rounding off the value of PV to 1 decimal\n", - "\n", - "#Result\n", - "print \"The percentage of actual volume occupied by the spheres in fcc structure is\",PV, \"percent\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.72*10**-8; #electrical resistivity(ohm m)\nL = 2.26*10**-8; #Lorentz number(ohm W/K**2)\nT = 27; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nK = L*T/rho; #thermal conductivity(W/mK)\n\n#Result\nprint \"thermal conductivity is\",int(K),\"W/mK\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The percentage of actual volume occupied by the spheres in fcc structure is 74.1 percent\n" - ] + "text": "thermal conductivity is 394 W/mK\n" } ], "prompt_number": 7 @@ -343,56 +164,40 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.9, Page number 137" - ] + "source": "Example number 6.8, Page number 174" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "#For (221) planes\n", - "h = 2; \n", - "k = 2; \n", - "l = 1; #Miller Indices for planes in a cubic crystal\n", - "a = 2.68; #Interatomic spacing(A)\n", - "n1 = 1; #First Order of diffraction \n", - "n2 = 2; #Second order of diffraction\n", - "theta1 = 8.5; #Glancing angle at which Bragg's reflection occurs(degrees)\n", - "\n", - "#Calculation\n", - "theta1 = theta1*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", - "a = a*10**-10; #Interatomic spacing(m)\n", - "d = a/(h**2+k**2+l**2)**(1/2); #The interplanar spacing for cubic crystal(m)\n", - "lamda = 2*d*math.sin(theta1)/n1; #Bragg's Law for wavelength of X-rays(m)\n", - "lamda_A = lamda*10**10; #Bragg's Law for wavelength of X-rays(A)\n", - "lamda_A = math.ceil(lamda_A*10**4)/10**4; #rounding off the value of lamda_A to 4 decimals\n", - "theta2 = math.asin(n2*lamda/(2*d)); #Angle at which second order Bragg reflection occurs(radians)\n", - "theta2 = theta2*57.2957795; #Angle at which second order Bragg reflection occurs(degrees)\n", - "theta2 = math.ceil(theta2*10)/10; #rounding off the value of theta2 to 1 decimal\n", - "\n", - "#Result\n", - "print \"The interplanar spacing between consecutive (221) planes is\",d, \"m\"\n", - "print \"The wavelength of X-rays is\",lamda_A, \"angstrom\"\n", - "print \"The angle at which second order Bragg reflection occurs is\",theta2, \"degrees\"" + "input": "#importing modules\nimport math\n\n#Variable declaration\nsigma = 5.87*10**7; #electrical conductivity(per ohm m)\nK = 390; #thermal conductivity(W/mK)\nT = 20; #temperature(C)\n\n#Calculation\nT = T+273; #temperature(K)\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"Lorentz number is\",L,\"W ohm/K**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Lorentz number is 2.26756051189e-08 W ohm/K**2\n" + } ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.9, Page number 174" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nE_EF = 0.01; #energy(eV)\ne = 1.6*10**-19; #conversion factor from eV to J\nT = 200; #temperature(K)\nk = 1.38*10**-23; #boltzmann constant(J/K)\n\n#Calculation\nE_EF = E_EF*e; #energy(J)\nA = E_EF/(k*T);\nFofE = 1/(1+(math.exp(A))); #value of F(E)\nFofE=math.ceil(FofE*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"value of F(E) is\",FofE", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The interplanar spacing between consecutive (221) planes is 8.93333333333e-11 m\n", - "The wavelength of X-rays is 0.2641 angstrom\n", - "The angle at which second order Bragg reflection occurs is 17.2 degrees\n" - ] + "text": "value of F(E) is 0.36\n" } ], "prompt_number": 9 @@ -401,45 +206,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.10, Page number 137" - ] + "source": "Example number 6.10, Page number 175" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "h = 1; \n", - "k = 1;\n", - "l = 0; #Miller Indices for planes in a cubic crystal\n", - "n = 1; #First Order of diffraction \n", - "theta = 25; #Glancing angle at which Bragg's reflection occurs(degrees)\n", - "lamda = 0.7; #Wavelength of X-rays(A)\n", - "\n", - "#Calculation\n", - "theta = theta*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", - "d = n*lamda/(2*math.sin(theta)); #Interplanar spacing of cubic crystal(A)\n", - "a = d*(h**2+k**2+l**2)**(1/2); #The lattice parameter for cubic crystal(A)\n", - "a = math.ceil(a*10**3)/10**3; #rounding off the value of a to 3 decimals\n", - "\n", - "#Result\n", - "print \"The lattice parameter for cubic crystal is\",a, \"angstrom\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nlamda = 4*10**-8; #mean free path(m)\nn = 8.4*10**28; #density(per m**3)\nvthbar = 1.6*10**6; #average thermal velocity(m/s)\ne = 1.6*10**-19; #charge of electron(c)\nm = 9.11*10**-31; #mass of electron\n\n#Calculation\nsigma = n*e**2*lamda/(m*vthbar); #electrical conductivity(ohm-1 m-1)\nsigma = sigma*10**-7;\nsigma=math.ceil(sigma*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**7 ohm-1 m-1\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The lattice parameter for cubic crystal is 1.172 angstrom\n" - ] + "text": "electrical conductivity is 5.91 *10**7 ohm-1 m-1\n" } ], "prompt_number": 10 @@ -448,46 +227,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.11, Page number 138" - ] + "source": "Example number 6.11, Page number 176" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "d = 0.31; #Interplanar spacing(nm)\n", - "n = 1; #First Order of diffraction \n", - "theta = 9.25; #Glancing angle at which Bragg's reflection occurs(degrees)\n", - "theta_max = 90; #Maximum possible angle at which reflection can occur(degrees)\n", - "theta_max = theta_max*0.0174532925; #Maximum possible angle at which reflection can occur(radians)\n", - "\n", - "#Calculation\n", - "theta = theta*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", - "lamda = 2*d*math.sin(theta)/n; #Wavelength of X-rays(nm) (Bragg's Law)\n", - "lamda = math.ceil(lamda*10**5)/10**5; #rounding off the value of lamda to 5 decimals\n", - "n = 2*d*math.sin(theta_max)/lamda; #Maximum possible order of diffraction\n", - "\n", - "#Result\n", - "print \"The wavelength of X-rays is\",lamda, \"nm\"\n", - "print \"The Maximum possible order of diffraction is\",round(n)" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\ntow = 10**-14; #relaxation time(sec)\nT = 300; #temperature(K)\nn = 6*10**28; #electron concentration(per m**3)\ne = 1.6*10**-19; #charge of electron(c)\nme = 9.1*10**-31; #mass of electron\nk = 1.38*10**-23; #boltzmann constant(J/K)\n\n#Calculation\nsigma = n*e**2*tow/me; #electrical conductivity(ohm-1 m-1)\nsigmaa = sigma*10**-7;\nsigmaa=math.ceil(sigmaa*100)/100; #rounding off to 2 decimals\nK = 3*n*(k**2)*tow*T/(2*me); #thermal conductivity(W/mK)\nK=math.ceil(K*10)/10; #rounding off to 1 decimal\nL = K/(sigma*T); #Lorentz number(W ohm/K**2)\n\n#Result\nprint \"electrical conductivity is\",sigmaa,\"*10**7 ohm-1 m-1\"\nprint \"thermal conductivity is\",K,\"W/mK\"\nprint \"Lorentz number is\",L,\"W ohm/K**2\"\nprint \"answer for thermal conductivity and Lorentz number given in the book are wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The wavelength of X-rays is 0.09967 nm\n", - "The Maximum possible order of diffraction is 6.0\n" - ] + "text": "electrical conductivity is 1.69 *10**7 ohm-1 m-1\nthermal conductivity is 56.6 W/mK\nLorentz number is 1.11775173611e-08 W ohm/K**2\nanswer for thermal conductivity and Lorentz number given in the book are wrong\n" } ], "prompt_number": 11 @@ -496,51 +248,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.12, Page number 138" - ] + "source": "Example number 6.12, Page number 177" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "#For (110) planes\n", - "h1 = 1;\n", - "k1 = 1;\n", - "l1 = 0; #Miller indices for (110) planes\n", - "d_110 = 0.195; #Interplanar spacing between (110) planes(nm)\n", - "#For (210) planes\n", - "h2 = 2;\n", - "k2 = 1; \n", - "l2 = 0; #Miller indices for (110) planes\n", - "n = 2; #Second Order of diffraction \n", - "lamda = 0.071; #Wavelength of X-rays(nm)\n", - "\n", - "#Calculation\n", - "a = d_110*(h1**2 + k1**2 + l1**2)**(1/2); #Lattice parameter for bcc crystal(nm)\n", - "d_210 = a/(h2**2 + k2**2 + l2**2)**(1/2); #Interplanar spacing between (210) planes(nm)\n", - "theta = math.asin(n*lamda/(2*d_210)); #Bragg reflection angle for the second order diffraction(radians)\n", - "theeta = theta*57.2957795; #Bragg reflection angle for the second order diffraction(degrees)\n", - "theeta = math.ceil(theeta*10**3)/10**3; #rounding off the value of theeta to 3 decimals\n", - "\n", - "#Result\n", - "print \"Bragg reflection angle for the second order diffraction is\",theeta, \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 5.8*10**28; #electron concentration(per m**3)\ne = 1.6*10**-19; #charge of electron(c)\nm = 9.1*10**-31; #mass of electron\nrho = 1.54*10**-8; #resistivity of metal(ohm m)\n\n#Calculation\ntow = m/(n*rho*e**2); #relaxation time(sec)\n\n#Result\nprint \"relaxation time is\",tow,\"sec\"\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "Bragg reflection angle for the second order diffraction is 35.149 degrees\n" - ] + "text": "relaxation time is 3.97972178683e-14 sec\nanswer given in the book is wrong\n" } ], "prompt_number": 12 @@ -549,44 +269,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.13, Page number 138" - ] + "source": "Example number 6.13, Page number 177" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "d = 2182; #Density of rock salt(kg/m**3)\n", - "n = 4; #Number of atoms per unit cell for an fcc lattice of NaCl crystal\n", - "N = 6.02*10**26; #Avogadro's number(atoms/k-mol)\n", - "\n", - "#Calculation\n", - "M = 23+35.5; #Molecular weight of NaCl(kg/k-mole)\n", - "#V = a^3 = M*n/(N*d)\n", - "a = (n*M/(d*N))**(1/3); #Lattice constant of unit cell of NaCl(m)\n", - "D = a/2; #distance between nearest neighbours(m)\n", - "D = D*10**9; #distance between nearest neighbours(nm)\n", - "D = math.ceil(D*10**4)/10**4; #rounding off the value of D to 4 decimals\n", - "\n", - "#Result\n", - "print \"The distance between nearest neighbours of NaCl structure is\",D, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nrho = 1.54*10**-8; #resistivity(ohm m)\nE = 1; #electric field(V/cm)\nme = 9.1*10**-31; #mass of electron\ne = 1.6*10**-19; #charge of electron\nn = 5.8*10**28; #concentration of electrons(per m**3)\n\n#Calculation\nE = E*10**2; #electric field(V/m)\ntow = me/(rho*n*e**2); #relaxation time(sec)\nvd = e*E*tow/me; #drift velocity(m/s)\nvd=math.ceil(vd*10)/10; #rounding off to 1 decimal\nmew = vd/E; #mobility of electrons(m**2/Vs)\nmew = mew*10**2;\n\n#Result\nprint \"relaxation time of electrons is\",tow,\"sec\"\nprint \"drift velocity of electrons is\",vd,\"m/s\"\nprint \"mobility of electrons is\",mew,\"*10**-2 m**2/Vs\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The distance between nearest neighbours of NaCl structure is 0.2814 nm\n" - ] + "text": "relaxation time of electrons is 3.97972178683e-14 sec\ndrift velocity of electrons is 0.7 m/s\nmobility of electrons is 0.7 *10**-2 m**2/Vs\n" } ], "prompt_number": 13 @@ -595,59 +290,64 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 6.14, Page number 139" - ] + "source": "Example number 6.14, Page number 178" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "r1 = 1.258; #Atomic radius of bcc structure of iron(A)\n", - "N1 = 2; #Number of atoms per unit cell in bcc structure\n", - "#For fcc structure\n", - "r2 = 1.292; #Atomic radius of fcc structure of iron(A)\n", - "N2 = 4; #Number of atoms per unit cell in fcc structure\n", - "\n", - "#Calculation\n", - "a1 = 4*r1/math.sqrt(3); #Lattice parameter of bcc structure of iron(A)\n", - "V1 = a1**3; #Volume of bcc unit cell(A)\n", - "V_atom_bcc = V1/N1; #Volume occupied by one atom(A)\n", - "a2 = 2*math.sqrt(2)*r2; #Lattice parameter of fcc structure of iron(A)\n", - "V2 = a2**3; #Volume of fcc unit cell(A)\n", - "V_atom_fcc = V2/N2; #Volume occupied by one atom(A)\n", - "delta_V = (V_atom_bcc-V_atom_fcc)/V_atom_bcc*100; #Percentage change in volume due to structural change of iron\n", - "delta_V = math.ceil(delta_V*10**3)/10**3; #rounding off the value of delta_V to 3 decimals\n", - "\n", - "#Result\n", - "print \"The percentage change in volume of iron is\",delta_V, \"percent\"" + "input": "#importing modules\nimport math\n\n#Variable declaration\nT = 300; #temperature(K)\nl = 2; #length of wire(m)\nR = 0.02; #resistance(ohm)\nI = 15; #current(amp)\nmew = 4.3*10**-3; #mobility(m**2/Vs)\n\n#Calculation\nV = I*R; #voltage drop(V)\nE = V/l; #electric field(V/m)\nvd = mew*E; #drift velocity(m/s)\nvd = vd*10**3;\nvd=math.ceil(vd*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"drift velocity of electrons is\",vd,\"*10**-3 m/s\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "drift velocity of electrons is 0.65 *10**-3 m/s\n" + } ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.15, Page number 179" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nvf = 0.86*10**6; #fermi velocity(m/s)\nm = 9.1*10**-31; #mass of electron(kg)\ne = 1.6*10**-19; #charge of electron(C)\nk = 1.38*10**-23; #boltzmann constant\n\n#Calculation\nEF = m*vf**2/(2*e); #fermi energy(eV)\nEF=math.ceil(EF*100)/100; #rounding off to 2 decimals\nTF = EF*e/k; #fermi temperature(K)\n\n#Result\nprint \"Fermi energy is\",EF,\"eV\"\nprint \"Fermi temperature is\",int(TF),\"K\"\nprint \"answer for fermi temperature given in the book is wrong due to rounding off the value of EF\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The percentage change in volume of iron is 0.494 percent\n" - ] + "text": "Fermi energy is 2.11 eV\nFermi temperature is 24463 K\nanswer for fermi temperature given in the book is wrong due to rounding off the value of EF\n" } ], "prompt_number": 15 }, { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 6.16, Page number 179" + }, + { "cell_type": "code", "collapsed": false, - "input": [], + "input": "#importing modules\nimport math\n\n#Variable declaration\nTF = 2460; #fermi temperature(K)\nm = 9.11*10**-31; #mass of electron(kg)\nk = 1.38*10**-23; #boltzmann constant\n\n#Calculation\nvF = math.sqrt(2*k*TF/m); #fermi velocity(m/s)\nvF = vF*10**-5;\nvF=math.ceil(vF*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"Fermi velocity is\",vF,\"*10**5 m/s\"", "language": "python", "metadata": {}, - "outputs": [] + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi velocity is 2.731 *10**5 m/s\n" + } + ], + "prompt_number": 16 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter7.ipynb b/Engineering_Physics/Chapter7.ipynb new file mode 100755 index 00000000..d6a7ab3d --- /dev/null +++ b/Engineering_Physics/Chapter7.ipynb @@ -0,0 +1,468 @@ +{ + "metadata": { + "name": "Chapter7", + "signature": "sha256:043709ddd748250fcd3232cc251c6d71d665f281189e172a4c8d9b59233bdcee" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "7: Semiconducting Materials" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.1, Page number 208" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nme = 9.11*10**-31; #mass of electron(kg)\nepsilon_r = 13.2; \nepsilon0 = 8.85*10**-12;\nh = 6.63*10**-34;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nm_nc = 0.067*me;\nE = m_nc*e**4/(8*(epsilon0*epsilon_r*h)**2); #energy(J)\nE = E/e; #energy(eV)\nE = math.ceil(E*10**5)/10**5; #rounding off to 5 decimals\nE_meV = E*10**3; #energy(meV)\n\n#Result\nprint \"donor binding energy is\",E,\"eV or\",E_meV,\"meV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "donor binding energy is 0.00521 eV or 5.21 meV\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.2, Page number 208" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\n\n#Variable declaration\nNd = 10**16; #donor concentration(atoms/cm**3)\nni = 1.5*10**10; #concentration(per cm**3)\nT = 300; #temperature(K)\nkT = 0.0259;\n\n#Calculation\nn0 = Nd; #for Nd>>ni, assume n0=Nd\np0 = ni**2/n0; #equilibrium hole concentration(per cm**3)\np0 = p0*10**-4;\nEF_Ei = kT*np.log(n0/ni);\nEF_Ei = math.ceil(EF_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n\n#Result\nprint \"equilibrium hole concentration is\",p0,\"*10**4 per cm**3\"\nprint \"value of EF-Ei is\",EF_Ei,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "equilibrium hole concentration is 2.25 *10**4 per cm**3\nvalue of EF-Ei is 0.3474 eV\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.3, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nNd = 10**14; #donor density(atoms/cm**3)\nmew_n = 3900;\n\n#Calculation\nn = Nd;\nsigma = n*e*mew_n; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*100)/100; #rounding off to 2 decimals\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 16.03 ohm cm\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.4, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nn0 = 5*10**16; #donor density(atoms/cm**3)\nmew_0 = 800;\nIx = 2; #current(mA)\nBz = 5*10**-5;\nd = 200; #thickness(micrometre)\n\n#Calculation\nIx = Ix*10**-3; #current(A)\nd = d*10**-4; #thickness(m)\nsigma = e*n0*mew_0; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\nRH = -1/(e*n0); #Hall coefficient(cm**3/C)\nVH = Ix*Bz*RH/d; #Hall voltage(V)\nVH = VH*10**5;\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"\nprint \"Hall coefficient is\",RH,\"cm**3/C\"\nprint \"Hall voltage is\",VH,\"*10**-5 V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 0.1563 ohm cm\nHall coefficient is -125.0 cm**3/C\nHall voltage is -62.5 *10**-5 V\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.5, Page number 210" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\nEg = 0.7; #band gap(eV)\nme = 9.11*10**-31; #mass of electron(kg)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nh = 6.625*10**-34;\nkT = 0.0259;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\na = (2*math.pi*k*T/(h**2))**(3/2);\nb = (mn_star*mp_star)**(3/4);\nc = math.exp(-Eg/(2*kT));\nni = 2*a*b*c; #intrinsic concentration(per m**3)\nsigma = ni*e*(mew_n+mew_p); #intrinsic conductivity(per ohm m)\nsigma = math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\nrho = 1/sigma; #intrinsic resistivity(ohm m)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"intrinsic concentration is\",ni,\"per m**3\"\nprint \"intrinsic conductivity is\",sigma,\"per ohm m\"\nprint \"intrinsic resistivity is\",rho,\"ohm m\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic concentration is 1.02825111151e+19 per m**3\nintrinsic conductivity is 0.9872 per ohm m\nintrinsic resistivity is 1.013 ohm m\nanswers given in the book are wrong\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.6, Page number 211" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nNd = 10**16; #donor concentration(per cm**3)\nni = 1.45*10**10; #concentration(per cm**3)\nkT = 0.0259;\n\n#Calculation\n#ni = Nc*math.exp(-(Ec-Ei)/kT)\n#Nd = Nc*(math.exp(-(Ec-Efd)/kT)\n#dividing Nd/ni we get \nEFd_Ei = kT*np.log(Nd/ni);\nEFd_Ei = math.ceil(EFd_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"Fermi energy is\",EFd_Ei,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Fermi energy is 0.3482 eV\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.7, Page number 211, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.8, Page number 212" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.36; #electron mobility(m**2/Vs)\nmew_p = 0.17; #hole mobility(m**2/Vs)\nrho = 2.12; #resistivity(ohm m)\nme = 9.11*10**-31; #mass of electron(kg)\nkT = 0.0259;\nh = 6.625*10**-34;\nk = 1.38*10**-23; #boltzmann constant\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\nsigma = 1/rho; #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\nni = sigma/(e*(mew_n+mew_p)); #concentration of electrons(per m**3)\na = (2*math.pi*kT/(h**2))**(3/2);\nNc = 2*a*(mn_star**(3/2)); \nNv = 2*a*(mp_star**(3/2)); \nb = (Nc*Nv)**(1/2);\nEg = 2*kT*np.log(b/ni);\n\n#Result\nprint \"forbidden energy gap is\",Eg,\"eV\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "forbidden energy gap is 4.09465494989 eV\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.9, Page number 213" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nni = 2.4*10**19; #concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"conductivity of sample is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "conductivity of sample is 2.228 ohm-1 m-1\n" + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.10, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nEc = 0.3; #initial position(eV)\nT1 = 300; #initial temperature(K)\nT2 = 330; #increased temperature\n\n#Calculation\n#Ec/T1 = Ec_EF330/T2\nEc_EF330 = Ec*T2/T1; #new position of Fermi level(eV)\n\n#Result\nprint \"new position of Fermi level is\",Ec_EF330,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "new position of Fermi level is 0.33 eV\n" + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.11, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nme = 9.1*10**-31; #mass of electron(kg)\nh = 6.63*10**-34; #planck's constant\nEc_Ev = 1.1; #energy gap(eV)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nme_star = 0.31*me;\nA = (2*math.pi*k*T*me_star/(h**2))**(3/2);\nB = math.exp(-(Ec_Ev*e)/(2*k*T));\nni = A*B; #concentration in conduction band(per m**3)\n\n#Result\nprint \"intrinsic electron concentration is\",ni,\"per m**3\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic electron concentration is 1.26605935487e+15 per m**3\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.12, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nRH = 0.55*10**-10; #Hall coefficient(m**3/As)\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nmew = RH*sigma; #drift mobility(m**2/Vs)\nmew = mew*10**3;\nmew = math.ceil(mew*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"drift mobility of electrons is\",mew,\"*10**-3 m**2/Vs\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "drift mobility of electrons is 3.25 *10**-3 m**2/Vs\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.13, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nA = 6.022*10**23; #avagadro constant\nd = 8.96*10**-9; #density(kg/m**3)\nn = 9.932*10**14; #no. of free electrons per atom\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\ne = 1.6*10**-19; #electron charge(C)\nmew = 3.2*10**-3; #drift mobility(m**2/Vs)\nw = 63.5; #atomic weight of Cu(kg)\n\n#Calculation\nni = sigma/(mew*e); #conductivity(per m**3)\nN = A*d*n/w; #concentration of free electrons in pure Cu\nAN = ni/N; #average number of electrons contributed per Cu atom\n\n#Result\nprint \"concentration of free electrons in pure Cu is\",N,\"per m**3\"\nprint \"average number of electrons contributed per Cu atom is\",int(AN)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "concentration of free electrons in pure Cu is 8.43940339906e+28 per m**3\naverage number of electrons contributed per Cu atom is 1\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.14, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nRH = 3.66*10**-11; #hall coefficient(m**3/As)\ne = 1.6*10**-19; #electron charge(C)\nsigma = 112*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nn = 1/(e*RH); #charge carrier density(per m**3)\nmew_n = sigma/(n*e); #electron mobility(m**2/As)\nmew_n = math.ceil(mew_n*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"charge carrier density is\",n,\"per m**3\"\nprint \"electron mobility is\",mew_n,\"m**2/As\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "charge carrier density is 1.70765027322e+29 per m**3\nelectron mobility is 0.041 m**2/As\nanswers given in the book are wrong\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.15, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nB = 1.5; #magnetic field(T)\nI = 50; #current(Amp)\nn = 8.4*10**28; #free electron concentration(per m**3)\nd = 0.2; #thickness of slab(cm)\n\n#Calculation\nd = d*10**-2; #thickness of slab(m)\nVH = B*I/(n*e*d); #hall voltage(V)\n\n#Result\nprint \"magnitude of Hall voltage is\",VH,\"V\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnitude of Hall voltage is 2.79017857143e-06 V\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.16, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nn = 2.5*10**19; #free electron concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\nL = 1; #length(cm)\nw = 1; #width(mm)\nt = 1; #thickness(mm)\n\n#Calculation\nL = L*10**-2; #length(m)\nw = w*10**-3; #width(m)\nt = t*10**-3; #thickness(m)\nA = w*t; #area(m**2)\nsigma = n*e*(mew_n+mew_p); #conductivity(ohm-1 m-1)\nR = L/(sigma*A); #resistance(ohm)\n\n#Result\nprint \"resistance of intrinsic Ge rod is\",int(R),\"ohm\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistance of intrinsic Ge rod is 4310 ohm\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.17, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nEg = 1.12; #band gap(eV)\nme = 1;\nmn_star = 0.12*me; #electron mobility(m**2/Vs)\nmp_star = 0.28*me; #hole mobility(m**2/Vs)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature\n\n#Calculation\na = mp_star/mn_star;\nEF = (Eg/2)+((3*k*T/(4*e))*np.log(a));\nEF = math.ceil(EF*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"position of Fermi level is\",EF,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "position of Fermi level is 0.577 eV\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.18, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 1.5*10**16; #intrinsic carrier density(per m**3)\nmew_n = 0.13; #electron mobility(m**2/Vs)\nmew_p = 0.05; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\nsigma = sigma*10**4;\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**-4 ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 4.32 *10**-4 ohm-1 m-1\n" + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.19, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.15*10**-13; #intrinsic carrier density(per cm**3)\nmew_n = 3900; #electron mobility(cm**2/Vs)\nmew_p = 1900; #hole mobility(cm**2/Vs)\n\n#Calculation\nsigmai = ni*e*(mew_n+mew_p); #electrical conductivity(ohm-1 cm-1)\nrhoi = 1/sigmai; #intrinsic resistivity(ohm cm)\n\n#Result\nprint \"intrinsic resistivity is\",rhoi,\"ohm cm\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 5.01202886929e+27 ohm cm\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.20, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.1*10**19; #intrinsic carrier density(per m**3)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\n\n#Result\nprint \"intrinsic resistivity is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 2.016 ohm-1 m-1\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.21, Page number 218" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nV = 1.35; #voltage supply(V)\nI = 5; #current(mA)\nb = 5; #breadth(mm)\nd = 1; #thickness(mm)\nL = 1; #length(cm)\nH = 0.45; #magnetic field(Wb/m**2)\nVy =20; #Hall voltage(mV)\n\n#Calculation\nVy = Vy*10**-3; #Hall voltage(V)\nL = L*10**-2; #length(m)\nd = d*10**-3; #thickness(m)\nb = b*10**-3; #breadth(m)\nI = I*10**-3; #current(A)\nR = V/I; #resistance(ohm)\nA = b*d; #area(m**2)\nrho = R*A/L; #resistivity(ohm m)\nEy = Vy/d; #Hall field(V/m)\nJx = I/A; \na = Ey/(H*Jx); #current density(m**3/C).Here a is 1/ne \nRH = a; #Hall coefficient(m**3/C)\nRH = math.ceil(RH*10**4)/10**4; #rounding off to 4 decimals\nmew_n = RH/rho; #electron mobility(m**2/Vs)\nmew_n = math.ceil(mew_n*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"Hall coefficient is\",RH,\"m**3/C\"\nprint \"electron mobility is\",mew_n,\"m**2/Vs\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall coefficient is 0.0445 m**3/C\nelectron mobility is 0.33 m**2/Vs\n" + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.22, Page number 219" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nIx = 200; #current(A)\nBz = 1.5; #magnetic field(Wb/m**2)\np = 8.4*10**28; #electron concentration(per m**3)\nd = 1; #thickness(mm)\n\n#Calculation\nd = d*10**-3; #thickness(m)\nVH = Ix*Bz/(e*p*d); #Hall potential(V)\nVH = VH*10**6; #Hall potential(micro V)\n\n#Result\nprint \"Hall potential is\",int(VH),\"micro V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall potential is 22 micro V\n" + } + ], + "prompt_number": 22 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter7_1.ipynb b/Engineering_Physics/Chapter7_1.ipynb index cd558c19..d6a7ab3d 100755 --- a/Engineering_Physics/Chapter7_1.ipynb +++ b/Engineering_Physics/Chapter7_1.ipynb @@ -1,7 +1,7 @@ { "metadata": { - "name": "", - "signature": "sha256:7187247d22d4e816cffb8e16cb739591c46b8ff453a1af7a76514de7cc4fae35" + "name": "Chapter7", + "signature": "sha256:043709ddd748250fcd3232cc251c6d71d665f281189e172a4c8d9b59233bdcee" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,48 +12,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "7: Superconductivity" - ] + "source": "7: Semiconducting Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.1, Page number 152" - ] + "source": "Example number 7.1, Page number 208" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "Tc=3.722; #critical temperature(K)\n", - "T=2; #temperature(K)\n", - "Bc_0=0.0305; #critical field(T)\n", - "\n", - "#Calculation\n", - "Bc_T=Bc_0*(1-(T/Tc)**2); #critical field at 2K(T)\n", - "Bc_T = math.ceil(Bc_T*10**4)/10**4; #rounding off the value of Bc_T to 4 decimals\n", - "\n", - "#Result\n", - "print \"The critical field at 2K is\",Bc_T, \"T\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nme = 9.11*10**-31; #mass of electron(kg)\nepsilon_r = 13.2; \nepsilon0 = 8.85*10**-12;\nh = 6.63*10**-34;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nm_nc = 0.067*me;\nE = m_nc*e**4/(8*(epsilon0*epsilon_r*h)**2); #energy(J)\nE = E/e; #energy(eV)\nE = math.ceil(E*10**5)/10**5; #rounding off to 5 decimals\nE_meV = E*10**3; #energy(meV)\n\n#Result\nprint \"donor binding energy is\",E,\"eV or\",E_meV,\"meV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The critical field at 2K is 0.0217 T\n" - ] + "text": "donor binding energy is 0.00521 eV or 5.21 meV\n" } ], "prompt_number": 1 @@ -62,42 +39,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.2, Page number 152" - ] + "source": "Example number 7.2, Page number 208" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "V = 1; #DC voltage applied across the Josephson junction(micro-volt)\n", - "e = 1.6*10**-19; #Charge on an electron(C)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "\n", - "#Calculation\n", - "V = V*10**-6; #DC voltage applied across the Josephson junction(V)\n", - "f = 2*e*V/h; #Frequency of Josephson current(Hz)\n", - "f = f*10**-6; #Frequency of Josephson current(MHz)\n", - "f = math.ceil(f*10**2)/10**2; #rounding off the value of f to 2 decimals\n", - "\n", - "#Result\n", - "print \"The frequency of Josephson current is\",f, \"MHz\"" - ], + "input": "#importing modules\nimport math\nimport numpy as np\n\n#Variable declaration\nNd = 10**16; #donor concentration(atoms/cm**3)\nni = 1.5*10**10; #concentration(per cm**3)\nT = 300; #temperature(K)\nkT = 0.0259;\n\n#Calculation\nn0 = Nd; #for Nd>>ni, assume n0=Nd\np0 = ni**2/n0; #equilibrium hole concentration(per cm**3)\np0 = p0*10**-4;\nEF_Ei = kT*np.log(n0/ni);\nEF_Ei = math.ceil(EF_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n\n#Result\nprint \"equilibrium hole concentration is\",p0,\"*10**4 per cm**3\"\nprint \"value of EF-Ei is\",EF_Ei,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The frequency of Josephson current is 482.95 MHz\n" - ] + "text": "equilibrium hole concentration is 2.25 *10**4 per cm**3\nvalue of EF-Ei is 0.3474 eV\n" } ], "prompt_number": 2 @@ -106,41 +60,109 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.3, Page number 152" - ] + "source": "Example number 7.3, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nNd = 10**14; #donor density(atoms/cm**3)\nmew_n = 3900;\n\n#Calculation\nn = Nd;\nsigma = n*e*mew_n; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*100)/100; #rounding off to 2 decimals\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 16.03 ohm cm\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.4, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nn0 = 5*10**16; #donor density(atoms/cm**3)\nmew_0 = 800;\nIx = 2; #current(mA)\nBz = 5*10**-5;\nd = 200; #thickness(micrometre)\n\n#Calculation\nIx = Ix*10**-3; #current(A)\nd = d*10**-4; #thickness(m)\nsigma = e*n0*mew_0; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\nRH = -1/(e*n0); #Hall coefficient(cm**3/C)\nVH = Ix*Bz*RH/d; #Hall voltage(V)\nVH = VH*10**5;\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"\nprint \"Hall coefficient is\",RH,\"cm**3/C\"\nprint \"Hall voltage is\",VH,\"*10**-5 V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 0.1563 ohm cm\nHall coefficient is -125.0 cm**3/C\nHall voltage is -62.5 *10**-5 V\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.5, Page number 210" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "T_c = 0.517; #Critical temperature for cadmium(K)\n", - "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "\n", - "#Calculation\n", - "E_g = 3.5*k*T_c/e; #Superconducting energy gap at absolute zero(eV)\n", - "E_g = E_g*10**4;\n", - "E_g = math.ceil(E_g*10**3)/10**3; #rounding off the value of E_g to 3 decimals\n", - "\n", - "#Result\n", - "print \"The superconducting energy gap for Cd at absolute zero is\",E_g,\"*10**-4 eV\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\nEg = 0.7; #band gap(eV)\nme = 9.11*10**-31; #mass of electron(kg)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nh = 6.625*10**-34;\nkT = 0.0259;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\na = (2*math.pi*k*T/(h**2))**(3/2);\nb = (mn_star*mp_star)**(3/4);\nc = math.exp(-Eg/(2*kT));\nni = 2*a*b*c; #intrinsic concentration(per m**3)\nsigma = ni*e*(mew_n+mew_p); #intrinsic conductivity(per ohm m)\nsigma = math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\nrho = 1/sigma; #intrinsic resistivity(ohm m)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"intrinsic concentration is\",ni,\"per m**3\"\nprint \"intrinsic conductivity is\",sigma,\"per ohm m\"\nprint \"intrinsic resistivity is\",rho,\"ohm m\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic concentration is 1.02825111151e+19 per m**3\nintrinsic conductivity is 0.9872 per ohm m\nintrinsic resistivity is 1.013 ohm m\nanswers given in the book are wrong\n" + } ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.6, Page number 211" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nNd = 10**16; #donor concentration(per cm**3)\nni = 1.45*10**10; #concentration(per cm**3)\nkT = 0.0259;\n\n#Calculation\n#ni = Nc*math.exp(-(Ec-Ei)/kT)\n#Nd = Nc*(math.exp(-(Ec-Efd)/kT)\n#dividing Nd/ni we get \nEFd_Ei = kT*np.log(Nd/ni);\nEFd_Ei = math.ceil(EFd_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"Fermi energy is\",EFd_Ei,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The superconducting energy gap for Cd at absolute zero is 1.561 *10**-4 eV\n" - ] + "text": "Fermi energy is 0.3482 eV\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.7, Page number 211, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.8, Page number 212" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.36; #electron mobility(m**2/Vs)\nmew_p = 0.17; #hole mobility(m**2/Vs)\nrho = 2.12; #resistivity(ohm m)\nme = 9.11*10**-31; #mass of electron(kg)\nkT = 0.0259;\nh = 6.625*10**-34;\nk = 1.38*10**-23; #boltzmann constant\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\nsigma = 1/rho; #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\nni = sigma/(e*(mew_n+mew_p)); #concentration of electrons(per m**3)\na = (2*math.pi*kT/(h**2))**(3/2);\nNc = 2*a*(mn_star**(3/2)); \nNv = 2*a*(mp_star**(3/2)); \nb = (Nc*Nv)**(1/2);\nEg = 2*kT*np.log(b/ni);\n\n#Result\nprint \"forbidden energy gap is\",Eg,\"eV\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "forbidden energy gap is 4.09465494989 eV\nanswer given in the book is wrong\n" } ], "prompt_number": 8 @@ -149,84 +171,103 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.4, Page number 152" - ] + "source": "Example number 7.9, Page number 213" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "c = 3*10**8; #Speed of light in free space(m/s)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "E_g = 1.5*10**-4; #Superconducting energy gap for a material(eV)\n", - "\n", - "#Calculation\n", - "#As E_g = h*new = h*c/lamda, solving for lambda\n", - "lamda = h*c/(E_g*e); #Wavelength of photon to break up a Cooper-pair(m)\n", - "lamda = lamda*10**3;\n", - "lamda = math.ceil(lamda*10**3)/10**3; #rounding off the value of lamda to 3 decimals\n", - "\n", - "#Result\n", - "print \"The wavelength of photon to break up a Cooper-pair is\",lamda,\"*10**-3 m\"" + "input": "#importing modules\nimport math\n\n#Variable declaration\nni = 2.4*10**19; #concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"conductivity of sample is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "conductivity of sample is 2.228 ohm-1 m-1\n" + } ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.10, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nEc = 0.3; #initial position(eV)\nT1 = 300; #initial temperature(K)\nT2 = 330; #increased temperature\n\n#Calculation\n#Ec/T1 = Ec_EF330/T2\nEc_EF330 = Ec*T2/T1; #new position of Fermi level(eV)\n\n#Result\nprint \"new position of Fermi level is\",Ec_EF330,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The wavelength of photon to break up a Cooper-pair is 8.283 *10**-3 m\n" - ] + "text": "new position of Fermi level is 0.33 eV\n" } ], - "prompt_number": 12 + "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.5, Page number 153" - ] + "source": "Example number 7.11, Page number 214" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lambda_0 = 37; #Penetration depth of lead at 0 kelvin(nm)\n", - "T_c = 7.193; #Critical temperature of superconducting transition for lead(kelvin)\n", - "T = 5.2; #Temperature at which penetration depth for lead becomes lambda_T(kelvin) \n", - "\n", - "#Calculation\n", - "lambda_T = lambda_0*(1-(T/T_c)**4)**(-1/2); #Penetration depth of lead at 5.2 kelvin(nm)\n", - "lambda_T = math.ceil(lambda_T*10)/10; #rounding off the value of lamda_T to 1 decimal\n", - "\n", - "#Result\n", - "print \"The penetration depth of lead is\",lambda_T, \"nm\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nme = 9.1*10**-31; #mass of electron(kg)\nh = 6.63*10**-34; #planck's constant\nEc_Ev = 1.1; #energy gap(eV)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nme_star = 0.31*me;\nA = (2*math.pi*k*T*me_star/(h**2))**(3/2);\nB = math.exp(-(Ec_Ev*e)/(2*k*T));\nni = A*B; #concentration in conduction band(per m**3)\n\n#Result\nprint \"intrinsic electron concentration is\",ni,\"per m**3\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic electron concentration is 1.26605935487e+15 per m**3\nanswer given in the book is wrong\n" + } ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.12, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nRH = 0.55*10**-10; #Hall coefficient(m**3/As)\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nmew = RH*sigma; #drift mobility(m**2/Vs)\nmew = mew*10**3;\nmew = math.ceil(mew*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"drift mobility of electrons is\",mew,\"*10**-3 m**2/Vs\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The penetration depth of lead is 43.4 nm\n" - ] + "text": "drift mobility of electrons is 3.25 *10**-3 m**2/Vs\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.13, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nA = 6.022*10**23; #avagadro constant\nd = 8.96*10**-9; #density(kg/m**3)\nn = 9.932*10**14; #no. of free electrons per atom\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\ne = 1.6*10**-19; #electron charge(C)\nmew = 3.2*10**-3; #drift mobility(m**2/Vs)\nw = 63.5; #atomic weight of Cu(kg)\n\n#Calculation\nni = sigma/(mew*e); #conductivity(per m**3)\nN = A*d*n/w; #concentration of free electrons in pure Cu\nAN = ni/N; #average number of electrons contributed per Cu atom\n\n#Result\nprint \"concentration of free electrons in pure Cu is\",N,\"per m**3\"\nprint \"average number of electrons contributed per Cu atom is\",int(AN)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "concentration of free electrons in pure Cu is 8.43940339906e+28 per m**3\naverage number of electrons contributed per Cu atom is 1\n" } ], "prompt_number": 13 @@ -235,52 +276,190 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.6, Page number 153" - ] + "source": "Example number 7.14, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nRH = 3.66*10**-11; #hall coefficient(m**3/As)\ne = 1.6*10**-19; #electron charge(C)\nsigma = 112*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nn = 1/(e*RH); #charge carrier density(per m**3)\nmew_n = sigma/(n*e); #electron mobility(m**2/As)\nmew_n = math.ceil(mew_n*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"charge carrier density is\",n,\"per m**3\"\nprint \"electron mobility is\",mew_n,\"m**2/As\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "charge carrier density is 1.70765027322e+29 per m**3\nelectron mobility is 0.041 m**2/As\nanswers given in the book are wrong\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.15, Page number 216" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "M1 = 199; #Mass of an isotope of mercury(amu)\n", - "T_C1 = 4.185; #Transition temperature of the isoptope of Hg(K)\n", - "T_C2 = 4.153; #Transition temperature of another isoptope of Hg(K)\n", - "alpha = 0.5; #Isotope coefficient\n", - "\n", - "#Calculation\n", - "M2 = M1*(T_C1/T_C2)**(1/alpha); #Mass of another isotope of mercury(amu)\n", - "M2 = math.ceil(M2*100)/100; #rounding off the value of M2 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The mass of another isotope of mercury is\",M2, \"amu\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nB = 1.5; #magnetic field(T)\nI = 50; #current(Amp)\nn = 8.4*10**28; #free electron concentration(per m**3)\nd = 0.2; #thickness of slab(cm)\n\n#Calculation\nd = d*10**-2; #thickness of slab(m)\nVH = B*I/(n*e*d); #hall voltage(V)\n\n#Result\nprint \"magnitude of Hall voltage is\",VH,\"V\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnitude of Hall voltage is 2.79017857143e-06 V\nanswer given in the book is wrong\n" + } ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.16, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nn = 2.5*10**19; #free electron concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\nL = 1; #length(cm)\nw = 1; #width(mm)\nt = 1; #thickness(mm)\n\n#Calculation\nL = L*10**-2; #length(m)\nw = w*10**-3; #width(m)\nt = t*10**-3; #thickness(m)\nA = w*t; #area(m**2)\nsigma = n*e*(mew_n+mew_p); #conductivity(ohm-1 m-1)\nR = L/(sigma*A); #resistance(ohm)\n\n#Result\nprint \"resistance of intrinsic Ge rod is\",int(R),\"ohm\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The mass of another isotope of mercury is 202.08 amu\n" - ] + "text": "resistance of intrinsic Ge rod is 4310 ohm\n" } ], "prompt_number": 16 }, { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.17, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nEg = 1.12; #band gap(eV)\nme = 1;\nmn_star = 0.12*me; #electron mobility(m**2/Vs)\nmp_star = 0.28*me; #hole mobility(m**2/Vs)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature\n\n#Calculation\na = mp_star/mn_star;\nEF = (Eg/2)+((3*k*T/(4*e))*np.log(a));\nEF = math.ceil(EF*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"position of Fermi level is\",EF,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "position of Fermi level is 0.577 eV\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.18, Page number 217" + }, + { "cell_type": "code", "collapsed": false, - "input": [], + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 1.5*10**16; #intrinsic carrier density(per m**3)\nmew_n = 0.13; #electron mobility(m**2/Vs)\nmew_p = 0.05; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\nsigma = sigma*10**4;\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**-4 ohm-1 m-1\"", "language": "python", "metadata": {}, - "outputs": [] + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 4.32 *10**-4 ohm-1 m-1\n" + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.19, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.15*10**-13; #intrinsic carrier density(per cm**3)\nmew_n = 3900; #electron mobility(cm**2/Vs)\nmew_p = 1900; #hole mobility(cm**2/Vs)\n\n#Calculation\nsigmai = ni*e*(mew_n+mew_p); #electrical conductivity(ohm-1 cm-1)\nrhoi = 1/sigmai; #intrinsic resistivity(ohm cm)\n\n#Result\nprint \"intrinsic resistivity is\",rhoi,\"ohm cm\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 5.01202886929e+27 ohm cm\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.20, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.1*10**19; #intrinsic carrier density(per m**3)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\n\n#Result\nprint \"intrinsic resistivity is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 2.016 ohm-1 m-1\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.21, Page number 218" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nV = 1.35; #voltage supply(V)\nI = 5; #current(mA)\nb = 5; #breadth(mm)\nd = 1; #thickness(mm)\nL = 1; #length(cm)\nH = 0.45; #magnetic field(Wb/m**2)\nVy =20; #Hall voltage(mV)\n\n#Calculation\nVy = Vy*10**-3; #Hall voltage(V)\nL = L*10**-2; #length(m)\nd = d*10**-3; #thickness(m)\nb = b*10**-3; #breadth(m)\nI = I*10**-3; #current(A)\nR = V/I; #resistance(ohm)\nA = b*d; #area(m**2)\nrho = R*A/L; #resistivity(ohm m)\nEy = Vy/d; #Hall field(V/m)\nJx = I/A; \na = Ey/(H*Jx); #current density(m**3/C).Here a is 1/ne \nRH = a; #Hall coefficient(m**3/C)\nRH = math.ceil(RH*10**4)/10**4; #rounding off to 4 decimals\nmew_n = RH/rho; #electron mobility(m**2/Vs)\nmew_n = math.ceil(mew_n*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"Hall coefficient is\",RH,\"m**3/C\"\nprint \"electron mobility is\",mew_n,\"m**2/Vs\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall coefficient is 0.0445 m**3/C\nelectron mobility is 0.33 m**2/Vs\n" + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.22, Page number 219" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nIx = 200; #current(A)\nBz = 1.5; #magnetic field(Wb/m**2)\np = 8.4*10**28; #electron concentration(per m**3)\nd = 1; #thickness(mm)\n\n#Calculation\nd = d*10**-3; #thickness(m)\nVH = Ix*Bz/(e*p*d); #Hall potential(V)\nVH = VH*10**6; #Hall potential(micro V)\n\n#Result\nprint \"Hall potential is\",int(VH),\"micro V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall potential is 22 micro V\n" + } + ], + "prompt_number": 22 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter8.ipynb b/Engineering_Physics/Chapter8.ipynb new file mode 100755 index 00000000..54d83b1d --- /dev/null +++ b/Engineering_Physics/Chapter8.ipynb @@ -0,0 +1,125 @@ +{ + "metadata": { + "name": "Chapter8" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "8: Magnetic Materials" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 8.1, Page number 238" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nI = 12; #current(Ampere)\nA = 7.5*10**-4 #area of loop(m**2)\n\n#Calculation\nM = I*A; #magnetic moment(Am**2)\nM = M*10**3;\n\n#Result\nprint \"magnetic moment is\",M,\"*10**-3 Am**2\"\nprint \"magnetic moment is in opposite direction from the observer\"\nprint \"M is perpendicular to the plane\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnetic moment is 9.0 *10**-3 Am**2\nmagnetic moment is in opposite direction from the observer\nM is perpendicular to the plane\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 8.2, Page number 238" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 0.5; #radius of orbit(Angstrom)\ne = 1.6*10**-19; #charge of electron(C)\nnew = 10**16; #frequency(rps)\n\n#Calculation\nr = r*10**-10; #radius of orbit(m)\nI = e*new; #current(Ampere)\nA = math.pi*r**2; #area enclosed(m**2)\nM = I*A; #magnetic moment(Am**2)\n\n#Result\nprint \"magnetic moment is\",M,\"Am**2\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnetic moment is 1.25663706144e-23 Am**2\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 8.3, Page number 239" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nmew_r = 5000; #relative permeability\n\n#Calculation\nchi_m = mew_r-1; #magnetic susceptibility\n\n#Result\nprint \"magnetic susceptibility is\",chi_m", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnetic susceptibility is 4999\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 8.4, Page number 239" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nH = 1800; #magnetic field(A/m)\nphi = 3*10**-5; #magnetic flux(Wb)\nA = 0.2; #cross sectional area(cm**2)\n\n#Calculation\nA = A*10**-4; #cross sectional area(m**2)\nB = phi/A; #magnetic flux density(Wb/m**2)\nmew = B/H; #permeability(H/m)\nmew = mew*10**4;\nmew=math.ceil(mew*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"permeability is\",mew,\"*10**-4 H/m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "permeability is 8.34 *10**-4 H/m\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 8.5, Page number 239" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nB = 0.65; #magnetic induction(Wb/m**2)\nrho = 8906; #density(kg/m**3)\nM = 58.7; #atomic weight\nmew0 = 4*math.pi*10**-7;\nmb = 9.27*10**-24;\nNa = 6.023*10**26; #avagadro constant\n\n#Calculation\nN = rho*Na/M; #number of atoms per unit volume(atoms/m**3)\nmew_r = B/(N*mew0); #relative permeability(A/m**2)\nM = mew_r/mb; #magnetic moment in mew_B \nM=math.ceil(M*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"magnetic moment is\",M,\"mew_B\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnetic moment is 0.611 mew_B\n" + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter8_1.ipynb b/Engineering_Physics/Chapter8_1.ipynb index 809f0bc8..54d83b1d 100755 --- a/Engineering_Physics/Chapter8_1.ipynb +++ b/Engineering_Physics/Chapter8_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:6cf74f56ec30435213713191af54de81cab98f4f30811b6d81fe0fb6a9021553" + "name": "Chapter8" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,49 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "8: Special Theory of Relativity" - ] + "source": "8: Magnetic Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.1, Page number 171" - ] + "source": "Example number 8.1, Page number 238" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "L_0 = 1; #For simplicity, we assume classical length to be unity(m)\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "\n", - "#Calculation\n", - "L = (1-1/100)*L_0; #Relativistic length(m)\n", - "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", - "v = math.sqrt(1-(L/L_0)**2)*c; #Speed at which relativistic length is 1 percent of the classical length(m/s)\n", - "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed at which relativistic length is 1 percent of the classical length is\",v, \"c\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nI = 12; #current(Ampere)\nA = 7.5*10**-4 #area of loop(m**2)\n\n#Calculation\nM = I*A; #magnetic moment(Am**2)\nM = M*10**3;\n\n#Result\nprint \"magnetic moment is\",M,\"*10**-3 Am**2\"\nprint \"magnetic moment is in opposite direction from the observer\"\nprint \"M is perpendicular to the plane\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed at which relativistic length is 1 percent of the classical length is 0.1411 c\n" - ] + "text": "magnetic moment is 9.0 *10**-3 Am**2\nmagnetic moment is in opposite direction from the observer\nM is perpendicular to the plane\n" } ], "prompt_number": 1 @@ -63,39 +38,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.2, Page number 171" - ] + "source": "Example number 8.2, Page number 238" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "delta_t = 5*10**-6; #Mean lifetime of particles as observed in the lab frame(s)\n", - "\n", - "#Calculation\n", - "v = 0.9*c; #Speed at which beam of particles travel(m/s)\n", - "delta_tau = delta_t*math.sqrt(1-(v/c)**2); #Proper lifetime of particle as per Time Dilation rule(s)\n", - "\n", - "#Result\n", - "print \"The proper lifetime of particle is\",delta_tau, \"s\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 0.5; #radius of orbit(Angstrom)\ne = 1.6*10**-19; #charge of electron(C)\nnew = 10**16; #frequency(rps)\n\n#Calculation\nr = r*10**-10; #radius of orbit(m)\nI = e*new; #current(Ampere)\nA = math.pi*r**2; #area enclosed(m**2)\nM = I*A; #magnetic moment(Am**2)\n\n#Result\nprint \"magnetic moment is\",M,\"Am**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The proper lifetime of particle is 2.17944947177e-06 s\n" - ] + "text": "magnetic moment is 1.25663706144e-23 Am**2\n" } ], "prompt_number": 2 @@ -104,549 +59,64 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.3, Page number 171. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.4, Page number 172" - ] + "source": "Example number 8.3, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "\n", - "#Calculation\n", - "v = 0.6*c; #Speed with which the rocket leaves the earth(m/s)\n", - "u_prime = 0.9*c; #Relative speed of second rocket w.r.t. the first rocket(m/s)\n", - "u1 = (u_prime+v)/(1+(u_prime*v)/c**2); #Speed of second rocket for same direction of firing as per Velocity Addition Rule(m/s)\n", - "u1 = math.ceil(u1*10**4)/10**4; #rounding off the value of u1 to 4 decimals\n", - "u2 = (-u_prime+v)/(1-(u_prime*v)/c**2); #Speed of second rocket for opposite direction of firing as per Velocity Addition Rule(m/s)\n", - "u2 = math.ceil(u2*10**4)/10**4; #rounding off the value of u2 to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed of second rocket for same direction of firing is\",u1,\"c\"\n", - "print \"The speed of second rocket for opposite direction of firing is\",u2,\"c\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nmew_r = 5000; #relative permeability\n\n#Calculation\nchi_m = mew_r-1; #magnetic susceptibility\n\n#Result\nprint \"magnetic susceptibility is\",chi_m", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed of second rocket for same direction of firing is 0.9741 c\n", - "The speed of second rocket for opposite direction of firing is -0.6521 c\n" - ] + "text": "magnetic susceptibility is 4999\n" } ], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.5, Page number 172" - ] + "source": "Example number 8.4, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "L0 = 1; #For simplicity assume length in spaceship's frame to be unity(m)\n", - "tau = 1; #Unit time in the spaceship's frame(s)\n", - "\n", - "#Calculation\n", - "L = 1/2*L0; #Length as observed on earth(m)\n", - "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", - "v = math.sqrt(1-(L/L0)**2)*c; #Speed at which length of spaceship is observed as half from the earth frame(m/s)\n", - "t = tau/math.sqrt(1-(v/c)**2); #Time dilation of the spaceship's unit time(s)\n", - "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed at which length of spaceship is observed as half from the earth frame is\",v, \"c\"\n", - "print \"The time dilation of the spaceship unit time is\",t,\"delta_tau\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nH = 1800; #magnetic field(A/m)\nphi = 3*10**-5; #magnetic flux(Wb)\nA = 0.2; #cross sectional area(cm**2)\n\n#Calculation\nA = A*10**-4; #cross sectional area(m**2)\nB = phi/A; #magnetic flux density(Wb/m**2)\nmew = B/H; #permeability(H/m)\nmew = mew*10**4;\nmew=math.ceil(mew*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"permeability is\",mew,\"*10**-4 H/m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed at which length of spaceship is observed as half from the earth frame is 0.8661 c\n", - "The time dilation of the spaceship unit time is 2.0 delta_tau\n" - ] + "text": "permeability is 8.34 *10**-4 H/m\n" } ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.6, Page number 172" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "t1 = 2*10**-7; #Time for which first event occurs(s)\n", - "t2 = 3*10**-7; #Time for which second event occurs(s)\n", - "x1 = 10; #Position at which first event occurs(m)\n", - "x2 = 40; #Position at which second event occurs(m)\n", - "\n", - "#Calculation\n", - "v = 0.6*c; #Velocity with which S2 frame moves relative to S1 frame(m/s)\n", - "L_factor = 1/math.sqrt(1-(v/c)**2); #Lorentz factor\n", - "delta_t = L_factor*(t2 - t1)+L_factor*v/c**2*(x1 - x2); #Time difference between the events(s)\n", - "delta_x = L_factor*(x2 - x1)-L_factor*v*(t2 - t1); #Distance between the events(m)\n", - "\n", - "#Result\n", - "print \"The time difference between the events is\",delta_t, \"s\" \n", - "print \"The distance between the events is\",delta_x, \"m\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The time difference between the events is 5e-08 s\n", - "The distance between the events is 15.0 m\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.7, Page number 173" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "tau = 2.6*10**-8; #Mean lifetime the particle in its own frame(s)\n", - "d = 20; #Distance which the unstable particle travels before decaying(m)\n", - "\n", - "#Calculation\n", - "#As t = d/v and also t = tau/sqrt(1-(v/c)^2), so that\n", - "#d/v = tau/sqrt(1-(v/c)^2), solving for v\n", - "v = math.sqrt(d**2/(tau**2+(d/c)**2)); #Speed of the unstable particle in lab frame(m/s)\n", - "v = v/10**8;\n", - "v = math.ceil(v*10)/10; #rounding off the value of v to 1 decimal\n", - "\n", - "#Result\n", - "print \"The speed of the unstable particle in lab frame is\",v,\"*10**8 m/s\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of the unstable particle in lab frame is 2.8 *10**8 m/s\n" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.8, Page number 174" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "me = 1; #For simplicity assume mass of electron to be unity(kg)\n", - "tau = 2.3*10**-6; #Average lifetime of mu-meson in rest frame(s)\n", - "t = 6.9*10**-6; #Average lifetime of mu-meson in laboratory frame(s)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "C = 3*10**8; #Speed of light in vacuum(m/s)\n", - "m_e = 9.1*10**-31; #Mass of an electron(kg)\n", - "\n", - "#Calculation\n", - "#Fromm Time Dilation Rule, tau = t*sqrt(1-(v/c)^2), solving for v\n", - "v = c*math.sqrt(1-(tau/t)**2); #Speed of mu-meson in the laboratory frame(m/s)\n", - "v = math.ceil(v*10**5)/10**5; #rounding off the value of v to 5 decimals\n", - "m0 = 207*me; #Rest mass of mu-meson(kg)\n", - "m = m0/math.sqrt(1-(v/c)**2); #Relativistic variation of mass with velocity(kg)\n", - "m = math.ceil(m*10)/10; #rounding off the value of m to 1 decimal\n", - "T = (m*m_e*C**2 - m0*m_e*C**2)/e; #Kinetic energy of mu-meson(eV)\n", - "T = T*10**-6; #Kinetic energy of mu-meson(MeV)\n", - "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", - " \n", - "#Result\n", - "print \"The speed of mu-meson in the laboratory frame is\",v, \"c\"\n", - "print \"The effective mass of mu-meson is\",m, \"me\"\n", - "print \"The kinetic energy of mu-meson is\",T, \"MeV\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of mu-meson in the laboratory frame is 0.94281 c\n", - "The effective mass of mu-meson is 621.1 me\n", - "The kinetic energy of mu-meson is 211.97 MeV\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.9, Page number 174" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "m0 = 1; #For simplicity assume rest mass to be unity(kg)\n", - "\n", - "#Calculation\n", - "m = (20/100+1)*m0; #Mass in motion(kg)\n", - "#As m = m0/sqrt(1-(u/c)^2), solving for u\n", - "u = math.sqrt(1-(m0/m)**2)*c; #Speed of moving mass(m/s) \n", - "u = math.ceil(u*10**3)/10**3; #rounding off the value of u to 3 decimals\n", - "\n", - "#Result\n", - "print \"The speed of moving body is\",u, \"c\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of moving body is 0.553 c\n" - ] - } - ], - "prompt_number": 14 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.10, Page number 175" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "dE = 4*10**26; #Energy radiated per second my the sun(J/s)\n", - "\n", - "#Calculation\n", - "dm = dE/c**2; #Rate of decrease of mass of sun(kg/s)\n", - "dm = dm/10**9;\n", - "dm = math.ceil(dm*10**3)/10**3; #rounding off the value of dm to 3 decimals\n", - "\n", - "#Result\n", - "print \"The rate of decrease of mass of sun is\",dm,\"*10**9 kg/s\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The rate of decrease of mass of sun is 4.445 *10**9 kg/s\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.11, Page number 175" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "m0 = 9.1*10**-31; #Mass of the electron(kg)\n", - "E0 = 0.512; #Rest energy of electron(MeV)\n", - "T = 10; #Kinetic energy of electron(MeV)\n", - "\n", - "#Calculation\n", - "E = T + E0; #Total energy of electron(MeV)\n", - "# From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for p\n", - "p = math.sqrt(E**2-m0**2*c**4)/c; #Momentum of the electron(MeV)\n", - "p = math.ceil(p*100)/100; #rounding off the value of p to 2 decimals\n", - "#As E = E0/sqrt(1-(u/c)^2), solving for u\n", - "u = math.sqrt(1-(E0/E)**2)*c; #Velocity of the electron(m/s)\n", - "u = math.ceil(u*10**4)/10**4; #rounding off the value of u to 4 decimals\n", - "\n", - "#Result\n", - "print \"The momentum of the electron is\",p,\"/c MeV\"\n", - "print \"The velocity of the electron is\",u, \"c\"\n", - "\n", - "#answer for velocity given in the book is wrong" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The momentum of the electron is 10.52 /c MeV\n", - "The velocity of the electron is 0.9989 c\n" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.12, Page number 175. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.13, Page number 176" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "E = 4.5*10**17; #Total energy of object(J)\n", - "px = 3.8*10**8; #X-component of momentum(kg-m/s)\n", - "py = 3*10**8; #Y-component of momentum(kg-m/s)\n", - "pz = 3*10**8; #Z-component of momentum(kg-m/s)\n", - "\n", - "#Calculation\n", - "p = math.sqrt(px**2+py**2+pz**2); #Total momentum of the object(kg-m/s)\n", - "#From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for m0\n", - "m0 = math.sqrt(E**2/c**4 - p**2/c**2); #Rest mass of the body(kg)\n", - "m0 = math.ceil(m0*100)/100; #rounding off the value of m0 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The rest mass of the body is\",m0, \"kg\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The rest mass of the body is 4.63 kg\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.14, Page number 176" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "m = 50000; #Mass of high speed probe(kg)\n", - "\n", - "#Calculation\n", - "u = 0.8*c; #Speed of the probe(m/s)\n", - "p = m*u/math.sqrt(1-(u/c)**2); #Momentum of the probe(kg-m/s)\n", - "\n", - "#Result\n", - "print \"The momentum of the high speed probe is\",p, \"kg-m/s\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The momentum of the high speed probe is 2e+13 kg-m/s\n" - ] - } - ], - "prompt_number": 21 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.15, Page number 177" - ] + "source": "Example number 8.5, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Electronic charge, C = Energy equivalent of 1 eV(J/eV)\n", - "m0 = 9.11*10**-31; #Rest mass of electron(kg)\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "\n", - "#Calculation\n", - "u1 = 0.98*c; #Inital speed of electron(m/s)\n", - "u2 = 0.99*c; #Final speed of electron(m/s)\n", - "m1 = m0/math.sqrt(1-(u1/c)**2); #Initial relativistic mass of electron(kg)\n", - "m2 = m0/math.sqrt(1-(u2/c)**2); #Final relativistic mass of electron(kg)\n", - "dm = m2 - m1; #Change in relativistic mass of the electron(kg)\n", - "W = dm*c**2/e; #Work done on the electron to change its velocity(eV)\n", - "W = W*10**-6; #Work done on the electron to change its velocity(MeV)\n", - "W = math.ceil(W*100)/100; #rounding off the value of W to 2 decimals\n", - "#As W = eV, V = accelerating potential, solving for V\n", - "V = W*10**6; #Accelerating potential(volt)\n", - "V = V/10**6;\n", - "\n", - "#Result\n", - "print \"The change in relativistic mass of the electron is\",dm, \"kg\"\n", - "print \"The work done on the electron to change its velocity is\",W, \"MeV\"\n", - "print \"The accelerating potential is\",V, \"*10**6 volt\"\n", - "\n", - "#answers given in the book are wrong" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nB = 0.65; #magnetic induction(Wb/m**2)\nrho = 8906; #density(kg/m**3)\nM = 58.7; #atomic weight\nmew0 = 4*math.pi*10**-7;\nmb = 9.27*10**-24;\nNa = 6.023*10**26; #avagadro constant\n\n#Calculation\nN = rho*Na/M; #number of atoms per unit volume(atoms/m**3)\nmew_r = B/(N*mew0); #relative permeability(A/m**2)\nM = mew_r/mb; #magnetic moment in mew_B \nM=math.ceil(M*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"magnetic moment is\",M,\"mew_B\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The change in relativistic mass of the electron is 1.87996052912e-30 kg\n", - "The work done on the electron to change its velocity is 1.06 MeV\n", - "The accelerating potential is 1.06 *10**6 volt\n" - ] + "text": "magnetic moment is 0.611 mew_B\n" } ], - "prompt_number": 24 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 5 } ], "metadata": {} diff --git a/Engineering_Physics/Chapter9.ipynb b/Engineering_Physics/Chapter9.ipynb new file mode 100755 index 00000000..ff53dd34 --- /dev/null +++ b/Engineering_Physics/Chapter9.ipynb @@ -0,0 +1,62 @@ +{ + "metadata": { + "name": "Chapter9" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "9: Superconducting Materials" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 9.1, Page number 255" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nH0 = 6.5*10**4; #magnetic field intensity(A/m)\nT = 4.2; #temperature(K)\nTc = 7.18; #critical temperature(K)\n\n#Calculation\nHc = H0*(1-((T**2)/(Tc**2))); #critical magnetic field intensity(A/m)\nHc = Hc*10**-4;\nHc=math.ceil(Hc*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"critical magnetic field intensity is\",Hc,\"*10**4 A/m\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "critical magnetic field intensity is 4.276 *10**4 A/m\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 9.2, Page number 255" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nTc1 = 4.185; #critical temperature for M1(K)\nTc2 = 4.133; #critical temperature for M2(K)\nM1 = 199.5; #isotopic mass\nalpha = 0.5;\n\n#Calculation\nA = math.pow(M1,alpha)*Tc1/Tc2;\nM2 = math.pow(A,1/alpha); #isotopic mass\nM2=math.ceil(M2*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"isotopic mass is\",M2\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "isotopic mass is 204.552\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 2 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics/Chapter9_1.ipynb b/Engineering_Physics/Chapter9_1.ipynb index bea06702..ff53dd34 100755 --- a/Engineering_Physics/Chapter9_1.ipynb +++ b/Engineering_Physics/Chapter9_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:1c769d85a6ecede1e3083e9252f10446216c71537365688b1cba3c5693bdfee6" + "name": "Chapter9" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,45 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "9: Quantum Mechanics" - ] + "source": "9: Superconducting Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 9.1, Page number 202" - ] + "source": "Example number 9.1, Page number 255" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "V = 100; #Accelerating potential for electron(volt)\n", - "\n", - "#Calculation\n", - "lamda = math.sqrt(150/V)*10**-10; #de-Broglie wavelength of electron(m)\n", - "\n", - "#Result\n", - "print \"The De-Broglie wavelength of electron is\",lamda, \"m\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nH0 = 6.5*10**4; #magnetic field intensity(A/m)\nT = 4.2; #temperature(K)\nTc = 7.18; #critical temperature(K)\n\n#Calculation\nHc = H0*(1-((T**2)/(Tc**2))); #critical magnetic field intensity(A/m)\nHc = Hc*10**-4;\nHc=math.ceil(Hc*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"critical magnetic field intensity is\",Hc,\"*10**4 A/m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The De-Broglie wavelength of electron is 1.22474487139e-10 m\n" - ] + "text": "critical magnetic field intensity is 4.276 *10**4 A/m\n" } ], "prompt_number": 1 @@ -59,296 +38,22 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 9.2, Page number 203" - ] + "source": "Example number 9.2, Page number 255" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "m = 9.11*10**-31; #Mass of the electron(kg)\n", - "Ek = 10; #Kinetic energy of electron(eV)\n", - "\n", - "#Calculation\n", - "p = math.sqrt(2*m*Ek*e); #Momentum of the electron(kg-m/s)\n", - "lamda = h/p ; #de-Broglie wavelength of electron from De-Broglie relation(m)\n", - "lamda = lamda*10**9; #de-Broglie wavelength of electron from De-Broglie relation(nm)\n", - "lamda = math.ceil(lamda*10**2)/10**2; #rounding off the value of lamda to 2 decimals\n", - "\n", - "#Result\n", - "print \"The de-Broglie wavelength of electron is\",lamda, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nTc1 = 4.185; #critical temperature for M1(K)\nTc2 = 4.133; #critical temperature for M2(K)\nM1 = 199.5; #isotopic mass\nalpha = 0.5;\n\n#Calculation\nA = math.pow(M1,alpha)*Tc1/Tc2;\nM2 = math.pow(A,1/alpha); #isotopic mass\nM2=math.ceil(M2*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"isotopic mass is\",M2\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The de-Broglie wavelength of electron is 0.39 nm\n" - ] + "text": "isotopic mass is 204.552\nanswer given in the book is wrong\n" } ], "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.3, Page number 203. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.4, Page number 203" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "m = 9.11*10**-31; #Mass of the electron(kg)\n", - "v = 1.1*10**6; #Speed of the electron(m/s)\n", - "pr = 0.1; #precision in percent\n", - "\n", - "#Calculation\n", - "p = m*v; #Momentum of the electron(kg-m/s)\n", - "dp = pr/100*p; #Uncertainty in momentum(kg-m/s)\n", - "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", - "dx = h_bar/(2*dp); #Uncertainty in position(m)\n", - "\n", - "#Result\n", - "print \"The uncertainty in position of electron is\",dx, \"m\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The uncertainty in position of electron is 5.26175358211e-08 m\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.5, Page number 203" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "dt = 10**-8; #Uncertainty in time(s)\n", - "\n", - "#Calculation\n", - "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", - "dE = h_bar/(2*dt*e); #Uncertainty in energy of the excited state(m)\n", - "\n", - "#Result\n", - "print \"The uncertainty in energy of the excited state is\",dE, \"eV\"\n", - "\n", - "#answer given in the book is wrong" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The uncertainty in energy of the excited state is 3.2955020404e-08 eV\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.6, Page number 204" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light(m/s)\n", - "dt = 10**-8; #Average lifetime(s)\n", - "lamda = 400; #Wavelength of spectral line(nm)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of spectral line(m)\n", - "#From Heisenberg uncertainty principle,\n", - "#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give\n", - "#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda\n", - "d_lamda = (lamda**2)/(4*math.pi*c*dt); #Width of spectral line(m)\n", - "\n", - "#Result\n", - "print \"The width of spectral line is\",d_lamda, \"m\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The width of spectral line is 4.24413181578e-15 m\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.7, Page number 204. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.8, Page number 204. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.9, Page number 205. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.10, Page number 205. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.11, Page number 205. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.12, Page number 206. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.13, Page number 206. theoritical proof " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 9.14, Page number 207" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "from scipy.integrate import quad\n", - "\n", - "#Variable declaration\n", - "a = 2*10**-10; # Width of 1D box(m)\n", - "x1=0; # Position of first extreme of the box(m)\n", - "x2=1*10**-10; # Position of second extreme of the box(m)\n", - "\n", - "#Calculation\n", - "def intg(x):\n", - " return ((2/a)*(math.sin(2*math.pi*x/a))**2)\n", - "S=quad(intg,x1,x2)[0]\n", - "\n", - "#Result\n", - "print \"The probability of finding the electron between x = 0 and x = 10**-10 is\",S" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The probability of finding the electron between x = 0 and x = 10**-10 is 0.5\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] } ], "metadata": {} diff --git a/Engineering_Physics/README.txt b/Engineering_Physics/README.txt index a2116ca8..bd7c4bfa 100755 --- a/Engineering_Physics/README.txt +++ b/Engineering_Physics/README.txt @@ -1,10 +1,10 @@ -Contributed By: ADITYA DHARMASAGAR KALIDAS +Contributed By: KRISHNA CHAITANYA Course: btech -College/Institute/Organization: vaageswari college of engineering -Department/Designation: ECE +College/Institute/Organization: JNTUH +Department/Designation: Computer Science Book Title: Engineering Physics -Author: Dr. K. Vijaya Kumar -Publisher: S. Chand & Company Ltd., New Delhi -Year of publication: 2011 -Isbn: 81-219-3852-X +Author: D. K. Bhattacharya & A. Bhaskaran +Publisher: Oxford University Press, New Delhi +Year of publication: 2013 +Isbn: 9780198065425 Edition: 1
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