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diff --git a/Applied_Physics_for_Engineers/Chapter_2.ipynb b/Applied_Physics_for_Engineers/Chapter_2.ipynb new file mode 100755 index 00000000..b9063ed3 --- /dev/null +++ b/Applied_Physics_for_Engineers/Chapter_2.ipynb @@ -0,0 +1,442 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1, Page 79" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable Declaration\n", + "V = 50; # Given potential difference, V\n", + "\n", + "#Calculations\n", + "lamda = 12.24/sqrt(V); # Wavelength of the light, angstrom\n", + "\n", + "#Result\n", + "print \"The de-broglie wavelength of electron = %4.2f angstrom\"%lamda\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de-broglie wavelength of electron = 1.73 angstrom\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2, Page 79" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable Declaration\n", + "h = 6.62e-34; # Planck's constant, J-s\n", + "m0 = 1.6e-27; # Rest mass of proton, kg\n", + "c = 3.0e+8; # Speed of light, in m/s\n", + "v = c/20; # Velocity of the proton, in m/s\n", + "\n", + "#Calculations\n", + "lamda = (h*sqrt(1-v**2/c**2))/(m0*v);\n", + "\n", + "#Result\n", + "print \"The de broglie wavelength associated with the proton = %4.2e m\"%lamda\n", + "#answer differs due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de broglie wavelength associated with the proton = 2.75e-14 m\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3, Page 79" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "c = 3.0e+8; # Speed of light, m/s\n", + "v = 2.0e+8; # Velocity of the proton, m/s\n", + "m0 = 1.6e-27; # Rest mass of proton, kg\n", + "h = 6.62e-34; # Plancks constant,J-s\n", + "\n", + "#Calculations\n", + "lamda = (h*sqrt(1-(v**2/c**2)))/(m0*v);\n", + "\n", + "#Result\n", + "print \"The wavelength of matter wave associated with the proton = %5.3e m\"%lamda\n", + "\n", + "#answer differs due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength of matter wave associated with the proton = 1.542e-15 m\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5, Page 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "a = 0.003; # Accuracy of the electron,in percent\n", + "s = 5e+03; # Speed of the electron,in m/s\n", + "del_v = (a/100)*s; # Change in velocity,in m/s\n", + "m0 = 9.1e-31; # Rest mass of the electron,in kg\n", + "hcut = 1.054e-34; # Plancks constant,J-s\n", + "\n", + "#Calculations\n", + "del_x = hcut/(2*del_v*m0);\n", + "\n", + "#Result\n", + "print \"The uncertainity in the position of the electron = %4.2e m\"%del_x\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The uncertainity in the position of the electron = 3.86e-04 m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6, Page 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "del_t = 2.5e-14; # Lifetime of the hydrogen atom in excited state\n", + "hcut = 1.054e-34; # Planck's constant,in J-s\n", + "e = 1.6e-19; # Charge on electron,in C\n", + "\n", + "#Calculations\n", + "del_E = hcut/(2*del_t*e); # Energy of the state, in eV\n", + "\n", + "#Result\n", + "print \"The minimum error in measurement of lifetime of excited state of hydrogen atom = %6.4f eV\"%del_E\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The minimum error in measurement of lifetime of excited state of hydrogen atom = 0.0132 eV\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7, Page 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "del_x = 1e-09; # Uncertainty in position of the electron, m\n", + "m0 = 9.1e-031; # Rest mass of an electron, kg\n", + "hcut = 1.054e-034; # Planck's constant,in J-s\n", + "\n", + "#Calculations\n", + "del_v = hcut/(2*del_x*m0); # Uncertainity in velocity of the electron\n", + "\n", + "#Result\n", + "print \"The uncertainity in the velocity of an electron = %4.2e m/s\"%del_v\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The uncertainity in the velocity of an electron = 5.79e+04 m/s\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8, Page 81" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "hcut = 1.054e-34; # Reduced Planck's constant, Js\n", + "v = 3e+07; # Velocity of the electron, m/s\n", + "c = 3e+08; # Speed of light in vacuum, m/s\n", + "m0 = 9.1e-31; # Rest mass of an electron, kg\n", + "del_v = 3e+08; # Uncertainty in velocity of the electron, m/s\n", + "\n", + "#Calculations\n", + "del_x = (hcut*sqrt(1-v**2/c**2))/(2*m0*del_v);\n", + "\n", + "#Result\n", + "print \"The smallest possible uncertainity in position of the electron = %6.4f angstrom\"%(del_x/1e-010)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The smallest possible uncertainity in position of the electron = 0.0019 angstrom\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9, Page 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "n = 1;\n", + "m0 = 9.1e-031; # Mass of the electron, kg\n", + "a = 1e-10; # Width of the box, m\n", + "h = 6.63e-034; # Planck's constant, J-s\n", + "\n", + "#Calculations\n", + "E = n**2*h**2/(8*m0*a**2);\n", + "\n", + "#Result\n", + "print \"The energy of the electron moving in 1D infinetly high potential box = %5.2e J\"%E\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy of the electron moving in 1D infinetly high potential box = 6.04e-18 J\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10, Page 83" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "#n = [1,2]; # Shell numbers for two lowest permitted energy of the electron \n", + "m0 = 9.1e-31; # Mass of the electron, kg\n", + "a = 2.5e-10; # Width of the box, m\n", + "h = 6.63e-34; # Planck's constant, J-s\n", + "e = 1.6e-19; # Charge on electron, C\n", + "\n", + "#Calculations&Results\n", + "E = round((h**2)/(8*m0*a**2*e));\n", + "for n in range(1,3):\n", + " print \"The lowest two permitted energy values of an electron are\"\n", + " print E*n**2,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest two permitted energy values of an electron are\n", + "6.0 eV\n", + "The lowest two permitted energy values of an electron are\n", + "24.0 eV\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11, Page 83" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "m0 = 1.67e-27; # Rest mass,in kg\n", + "a = 1e-14; # Size of the box\n", + "h = 6.63e-34; # Planck's constant,in J-s\n", + "n = 1; # Quantum number for lowest energy state\n", + "\n", + "#Calculations\n", + "E_n = n**2*h**2/(8*m0*a**2);\n", + "\n", + "#Result\n", + "print \"The lowest energy of the neutron confined to the nucleus = %4.2e J\"%E_n\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest energy of the neutron confined to the nucleus = 3.29e-13 J\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12, Page 83" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Declaration\n", + "m0 = 9.1e-31; # Rest mass, kg\n", + "a = 1e-10; # Length of the box, m\n", + "h = 6.62e-34; # Planck's constat, J-s\n", + "n1 = 1; # Ground state\n", + "n2 = 2; # First excited state\n", + "e = 1.6e-19; # Charge on electron, C\n", + "\n", + "#Calculations\n", + "E1 = (n1**2*h**2)/(8*m0*a**2*e);\n", + "E2 = (n2**2*h**2)/(8*m0*a**2*e);\n", + "del_E = E2-E1; \n", + "\n", + "#Result\n", + "print \"The energy difference between the ground state and the first excited state = %5.1f eV\"%del_E\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy difference between the ground state and the first excited state = 112.9 eV\n" + ] + } + ], + "prompt_number": 11 + } + ], + "metadata": {} + } + ] +}
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