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diff --git a/Engineering_Physics_Malik/Chapter_16.ipynb b/Engineering_Physics_Malik/Chapter_16.ipynb new file mode 100644 index 00000000..0fab1922 --- /dev/null +++ b/Engineering_Physics_Malik/Chapter_16.ipynb @@ -0,0 +1,467 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 16: Free Electron Theory" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.1, Page 16.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 0 # temperature in K\n", + "E = 10 # Fermi energy of electron in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E_ = E * 3 / 5\n", + "v = sqrt(2 * E_ * e / m)\n", + "\n", + "#Result\n", + "print \"\\nAverage energy of electron is %.f eV\\nSpeed of electron is %.2e m/sec\"%(E_,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Average energy of electron is 6 eV\n", + "Speed of electron is 1.45e+06 m/sec\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.2, Page 16.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "t = 0 # temperature in K\n", + "E = 7.9 # Fermi energy in eV\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "E_ = E * 3 / 5\n", + "v = sqrt(2 * E_ * e / m)\n", + "\n", + "#Result\n", + "print \"Average energy of electron is %.2f eV\\nSpeed of electron is %.2e m/sec\"%(E_,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Average energy of electron is 4.74 eV\n", + "Speed of electron is 1.29e+06 m/sec\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.3, Page 16.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 2.5e28 # no. of free electron in per meter cube\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1. / e)\n", + "v = (h / (2 * pi * m)) * (3 * pi**2 * n)**(1./3)\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.2f eV\\nSpeed of electron is %.2e m/sec\"%(E,v)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 3.12 eV\n", + "Speed of electron is 1.05e+06 m/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.4, Page 16.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 8940 # density of copper in kg/m^3\n", + "w = 63.55 # atomic weight of copper\n", + "t = 0 # temperature in K\n", + "N = 6.02e26 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = w / d\n", + "n = N / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1. / e)\n", + "E_ = 3 * E / 5\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.3f eV\\nAverage energy is %.2f eV\"%(E,E_)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 7.036 eV\n", + "Average energy is 4.22 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.5, Page 16.16\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 10.5e6 # density of silver in g/m^3\n", + "w = 108 # atomic weight of silver\n", + "t = 0 # temperature in K\n", + "N = 6.02e23 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = w / d\n", + "n = N / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Fermi energy is %.1f eV\"%E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 5.5 eV\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.6, Page 16.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "a = 4e-10 # lattice constant in mr\n", + "t = 0 # temperature in K\n", + "N = 6.02e23 # Avogadro no. in per kg\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = a**3\n", + "n = 4 / V \n", + "E = (h**2 / (8 * pi**2 * m)) * (3 * pi**2 * n)**(2./3) * (1 / e)\n", + "k = (3 * pi**2 *n)**(1./3)\n", + "KE = (3 * E / 5) * (n)\n", + "\n", + "#Results\n", + "print \"Fermi energy is %.2f eV\\nFermi vector is %.2e per m\\nTotal kinetic energy is %.2e eV\"%(E,k,KE)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi energy is 5.75 eV\n", + "Fermi vector is 1.23e+10 per m\n", + "Total kinetic energy is 2.15e+29 eV\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.7, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "d = 0.9e-3 # diameter of aluminium in m\n", + "i = 6 # current in amp\n", + "n = 4.5e28 # no. of electron available for conduction per meter^3 \n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "J = i * 4 / (pi * (d)**2)\n", + "v = J / (n * e)\n", + "\n", + "#Result\n", + "print \"Drift velocity of electron is %.3e m/sec\"%v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Drift velocity of electron is 1.310e-03 m/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.8, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "d = 8.92e3 # density of copper in kg/m^3\n", + "i = 5 # current in amp\n", + "w = 63.5 # atomic weight of copper\n", + "r = 0.7e-3 # radius in meter\n", + "N = 6.02e28 # Avogadro no.\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "V = (w / d)\n", + "n = N / V \n", + "J = i / (pi * r**2)\n", + "v = J / (n * e)\n", + "\n", + "#Result\n", + "print \"Current density = %.2e amp/m^2\\nDrift velocity is %.1e m/sec\"%(J,v)\n", + "#Incorrect units in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current density = 3.25e+06 amp/m^2\n", + "Drift velocity is 2.4e-06 m/sec\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.9, Page 16.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given\n", + "d1= 0.534*10**3 # densiy of Li in kg/m^3\n", + "d2= 0.971*10**3 # densiy of Na in kg/m^3\n", + "d3= 0.86*10**3 # densiy of K in kg/m^3\n", + "w1 = 6.939 # atomic weight of Li \n", + "w2 = 22.99 # atomic weight of Na\n", + "w3 = 39.202 # atomic weight of K\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "m = 9.1e-31 # mass of an electron in kg\n", + "NA = 6.023e26 # Avogadro no.\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "# For Li\n", + "n1 = NA * d1/w1\n", + "E1 = h**2/(8*pi**2*m)*(3*pi**2*n1)**(2./3)\n", + "# For Na\n", + "n2 = NA * d2/w2\n", + "E2 = h**2/(8*pi**2*m)*(3*pi**2*n2)**(2./3)\n", + "# For K\n", + "n3 = NA * d3/w3\n", + "E3 = h**2/(8*pi**2*m)*(3*pi**2*n3)**(2./3)\n", + "\n", + "#Results\n", + "print \"Fermi Energy \\nFor Li is %.2f eV\\nFor Na is %.3f eV \\nFor K is %.3f eV\"%(E1/e,E2/e,E3/e)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi Energy \n", + "For Li is 4.71 eV\n", + "For Na is 3.156 eV \n", + "For K is 2.039 eV\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.10, Page 16.18\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1e-10 #length of box in m\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "h = 6.62e-34 # Planck constant in J-sec\n", + "\n", + "#Calculations\n", + "n = 1 # for n=1\n", + "E = (n**2 * h**2) / (8 * m * l**2)\n", + "n = 2 # for n=2\n", + "E_ = (n**2 * h**2) / (8 * m * l**2)\n", + "d = (E_ - E) * (1 / e)\n", + "\n", + "#Result\n", + "print \"Energy difference is %.2f eV\"%d" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy difference is 112.87 eV\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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