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diff --git a/Solid_state_physics_by_P._K._Palanisamy/Chapter_6.ipynb b/Solid_state_physics_by_P._K._Palanisamy/Chapter_6.ipynb new file mode 100755 index 00000000..2b4f9a24 --- /dev/null +++ b/Solid_state_physics_by_P._K._Palanisamy/Chapter_6.ipynb @@ -0,0 +1,386 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:425f92ebc94b7b662d737292c7c739a2d9f7bf01d4a0a5239c1380861a6af3a7" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6: Electron theory of Metals" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.1, Page number 6.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "rho_s = 10.5*10**3 #density of silver(kg/m^3)\n", + "Na = 6.02*10**26 #Avogadro's number\n", + "Ma = 107.9 #atomic weight of silver\n", + "sigma = 6.8*10**7 #conductivity(/ohm-m)\n", + "e = 1.6*10**-19 #charge of an electron(C)\n", + "\n", + "#Calculations\n", + "n = (rho_s*Na)/Ma\n", + "u = sigma/(n*e)\n", + "\n", + "#Results\n", + "print \"Density of electrons =\",round((n/1E+28),2),\"*10^28\"\n", + "print \"Mobility of electrons =\",round((u/1E-2),3),\"*10^-2 m^2/V-s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of electrons = 5.86 *10^28\n", + "Mobility of electrons = 0.725 *10^-2 m^2/V-s\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.2, Page number 6.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "den = 8.92*10**3 #density(kg/m^3)\n", + "rho = 1.73*10**-8 #resistivity of copper(ohm-m)\n", + "Ma = 63.5 #atomic weight\n", + "e = 1.6*10**-19 #charge of an electron(C)\n", + "Na = 6.02*10**26 #Avogadro's number\n", + "m = 9.1*10**-31 #mass of an electron(kg)\n", + "\n", + "#Calculations\n", + "n = (den*Na)/Ma\n", + "u = 1/(rho*n*e)\n", + "tou = m/(n*e**2*rho)\n", + "\n", + "#Results\n", + "print \"Mobility of electrons =\",round((u/1E-2),3),\"*10^-2 m/V-s\"\n", + "print \"Average time of collision of electrons =\",round((tou/1E-14),2),\"*10^-14 s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mobility of electrons = 0.427 *10^-2 m/V-s\n", + "Average time of collision of electrons = 2.43 *10^-14 s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.3, Page number 6.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "P = 1.54*10**-8 #resistivity(ohm-m)\n", + "n = 5.8*10**28 #no. of electrons per m^3\n", + "m = 9.108*10**-31 #mass of an elecron(kg)\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "\n", + "#Calculations\n", + "tou = m/(n*e**2*P)\n", + "\n", + "#Result\n", + "print \"The relaxation time of conducton of electrons is\",round((tou/1E-14),2),\"*10^-14 s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relaxation time of conducton of electrons is 3.97 *10^-14 s\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4, Page number 6.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "R = 0.06 #resistance(ohms)\n", + "D = 5 #length of wire(m)\n", + "I = 15 #current(A)\n", + "p = 2.7*10**-8 #resistivity of aluminium(ohm-m)\n", + "Ma = 26.98 #atomic weight\n", + "Na = 6.025*10**26 #Avogadro's number\n", + "rho_s = 2.7*10**3 #sensity(kg/m^3)\n", + "\n", + "#Calculations\n", + "#Since each free atom atom contains 3 electrons, therefore,\n", + "n = (3*rho_s*Na)/Ma\n", + "\n", + "#For mobility\n", + "u = 1/(n*e*p)\n", + "\n", + "#For drift velocity\n", + "E = (I*R)/D\n", + "vd = u*E\n", + "\n", + "#Results\n", + "print \"Free electron concentration =\",round((n/1E+29),4),\"*10^29 electrons/m^2\"\n", + "print \"Mobility of electrons =\",round((u/1E-3),3),\"*10^-3 m/V-s\"\n", + "print \"Drift velocity of electrons =\",round((vd/1E-3),3),\"*10^-3 m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Free electron concentration = 1.8088 *10^29 electrons/m^2\n", + "Mobility of electrons = 1.278 *10^-3 m/V-s\n", + "Drift velocity of electrons = 0.23 *10^-3 m/s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "L = 0.1*10**-9 #length of each side of box(m)\n", + "h = 6.62*10**-34 #Planck's constant(J-s)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "#For lowest energy,\n", + "nx = 1\n", + "ny = 1\n", + "nz = 1\n", + "\n", + "#Calculations\n", + "E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))//(1.6*10**-19)\n", + "\n", + "#Result\n", + "print \"The lowest energy of electron is\",round(E1,2),\"eV\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest energy of electron is 112.0 eV\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exmple 6.6, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "Given, E-Ef = kT\n", + "therefore,\n", + "F(E) = 1\n", + " --------\n", + " 1+exp(1)\n", + "'''\n", + "\n", + "#Calculation\n", + "Fe = 1./(1.+math.exp(1.))\n", + "\n", + "#Result\n", + "print \"F(E) =\",round(Fe,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "F(E) = 0.269\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.7, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#Variable declaration\n", + "Fe = 10./100. #probability\n", + "Ef = 5.5 #Fermi energy(eV)\n", + "k = 1.38*10**-23\n", + " \n", + "#Calculations\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "'''\n", + "E = Ef+(Ef/100)\n", + "E_Ef = (E - Ef)*1.6*10**-19 #(J)\n", + "\n", + "#Let x be E-Ef/k\n", + "x = E_Ef/k\n", + "T = x/math.log(-(1-(1/Fe)))\n", + "\n", + "#Result\n", + "print \"Temperature =\",round(T,2),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature = 290.22 K\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8, Page number 6.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#Variable declaration\n", + "Fe = 1./100. #probability\n", + "Ef = 0.5 #Fermi energy(eV)\n", + "k = 1.38*10**-23\n", + " \n", + "#Calculations\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "'''\n", + "\n", + "E = Ef+0.5\n", + "E_Ef = (E - Ef)*1.6*10**-19 #(J)\n", + "\n", + "#Let x be E-Ef/k\n", + "x = E_Ef/k\n", + "T = x/math.log(-(1-(1/Fe)))\n", + "\n", + "#Result\n", + "print \"Temperature =\",round(T),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature = 1262.0 K\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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