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-{
- "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": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-04-04 04:19:39 +0000