From 4a1f703f1c1808d390ebf80e80659fe161f69fab Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- .../Chapter2_3.ipynb | 272 +++++++++++++++++++++ 1 file changed, 272 insertions(+) create mode 100644 ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter2_3.ipynb (limited to 'ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter2_3.ipynb') diff --git a/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter2_3.ipynb b/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter2_3.ipynb new file mode 100644 index 00000000..8b0abd3c --- /dev/null +++ b/ELECTRICAL_ENGINEERING_MATERIALS_by_R.K.Shukla/Chapter2_3.ipynb @@ -0,0 +1,272 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Chapter 2:Band Theory of Solids" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Example 2.1,Page No:2.2" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lowest three permissable quantum energies are E1 = 6 eV\n", + " E2 = 24 eV\n", + " E3 = 54 eV\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#variable declaration\n", + "h = 6.63*10**-34; # plancks constant in J.s\n", + "m = 9.1*10**-31; # mass of electron in kg\n", + "a = 2.5*10**-10; # width of infinite square well\n", + "e = 1.6*10**-19; # charge of electron coulombs\n", + "n2 = 2; #number of permiissable quantum\n", + "n3 = 3; #number of permiissable quantum\n", + "\n", + "# Calculations\n", + "E1 = (h**2)/float(8*m*a**2*e); # first lowest permissable quantum energy in eV\n", + "E2 = n2**2 *E1; # second lowest permissable quantum energy in eV\n", + "E3 = n3**2 *E1; # second lowest permissable quantum energy in eV\n", + "\n", + "# Result\n", + "print'Lowest three permissable quantum energies are E1 = %d'%E1,'eV';\n", + "print' E2 = %d'%E2,'eV';\n", + "print' E3 = %d'%E3,'eV';" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2,Page No:2.4" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Energy Difference = 113.21 eV\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#variable declaration\n", + "h = 6.63*10**-34; # plancks constant in J.s\n", + "m = 9.1*10**-31; # mass of electron in kg\n", + "a = 10**-10; # width of infinite square well in m\n", + "e = 1.6*10**-19; # charge of electron in coulombs\n", + "n1 = 1; #energy level constant\n", + "n2 = 2; #energy level constant\n", + "\n", + "# calculations\n", + "E1 = ((n1**2)*(h**2))/float(8*m*(a**2)*e); # ground state energy in eV\n", + "E2 = ((n2**2)*(h**2))/float(8*m*(a**2)*e); # first excited state in energy in eV\n", + "dE = E2-E1 # difference between first excited and ground state(E2 - E1)\n", + "\n", + "#Result\n", + "print'Energy Difference = %3.2f '%dE,'eV';\n", + "\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3,Page No:2.5" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "First Three Energy levels are \n", + " E1 = 1.51 eV\n", + " E2 = 6 eV\n", + " E3 = 13.59 eV\n", + "\n", + " Above calculation shows that the energy of the bound electron cannot be continuous\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variable declaration\n", + "h = 6.63*10**-34; # plancks constant in J.s\n", + "m = 9.1*10**-31; # mass of electron in kg\n", + "a = 5*10**-10; # width of infinite potential well in m\n", + "e = 1.6*10**-19; # charge of electron in coulombs\n", + "n1 = 1; # energy level constant\n", + "n2 = 2; # energy level constant\n", + "n3 = 3; # energy level constant\n", + "\n", + "#Calculations\n", + "E1 = ((n1**2)*(h**2))/(8*m*(a**2)*e); # first energy level in eV\n", + "E2 = ((n2**2)*(h**2))/(8*m*(a**2)*e); # second energy level in eV\n", + "E3 = ((n3**2)*(h**2))/(8*m*(a**2)*e); # third energy level in eV\n", + "\n", + "# Result\n", + "print'First Three Energy levels are \\n E1 = %3.2f'%E1,'eV';\n", + "print' E2 = %d'%E2,'eV';\n", + "print' E3 = %3.2f'%E3,'eV';\n", + "print'\\n Above calculation shows that the energy of the bound electron cannot be continuous';\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4,Page No:2.5" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lowest energy bandwidth = 0.452 eV\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#variable declaration\n", + "h = 1.054*10**-34; #plancks constant in J.s\n", + "m = 9.1*10**-31; #mass of electron in kg\n", + "a = 5*10**-10; #width of infinite potential well in m\n", + "e = 1.6*10**-19; # charge of electron coulombs\n", + "\n", + "# Calculations\n", + "#cos(ka) = ((Psin(alpha*a))/(alpha*a)) + cos(alpha*a)\n", + "#to find the lowest allowed energy bandwidth,we have to find the difference in αa values, as ka changes from 0 to π\n", + "# for ka = 0 in above eq becomes\n", + "# 1 = 10*sin(αa))/(αa)) + cos(αa)\n", + "# This gives αa = 2.628 rad\n", + "# ka = π , αa = π\n", + "# sqrt((2*m*E2)/h**2)*a = π\n", + "\n", + "E2 = ((math.pi*math.pi)*h**2)/(2*m*a**2*e); #energy in eV\n", + "E1 = ((2.628**2)*h**2)/(2*m*a**2*e); #for αa = 2.628 rad energy in eV\n", + "dE = E2 - E1; #lowest energy bandwidth in eV\n", + "\n", + "# Result\n", + "print'Lowest energy bandwidth = %3.3f'%dE,'eV';\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5,Page No:2.8" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Electron Momentum for first Brillouin zone appearance = 1.105e-24 eV\n", + "\n", + " Energy of free electron with this momentum = 4.2 eV\n", + "\n", + " Note: in Textbook Momentum value is wrongly printed as 1.1*10**-10\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variable declaration\n", + "a = 3*10**-10; # side of 2d square lattice in m\n", + "h = 6.63*10**-34; # plancks constant in J.s\n", + "e = 1.6*10**-19 # charge of electron in coulombs\n", + "m = 9.1*10**-31; # mass of electron in kg\n", + "\n", + "# calculations\n", + "#p = h*k # momentum of the electron\n", + "k = math.pi/float(a); # first Brillouin zone\n", + "p = (h/float(2*math.pi))*(math.pi/float(a)); # momentum of electron\n", + "E = (p**2)/float(2*m*e) # Energyin eV\n", + "\n", + "#Result\n", + "print'Electron Momentum for first Brillouin zone appearance = %g'%p,'eV';\n", + "print'\\n Energy of free electron with this momentum = %4.1f'%E,'eV';\n", + "print'\\n Note: in Textbook Momentum value is wrongly printed as 1.1*10**-10';" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- cgit