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-{
- "metadata": {
- "name": "",
- "signature": "sha256:cd8528b1343f720ba16c3255f8c2f531a0d8db6500634023001bba60d12d390a"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 5:Principles of Quantum Mechanics"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.1, Page number 5.12"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Varaible declaration\n",
- "c = 3*10**8 #velocity of air(m/s)\n",
- "m = 1.67*10**-27 #mass of proton(kg)\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "\n",
- "#Calculation\n",
- "v = c/10. #velocity of proton(m/s)\n",
- "lamda = h/(m*v)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",round((lamda/1E-14),3),\"*10^-14 m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 1.323 *10^-14 m\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.2, Page number 5.12"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "\n",
- "#Varaible declaration\n",
- "V = 400 #potential(V)\n",
- "\n",
- "#Calculation\n",
- "lamda = 12.26/math.sqrt(V)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",lamda,\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 0.613 A\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.3, Page number 5.12"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "\n",
- "#Varaible declaration\n",
- "E = 0.025 #kinetic energy of neutron(eV)\n",
- "m = 1.674*10**-27 #mass of neutron(kg)\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "\n",
- "#Calculations\n",
- "E_j = E*1.6*10**-19 #converting eV to joules\n",
- "lamda = h/math.sqrt(2*m*E_j)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",round((lamda/1E-11),3),\"*10^-11 m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 18.106 *10^-11 m\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.4, Page number 5.13"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "\n",
- "#Varaible declaration\n",
- "V = 1600 #potential(V)\n",
- "\n",
- "#Calculation\n",
- "lamda = 12.26/math.sqrt(V)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",lamda,\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 0.3065 A\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.5, Page number 5.21"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Varaible declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "L = 0.1*10**-9 #length of each side of box(m)\n",
- "#For lowest energy level,\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 113.08 eV\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.6, Page number 5.22"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "L = 0.1*10**-9 #length of each side of box(m)\n",
- "#For level next to lowest energy level,\n",
- "nx = 1\n",
- "ny = 1\n",
- "nz = 2\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 226.15 eV\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.7, Page number 5.23"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "E = 2000. #energy of electron(eV)\n",
- "\n",
- "#Calculations\n",
- "Ej = E*1.6*10**-19 #converting eV to joules\n",
- "lamda = h/math.sqrt(2*m*Ej)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",round((lamda/1E-9),4),\"nm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 0.0275 nm\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.8, Page number 5.23"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "L = 4*10**-10 #length of each side of box(m)\n",
- "#For minimum energy \n",
- "n = 1\n",
- "\n",
- "#Calculations\n",
- "E1 = ((h**2)*(n**2))/(8*m*L**2)\n",
- "\n",
- "#Result\n",
- "print \"Minimum energy =\",round((E1/1E-18),3),\"*10^-18 J\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Minimum energy = 0.377 *10^-18 J\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.9, Page number 5.24"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "L = 1*10**-10 #length of each side of box(m)\n",
- "n1 = 10 #For energy in ground state\n",
- "n2 = 2 #For energy in first excited state\n",
- "n3 = 3 #For energy in second excited state\n",
- "\n",
- "#Calculations\n",
- "E1 = ((h**2)*(n1**2))/(8*m*L**2)\n",
- "E2 = ((h**2)*(n2**2))/(8*m*L**2)\n",
- "E3 = ((h**2)*(n3**2))/(8*m*L**2)\n",
- "\n",
- "#Results\n",
- "print \"Energy in ground state =\",round((E1/1E-17),4),\"*10^17 J (Calculation mistake in textbook)\"\n",
- "print \"Energy in first excited state =\",round((E2/1E-17),4),\"*10^17 J\"\n",
- "print \"Energy in second excited state =\",round((E3/1E-17),4),\"*10^17 J\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Energy in ground state = 60.3075 *10^17 J (Calculation mistake in textbook)\n",
- "Energy in first excited state = 2.4123 *10^17 J\n",
- "Energy in second excited state = 5.4277 *10^17 J\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.10, Page number 5.24"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#Variable declaration\n",
- "h = 6.626*10**-34 #Planck's constant(J x sec)\n",
- "m = 9.1*10**-31 #mass of electron(kg)\n",
- "lamda = 1.66*10**-10 #wavelength(m)\n",
- "\n",
- "#Calculations\n",
- "v = h/(m*lamda)\n",
- "KE = (m*v**2)/(2*1.6*10**-19) #in joules\n",
- "\n",
- "#Result\n",
- "print \"Velocity of electron =\",round((v/1E+7),4),\"*10^7 m\"\n",
- "print \"Kinetic energy of electron =\",round(KE,2),\"eV\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Velocity of electron = 0.4386 *10^7 m\n",
- "Kinetic energy of electron = 54.71 eV\n"
- ]
- }
- ],
- "prompt_number": 22
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.11, Page number 5.25"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "\n",
- "#Varaible declaration\n",
- "V = 15*10**3 #potential(V)\n",
- "\n",
- "#Calculation\n",
- "lamda = 12.26/math.sqrt(V)\n",
- "\n",
- "#Result\n",
- "print \"The de Brogile wavelength is\",round(lamda,2),\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The de Brogile wavelength is 0.1 A\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 5.12, Page number 5.25"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "import math\n",
- "\n",
- "#Varaible declaration\n",
- "V = 344 #potential(V)\n",
- "theta = 60 #glancing angle(degrees)\n",
- "\n",
- "#Calculation\n",
- "lamda = 12.26/math.sqrt(V)\n",
- "#For first reflection \n",
- "n = 1\n",
- "d = (n*lamda)/(2*math.sin(math.radians(theta)))\n",
- "\n",
- "#Result\n",
- "print \"The interatomic spacing of the crystal is\",round(d,4),\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The interatomic spacing of the crystal is 0.3816 A\n"
- ]
- }
- ],
- "prompt_number": 24
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-04-06 05:42:44 +0000