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diff --git a/Applied_Physics-II_by_I_A_Shaikh/chapter5.ipynb b/Applied_Physics-II_by_I_A_Shaikh/chapter5.ipynb new file mode 100755 index 00000000..e9d81103 --- /dev/null +++ b/Applied_Physics-II_by_I_A_Shaikh/chapter5.ipynb @@ -0,0 +1,1166 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:fec7a7bbab2881090f60069cf3d4c856415ca45a1545225541a225f28ce72b8e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5: Foundations of Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1,Page number 5-23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=6.68*10**-27 #mass of alpha particle\n", + "V=30*10**3 #potential difference\n", + "e=1.6*10**-19 #charge of an electron\n", + "q=2*e #Charge of alpha particle\n", + "h=6.63*10**-34 #Planck's constant\n", + "\n", + "#Calculations:\n", + "lamda=h/math.sqrt(2*m*q*V) #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with alpha particle is =\" ,lamda,\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de Broglie wavelength associated with alpha particle is = 5.85429607723e-14 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2,Page number 5-23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #mass of given particle in kg\n", + "h=6.63*10**-34 #Planck's constant\n", + "v=1*10**3 #velocity of particle\n", + "\n", + "#Calculations:\n", + "lamda=h/(m*v) #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with particle is =\",lamda,\"m\"\n", + "print\"This wavelength is too small for any practical significance.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de Broglie wavelength associated with particle is = 6.63e-37 m\n", + "This wavelength is too small for any practical significance.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3,Page number 5-24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m1=40*10**-3 #mass of bullet in kg\n", + "m2=9.1*10**-31 #mass of electron in kg\n", + "h=6.63*10**-34 #Planck's constant\n", + "v=1100 #velocity of bullet and electron\n", + "\n", + "#Calculations:\n", + "lamda1=h/(m1*v) #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with bullet is =\",lamda1,\"m\"\n", + "\n", + "lamda2=h/(m2*v) #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with electron is =\",lamda2,\"m\"\n", + "\n", + "print\"Wavelength of bullet is too small.Hence it can not be measured with help of diffraction effect.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " de Broglie wavelength associated with bullet is = 1.50681818182e-35 m\n", + "de Broglie wavelength associated with electron is = 6.62337662338e-07 m\n", + "Wavelength of bullet is too small.Hence it can not be measured with help of diffraction effect.\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4,Page number 5-24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "V=100 #potential difference\n", + "d=2.15*10**-10 #lattice spacing\n", + "\n", + "#Calculations:\n", + "lamda=12.26*10**-10/(math.sqrt(V)) #wavelength associated with electron in meter\n", + "\n", + "#using bragg's law for first order lamda=2d sin(theta)\n", + "theta=math.degrees(math.asin(lamda/(2*d))) #glancing angle in degrees\n", + "print\"Glancing angle at which first reflection occurs is =\",theta,\"Degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Glancing angle at which first reflection occurs is = 16.5657992687 Degrees\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5,Page number 5-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "mn=1.674*10**-27 #mass of neutron\n", + "h=6.63*10**-34 #Planck's constant\n", + "lamda=1*10**-10 #wavelength of neutron\n", + "\n", + "#Calculations:\n", + "\n", + "#we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "E1=h**2/(2*mn*lamda**2) #Energy of neutron in joules\n", + "E=E1/(1.6*10**-19) #Energy of neutron in electron-Volts\n", + "\n", + "print\"Energy of neutron is =\",E,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of neutron is = 0.0820581317204 eV\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6,Page number 5-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "mn=1.67*10**-27 #mass of neutron\n", + "h=6.6*10**-34 #Planck's constant\n", + "lamda=3*10**-10 #wavelength of neutron\n", + "d=3.036*10**-10 #lattice spacing\n", + "\n", + "#Calculations:\n", + "\n", + "#we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "E1=h**2/(2*mn*lamda**2) #Energy of neutron in joules\n", + "E=E1/(1.6*10**-19) # Energy of neutron in electron-Volts\n", + "print\"Energy of neutron is =\",E,\"eV\"\n", + "\n", + "#using bragg's law for first order lamda=2d sin(theta)\n", + "theta=math.degrees(math.asin(lamda/(2*d))) #glancing angle in degrees\n", + "print\" Glancing angle at which first orde reflection occurs is =\",theta,\"Degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of neutron is = 0.00905688622754 eV\n", + " Glancing angle at which first orde reflection occurs is = 29.6085193042 Degrees\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7,Page number 5-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=9.108*10**-31 #mass of electron\n", + "h=6.625*10**-34 #Planck's constant\n", + "lamda=5*10**-7 #wavelength of electron\n", + "\n", + "#Calculations:\n", + "\n", + "#we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "E1=h**2/(2*m*lamda**2) #Energy of electron in joules\n", + "E=E1/(1.6*10**-19) #Energy of electron in electron-Volts\n", + "print\"Energy of electron is =\",E,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron is = 6.02363650088e-06 eV\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.8,Page number 5-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "mn=1.676*10**-27 #mass of neutron\n", + "me=9.1*10**-31 #mass of electron\n", + "h=6.625*10**-34 #Planck's constant\n", + "\n", + "#Calculations:\n", + "#Part 1:\n", + "En1=0.025 #Energy in eV of neutron\n", + "En=En1*(1.6*10**-19) #Energy in joules\n", + "\n", + "lamda1=h/math.sqrt(2*mn*En) #wavelength of a beam of neutron\n", + "print\"wavelength of a beam of neutron is =\",lamda1,\"m\"\n", + "\n", + "#Part 2:\n", + "lamda2=2*10**-10 #wavelength of electron and photon\n", + "\n", + "#//we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "Ee1=h**2/(2*me*lamda2**2) #Energy of electron in joules\n", + "Ee=Ee1/(1.6*10**-19) #Energy of electron in electron-Volts\n", + "print\"Energy of electron is =\",Ee,\"eV\"\n", + "\n", + "p1=h/lamda2 #momentum of electron\n", + "print\" Momentum of electron is =\",p1,\"kg.m/s\"\n", + "\n", + "C=3*10**8 #Velocity of light\n", + "Ep=h*C/lamda2 #Energy of photon in joules\n", + "print\"Energy of photon is =\",Ep,\"Joules\"\n", + "\n", + "p2=h/lamda2 #momentum of photon\n", + "print\"Momentum of photon is =\",p2,\"kg.m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of a beam of neutron is = 1.80927208246e-10 m\n", + "Energy of electron is = 37.6808250343 eV\n", + " Momentum of electron is = 3.3125e-24 kg.m/s\n", + "Energy of photon is = 9.9375e-16 Joules\n", + "Momentum of photon is = 3.3125e-24 kg.m/s\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9,Page number 5-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data:\n", + "#We have alpha particle,neutron,proton and electron.\n", + "\n", + "#To find: shortest wavelength\n", + "\n", + "print\"We know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\"\n", + "\n", + "#Wavelength is inversely proportional to mass of particle for constant energy\n", + "print\"i.e., Wavelength is inversely proportional to mass of particle for constant energy. \"\n", + "\n", + "print\"We have alpha particle,neutron,proton and electron.\"\n", + "\n", + "#AS,alpha particle has highest mass.Thus it will have shortest wavelength.\n", + "print\"Out of above, alpha particle has highest mass.\"\n", + "\n", + "print\"Hence it will have shortest wavelength.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "We know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "i.e., Wavelength is inversely proportional to mass of particle for constant energy. \n", + "We have alpha particle,neutron,proton and electron.\n", + "Out of above, alpha particle has highest mass.\n", + "Hence it will have shortest wavelength.\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10,Page number 5-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "me=9.108*10**-31 # mass of electron\n", + "mp=1.66*10**-27 # bmass of proton\n", + "h=6.625*10**-34 # Planck's constant\n", + "lamda=1*10**-10 # wavelength of electron and proton\n", + "\n", + "#Calculations:\n", + "\n", + "#we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "Ee1=h**2/(2*me*lamda**2) #Energy of electron in joules\n", + "Ee=Ee1/(1.6*10**-19) #Energy of electron in electron-Volts\n", + "print\"Energy of electron is =\",Ee,\"eV\"\n", + "\n", + "Ep1=h**2/(2*mp*lamda**2) #Energy of photon in joules\n", + "Ep=Ep1/(1.6*10**-19) #Energy of photon in electron-Volts\n", + "print\"Energy of photon is =\",Ep,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of electron is = 150.590912522 eV\n", + "Energy of photon is = 0.0826254235693 eV\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.11,Page number 5-29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m1=50*10**-9 #mass of particle in kg\n", + "m2=9.1*10**-31 #mass of electron in kg\n", + "h=6.625*10**-34 #Planck's constant\n", + "v1=1 #velocity of particle\n", + "v2=3*10**6 #velocity of electron\n", + "\n", + "#Calculations:\n", + "lamda1=h/(m1*v1)*10**10 #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with particle is =\",lamda1,\"Angstrom\"\n", + "\n", + "lamda2=h/(m2*v2)*10**10 #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with electron is =\",lamda2,\"Angstrom\"\n", + "\n", + "print\"Wavelength of electron is measurable.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de Broglie wavelength associated with particle is = 1.325e-16 Angstrom\n", + "de Broglie wavelength associated with electron is = 2.42673992674 Angstrom\n", + "Wavelength of electron is measurable.\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.12,Page number 5-29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "me=9.1*10**-31 #mass of electron in kg\n", + "h=6.63*10**-34 #Planck's constant\n", + "\n", + "#Calculations:\n", + "\n", + "E1=2*10**3 #Energy in eV of electron\n", + "E=E1*(1.6*10**-19) #Energy in joules\n", + " \n", + "lamda=h/math.sqrt(2*me*E) #wavelength of electron\n", + "print\"Wavelength of electron is =\",lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of electron is = 2.7472794985e-11 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.13,Page number 5-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "me=9.1*10**-31 #mass of electron\n", + "h=6.63*10**-34 #Planck's constant\n", + "lamda=2*10**-10 #wavelength of electron and photon\n", + "\n", + "#Calculations:\n", + "p1=h/lamda #momentum of electron\n", + "print\"Momentum of electron is =\",p1,\"kg.m/s\"\n", + "\n", + "Ee=p1**2/(2*me) #Energy of electron in joules\n", + "print\"Energy of electron is =\",Ee,\"Joules\"\n", + "\n", + "p2=h/lamda #momentum of photon\n", + "print\"Momentum of photon is =\",p2,\"kg.m/s\"\n", + "\n", + "c=3*10**8 #Velocity of light\n", + "Ep=h*c/lamda #Energy of photon in joules\n", + "print\"Energy of photon is =\",Ep,\"Joules\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Momentum of electron is = 3.315e-24 kg.m/s\n", + "Energy of electron is = 6.03803571429e-18 Joules\n", + "Momentum of photon is = 3.315e-24 kg.m/s\n", + "Energy of photon is = 9.945e-16 Joules\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.14,Page number 5-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1.676*10**-27 #mass of neutron\n", + "h=6.625*10**-34 #Planck's constant\n", + "lamda=1*10**-10 #wavelength of neutron\n", + "\n", + "#Calculations:\n", + "C=3*10**8 #Velocity of light\n", + "Ep1=h*C/lamda #Energy of photon in joules\n", + "E1=Ep1/(1.6*10**-19) #Energy of photon in electron-Volts\n", + "print\"Energy of photon is =\",E1,\"eV\"\n", + "\n", + "#we know, lamda=h/sqrt(2*m*E) #de Broglie wavelength\n", + "En1=h**2/(2*m*lamda**2) #Energy of neutron in joules\n", + "E2=En1/(1.6*10**-19) #Energy of neutron in electron-Volts\n", + "print\"Energy of neutron is =\",E2,\"eV\"\n", + "\n", + "R=E1/E2 #Ratio of energies of proton to neutron\n", + "print\"Ratio of energies of proton to neutron is =\",R\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of photon is = 12421.875 eV\n", + "Energy of neutron is = 0.0818366367094 eV\n", + "Ratio of energies of proton to neutron is = 151788.679245\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Example 5.14.1,Page number 5-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "v=900 #velocity of electron in m/s\n", + "delv=v*0.001/100 #uncertainity in velocity\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.1*10**-31 #mass of an electron\n", + "\n", + "#Calculations:\n", + "delp=m*delv #uncertainity in the measured values of momentum\n", + "\n", + "#using heisenberg's uncertainity formula\n", + "delx=h/(2*3.142*delp) #uncertainity in its position\n", + "print\"Uncertainity with which position of electron can be located is >=\",delx,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertainity with which position of electron can be located is >= 0.0128823012337 m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.14.2,Page number 5-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1.6*10**-27 #mass of proton in kg\n", + "h=6.63*10**-34 #Planck's constant\n", + "v=3./20*10**8 #velocity of particle\n", + "\n", + "#Calculations:\n", + "lamda=h/(m*v) #de Broglie wavelength\n", + "print\"de Broglie wavelength associated with proton is =\",lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "de Broglie wavelength associated with proton is = 2.7625e-14 m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.14.3,Page number 5-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1.676*10**-27 #mass of neutron\n", + "h=6.634*10**-34 #Planck's constant\n", + "\n", + "#Calculations:\n", + "E1=0.025 #Energy in eV of neutron\n", + "E=E1*(1.6*10**-19) #Energy in joules\n", + "#As E=m*v**2/2\n", + "v=math.sqrt(2*E/m) #Velocity of neutron beam\n", + "\n", + "lamda=h/(m*v) #wavelength of a beam of neutron\n", + "print\"wavelength of a beam of neutron is =\",lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of a beam of neutron is = 1.81172996152e-10 m\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.14.4,Page number 5-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "delx=10*10**-9 #uncertainity in position of electron\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.1*10**-31 #mass of an electron\n", + "E=10**3*1.6*10**-19 #Energy of electron in joules\n", + "\n", + "#Calculations:\n", + "p=math.sqrt(2*m*E) #momentum of electron\n", + "#using heisenberg's uncertainity formula\n", + "delp=h/(2*math.pi*delx) #uncertainity in the momentum\n", + "\n", + "P=delp/p*100 #percentage of uncertainity in momentum\n", + "print\"Percentage of uncertainity in momentum of electron is =\",P,\"percent\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage of uncertainity in momentum of electron is = 0.0618355139385 percent\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.15,Page number 5-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1.676*10**-27 #mass of neutron\n", + "h=6.63*10**-34 #Planck's constant\n", + "lamda=2*10**-12 #wavelength of neutron\n", + "c=3*10**8 #Velocity of light\n", + "\n", + "#Calculations:\n", + "p=h/lamda #momentum of neutron\n", + "KE=p**2/(2*m) #Kinetic Energy of neutron in joules\n", + "print\"Kinetic Energy of electron is =\",KE,\"Joules\"\n", + "\n", + "#velocity of particle is same as group velocity. Thus,\n", + "vg=p/m #group velocity\n", + "print\"group velocity of neutron is =\",vg,\"m/s\"\n", + "\n", + "#using, vg*vp=c**2\n", + "vp=c**2/vg #phase velocity\n", + "print\" phase velocity of neutron is =\",vp,\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Kinetic Energy of electron is = 3.27840841289e-17 Joules\n", + "group velocity of neutron is = 197792.362768 m/s\n", + " phase velocity of neutron is = 4.55022624434e+11 m/s\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.16,Page number 5-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1.157*10**-30 #mass of particle in kg\n", + "h=6.63*10**-34 #Planck's constant\n", + "c=3*10**8 #Velocity of light\n", + "\n", + "#Calculations:\n", + "E1=80 #Energy in eV of particle\n", + "E=E1*(1.6*10**-19) #Energy in joules\n", + " \n", + "lamda=h/math.sqrt(2*m*E) #wavelength of particle\n", + "print\"Wavelength of particle is =\",lamda,\"m\"\n", + "\n", + "#Now,\n", + "vg=h/(lamda*m) #group velocity\n", + "print\"Group velocity of particle is =\",vg,\"m/s\"\n", + "\n", + "#using, vg*vp=c**2\n", + "vp=c**2/vg #phase velocity\n", + "print\"Phase velocity of particle is =\",vp,\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of particle is = 1.21822320075e-10 m\n", + "Group velocity of particle is = 4703848.2563 m/s\n", + "Phase velocity of particle is = 19133270270.7 m/s\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.17,Page number 5-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "v=400 #velocity of electron in m/s\n", + "delv=0.01/100 #uncertainity in velocity\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.11*10**-31 #mass of an electron\n", + "\n", + "#Calculations:\n", + "p=m*v #momentum of an electron\n", + "delp=p*delv #uncertainity in the measured values of momentum\n", + "\n", + "#using heisenberg's uncertainity formula\n", + "delx=h/(2*math.pi*delp) #accuracy in its position\n", + "print\"Accuracy in its position is >=\",delx,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Accuracy in its position is >= 0.00289571150576 m\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.18,Page number 5-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#Given Data:\n", + "delx=10**-8 #maximum uncertainity in position of electron\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.1*10**-31 #mass of an electron\n", + "\n", + "#Calculations:\n", + "#using heisenberg's uncertainity formula\n", + "delp=h/(2*math.pi*delx) #minimum uncertainity in the measured values of momentum\n", + "\n", + "delv=delp/m #minimum uncertainity in the velocity of an electron\n", + "print\"Minimum uncertainity in the velocity of an electron is =\",delv,\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum uncertainity in the velocity of an electron is = 11595.5744253 m/s\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.19,Page number 5-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "delv=2*10**4 #uncertainity in velocity\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.1*10**-31 #mass of an electron\n", + "\n", + "#Calculations:\n", + "delp=m*delv #uncertainity in the measured values of momentum\n", + "\n", + "#using heisenberg's uncertainity formula\n", + "delx=h/(2*math.pi*delp) #accuracy in its position\n", + "print\"Minimum space required by electron to be confined in an atom is >=\",delx,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum space required by electron to be confined in an atom is >= 5.79778721263e-09 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.20,Page number 5-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "delt=1.4*10**-10 #uncertainity in time spent by nucleus in excited state\n", + "h=6.63*10**-34 #Planck's constant\n", + "\n", + "#Calculations:\n", + "\n", + "#using, delE*delt>= h/(2*math.pi)\n", + "delE1= h/(2*math.pi*delt) #uncertaininty in its energy in excited state in joules\n", + "delE=delE1/(1.6*10**-19) #uncertaininty in its energy in excited state in eV\n", + "print\"Uncertaininty in its energy in excited state is >=\",delE,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uncertaininty in its energy in excited state is >= 4.71070211026e-06 eV\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.21,Page number 5-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "a=2*10**-10 #width of potential well in m\n", + "h=6.63*10**-34 #Planck's constant\n", + "m=9.1*10**-31 #mass of an electron\n", + "\n", + "#Calculations:\n", + "#we know equation for energy of an electron\n", + "n0=1\n", + "E01=n0**2*h**2/(8*m*a**2) #Energy in ground state\n", + "E0=E01/(1.6*10**-19) #Energy in eV\n", + "print\"Energy of an electron in ground state is=\",E0,\"eV\"\n", + "\n", + "n1=2\n", + "E11=n1**2*h**2/(8*m*a**2) #Energy in first excited state\n", + "E1=E11/(1.6*10**-19) #Energy in eV\n", + "print\" Energy of an electron in first excited state is=\",E1,\"eV\"\n", + "\n", + "\n", + "n2=3\n", + "E21=n2**2*h**2/(8*m*a**2) #Energy in second excited state\n", + "E2=E21/(1.6*10**-19) #Energy in eV\n", + "print\"Energy of an electron in second excited state is=\",E2,\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of an electron in ground state is= 9.43443080357 eV\n", + " Energy of an electron in first excited state is= 37.7377232143 eV\n", + "Energy of an electron in second excited state is= 84.9098772321 eV\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.22,Page number 5-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "a=25*10**-10 #width of well\n", + "delx=5*10**-10 #uncertainity in position of particle\n", + "n=1 #ground state\n", + "\n", + "#calculation:\n", + "x1=a/2\n", + "psi1=math.sqrt(2/a)*math.sin(n*math.pi/a*x1)\n", + "P1=(psi1**2)*delx #Probability of finding particle at distance of x1\n", + "print\"Probability of finding particle at a distance of x1 is =\",P1\n", + "\n", + "x2=a/3\n", + "psi2=math.sqrt(2/a)*math.sin(n*math.pi/a*x2)\n", + "P2=(psi2**2)*delx #Probability of finding particle at distance of x2\n", + "print\"Probability of finding particle at a distance of x2 is =\",P2\n", + "print\"(There is print mistake in book).\"\n", + "\n", + "x3=a\n", + "psi3=math.sqrt(2/a)*math.sin(n*math.pi/a*x3)\n", + "P3=(psi3**2)*delx #Probability of finding particle at distance of x3\n", + "print\"Probability of finding particle at a distance of x3 is =\",P3\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Probability of finding particle at a distance of x1 is = 0.4\n", + "Probability of finding particle at a distance of x2 is = 0.3\n", + "(There is print mistake in book).\n", + "Probability of finding particle at a distance of x3 is = 5.99903913065e-33\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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