{ "metadata": { "name": "", "signature": "sha256:495ac96015f20ad80c50d2c1722e924721169f0ca7b7ca56739c5ef92f3f2a43" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "9: Quantum Theory" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.1, Page number 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "r=0.05; #radius of the wire(mm)\n", "l=4; #length of the wire(cm)\n", "e=1;\n", "T=3000; #temperature(K)\n", "s=5.6703*10**-8; #stefan's constant \n", "\n", "#Calculation \n", "A=2*math.pi*r*l*10**-5; #area(m**2)\n", "p=s*T**4*A*e; #power radiated by the filament(W)\n", "\n", "#Result\n", "print \"The power radiated by the filament is\",round(p,2),\"W\"\n", "print \"answer given in the book is wrong\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The power radiated by the filament is 57.72 W\n", "answer given in the book is wrong\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.2, Page number 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=550; #wavelength(nm)\n", "\n", "#Calculation \n", "E=(h*c)/(lamda*10**-9); #energy of photon(J)\n", "Es=0.1/E; #number of photons(per square cm per second)\n", "\n", "#Result\n", "print \"The number of photons are\",round(Es/10**17,2),\"*10**17 per square cm per second\"\n", "print \"answer in the book varies due to rounding off errors\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The number of photons are 2.77 *10**17 per square cm per second\n", "answer in the book varies due to rounding off errors\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.3, Page number 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=300*10**-9; #wavelength(m)\n", "e=1.6*10**-19;\n", "phi=2.2; #work function(eV)\n", "\n", "#Calculation \n", "E=(h*c)/lamda; #energy of photon(J)\n", "Kmax=(E-(phi*e))/e; #maximum kinetic energy(eV)\n", "\n", "#Result\n", "print \"The maximum kinetic energy is\",round(Kmax,2),\"eV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The maximum kinetic energy is 1.94 eV\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.4, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=175*10**-9; #wavelength of light(m)\n", "w=5; #work function of nickel(eV)\n", "\n", "#Calculation \n", "E=(h*c)/(lamda*1.6*10**-19); #Energy of 200 nm photon(eV)\n", "#From photoelectric equation E-w is the potential difference\n", "p=E-w; #potential difference required to stop the fastest electron(eV)\n", "\n", "#Result\n", "print \"The potential difference that should be applied is\",round(p,1),\"V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The potential difference that should be applied is 2.1 V\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.5, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "e=1.6*10**-19;\n", "V=50; #accelerating voltage(kV)\n", "\n", "#Calculation \n", "lambdamin=((h*c)/(e*V*10**3))*10**9; #shortest wavelength of X-rays(nm)\n", "\n", "#Result\n", "print \"The shortest wavelength of X-rays is\",round(lambdamin,4),\"nm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The shortest wavelength of X-rays is 0.0248 nm\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.6, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "lambda1=0.708; #wavelength of a certain line in an X-ray spectrum(angstrom)\n", "Z1=42; #atomic number\n", "Z2=24;\n", "a=1; #screening constant\n", "\n", "#Calculation \n", "lambda2=(lambda1*(Z1-a)**2)/((Z2-a)**2); #wavelength of same line(angstrom)\n", "\n", "#Result\n", "print \"The wavelength of same line is\",round(lambda2,2),\"angstrom\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The wavelength of same line is 2.25 angstrom\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.7, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "#From Bragg's law 2*d*sin(teta)=n*lambda\n", "n=1;\n", "lamda=0.32; #wavelength(nm)\n", "theta=28; #angle at which first order Bragg's reflection is observed(degrees)\n", "\n", "#Calculation \n", "theta=theta*math.pi/180; #angle(radian)\n", "d=lamda/(2*math.sin(theta)); #distance between atomic planes(nm)\n", "\n", "#Result\n", "print \"The distance between atomic planes is\",round(d,2),\"nm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The distance between atomic planes is 0.34 nm\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.8, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "theta=50; #angle(degrees)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "c=3*10**8; #speed of light(m/s)\n", "\n", "#Calculation \n", "theta=theta*math.pi/180; #angle(radian)\n", "deltalambda=(h/(m*c))*(1-math.cos(theta))*10**12; \n", "lambdafin=2.5; #wavelength of scattered X-rays\n", "lambdainit=lambdafin-deltalambda; #wavelength of X-rays in the incident beam(pm)\n", "\n", "#Result\n", "print \"The wavelength of X-rays in the incident beam is\",round(lambdainit,2),\"pm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The wavelength of X-rays in the incident beam is 1.63 pm\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.9, Page number 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=500*10**-9; #wavelength of laser(m)\n", "t=20*10**-3; #time(s)\n", "N=2.52*10**16; #number of photons in a 20ms pulse\n", "\n", "#Calculation \n", "E=(h*c)/lamda; #Energy of 500 nm photon(J)\n", "p=E*N/t; #power of the laser(W)\n", "\n", "#Result\n", "print \"The power of the laser is\",round(p,1),\"W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The power of the laser is 0.5 W\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.10, Page number 173" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=350*10**-9; #threshold wavelength(m)\n", "e=1.6*10**-19;\n", "\n", "#Calculation \n", "W=h*c/(lamda*e); #work function of the surface(eV)\n", "\n", "#Result\n", "print \"The work function of the surface is\",round(W,2),\"eV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The work function of the surface is 3.55 eV\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.11, Page number 173" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "e=1.6*10**-19;\n", "lambdamin=0.02*10**-9; #minimum wavelength(m)\n", "\n", "#Calculation \n", "V=(h*c/(lambdamin*e))*10**-3; #accelerating voltage(kV)\n", "\n", "#Result\n", "print \"The accelerating voltage needed to produce minimum wavelength is\",round(V,4),\"kV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The accelerating voltage needed to produce minimum wavelength is 62.1187 kV\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.12, Page number 173" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "#According to Bragg's eq.2*d*sin(teta)=n*lambda\n", "n=2; #since second order Bragg's eq.\n", "d=5; #since d=5(lambda)\n", "lamda=1;\n", "\n", "#Calculation \n", "a=(n*lamda)/(2*5*lamda);\n", "theta=math.asin(a); #angle of second order Braggs reflection(radian)\n", "theta=theta*180/math.pi; #angle(degrees)\n", "\n", "#Result\n", "print \"The angle of second order Braggs reflection is\",round(theta,2),\"degrees\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The angle of second order Braggs reflection is 11.54 degrees\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 9.13, Page number 173" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=6.626*10**-34; #plancks constant\n", "c=3*10**8; #speed of light(m/s)\n", "lamda=0.03; #wavelength(nm)\n", "p=80/100;\n", "\n", "#Calculation \n", "E=(h*c)/(lamda*10**-9); #energy of photon(J) \n", "TE=E/p; #Total energy.E=80% of TE(J)\n", "TE=TE*(10**-3)/e; #Total energy(keV)\n", "\n", "#Result\n", "print \"The electron must have been accelerated through a potential difference of\",round(TE,3),\"kV\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The electron must have been accelerated through a potential difference of 51.766 kV\n" ] } ], "prompt_number": 49 } ], "metadata": {} } ] }