{ "metadata": { "name": "chapter4s" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": "Chapter 4: Quantum Physics" }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 1, Page No: 4.52" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nlamda = 3*10**-10; # wavelength of incident photons in m\ntheta = 60; # viewing angle in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.11*10**-31 # mass in Kg\nc = 3*10**8; # vel. of light \n\n# Calculatioms\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\n\ntheta_r = theta*math.pi/180; # degree to radian conversion\nlamda1 = lamda+( (h/(mo*c))*(1-math.cos(theta_r))) # wavelength of scattered photons\n\n# Result\nprint 'Wavelength of Scattered photons = %3.4f'%(lamda1*10**10),'\u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Wavelength of Scattered photons = 3.0121 \u00c5\n" } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 2, Page No:4.52" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable declaration\ntheta = 135; # angle in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.1*10**-31 # mass in Kg\nc = 3*10**8; # vel. of light in m/s\n\n# Calculatioms\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\ntheta_r = theta*math.pi/180; # degree to radian conversion\nc_lamda = ( (h/(mo*c))*(1-math.cos(theta_r))) # Change in wavelength in m\n\n# Result\nprint 'Change in Wavelength = %3.5f' %(c_lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Change in Wavelength = 0.04143 \u00c5\n" } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 3, Page No:4.53" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nlamda = 0.1*10**-9; # wavelength of X-rays in m\ntheta = 90; # angle with incident beam in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.11*10**-31 # mass in Kg\nc = 3*10**8; # vel. of light \n\n# Calculatioms\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\ntheta_r = theta*math.pi/180; # degree to radian conversion\nlamda1 = lamda+( (h/(mo*c))*(1-math.cos(theta_r))) #wavelength of scattered beam\n\n# Result\nprint 'Wavelength of Scattered beam = %3.4f' %(lamda1*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Wavelength of Scattered beam = 1.0242 \u00c5\n" } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 4, Page No:4.53" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\ne = 1.6*10**-19 # charge of electron\nV = 150; # potential difference in volts\n\n# Calculations\n\nlamda = h/(math.sqrt(2*m*e*V)) # de Broglie wavelength\n\n#Result\nprint 'The de-Broglie wavelength = %d' %(lamda*10**10), '\u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength = 1 \u00c5\n" } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 5, Page No:4.54" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\ne = 1.6*10**-19 # charge of electron\nV = 5000; # potential in volts\n\n# Calculations\n\nlamda = h/(math.sqrt(2*m*e*V)) #de Broglie wavelength\n\n# Result\nprint 'The de-Broglie wavelength of electron = %3.5f' %(lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength of electron = 0.17353 \u00c5\n" } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 6, Page No:4.55" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nE = 100 # Energy of electron in eV\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\ne = 1.6*10**-19 # Charge of electron in Columbs\n\n# Calculations\n\nE1 = E*e # Energy conversion from eV to Joule\nlamda = h/(math.sqrt(2*m*E1)) # de Broglie wavelength\n\n# Result\nprint 'The de-Broglie wavelength = %3.3f' %(lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength = 1.227 \u00c5\n" } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 7, Page No:4.55" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable Declaration\nm = 1.675*10**-27; # Mass of proton in kg\nc = 3*10**8; # velocity of light in m/s\nh = 6.625*10**-34 # plancks constant\n\n# Calculations\n\nvp = c/20; # velocity of proton in m/s\nlamda = h/(m*vp) # de-Broglie wavelength in m\n\n# Result\nprint 'de-Broglie wavelength = %e'%(lamda),'lamda';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "de-Broglie wavelength = 2.636816e-14 lamda\n" } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 8, Page No:4.56" }, { "cell_type": "code", "collapsed": false, "input": "\nimport math;\n\n# Variable declaration\nE = 10000 # Energy of neutron in eV\nh = 6.625*10**-34 # plancks constant\nm = 1.675*10**-27 # mass of neutron in Kg\ne = 1.6*10**-19 \n\n# Calculations\n\nE1 = E*e # Energy conversion from eV to Joule\nlamda = h/(math.sqrt(2*m*E1)) # de Broglie wavelength\n\n# Result\nprint 'The de-Broglie wavelength of neutron = %3.3e' %lamda,' m';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength of neutron = 2.862e-13 m\n" } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 10, Page No:4.58" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable decalaration\nl = 0.1*10**-9; # side of cubical box\nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nKb = 1.38*10**-23 # Boltzmann constant \n\n# Calculations\n# for cubical box the energy eigen value is Enx ny nz = (h^2/(8*m*l^2))*(nx^2 + ny^2 +nz^2)\n# For the next energy level to the lowest energy level nx = 1 , ny = 1 and nz = 2\nnx = 1\nny = 1\nnz = 2\nE112 = (h**2/(8*m*l**2))*( nx**2 + ny**2 + nz**2);\n\n# We know the average energy of molecules of aperfect gas = (3/2)*(Kb*T)\nT = (2*E112)/(3*Kb); # Temperature in kelvin\n\n# Result\nprint 'E112 = %3.4e' %E112,'Joules'',\\n','Temperature of the molecules T = %3.4e' %T, 'K';\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "E112 = 3.6134e-17 Joules,\nTemperature of the molecules T = 1.7456e+06 K\n" } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 11, Page No:4.59" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable declaration\nl = 4*10**-9; # width of infinitely deep potential\nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn = 1; # minimum energy\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nE = (h**2 * n**2)/(8*m*l**2) # Energy of electron in an infinitely deep potential well \nE1 = E/e #energy conversion from joules to eV\n\n# Result\nprint 'Minimum energy of an electron = %3.4f' %E1,' eV';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Minimum energy of an electron = 0.0235 eV\n" } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 12, Page No:4.61" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nl = 0.1*10**-9; # length of one dimensional box \nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn = 1; # for ground state\nn5 = 6; # n value for fifth excited state\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nEg = (h**2 * n**2)/(8*m*l**2 * e ) # Energy in ground state in eV \nEe = (h**2 * n5**2)/(8*m*l**2 * e) # Energy in excited state in eV\nE = Ee - Eg; # energy req to excite electrons from ground state to fifth excited state\n\n# Result\nprint 'Energy required to excite an electron from ground state to fifth excited state = %3.2f' %E, 'eV';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Energy required to excite an electron from ground state to fifth excited state = 1317.38 eV\n" } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 13, Page No:4.62" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable decalration\nl = 0.1*10**-9; # length of one dimensional box \nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn = 1; # for ground state\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nE = (h**2 * n**2)/(8*m*l**2 *e ) # Energy of electron in eV \n\n# Result\nprint 'Energy of an electron = %3.3f' %E,' eV';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Energy of an electron = 37.639 eV\n" } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Example 14, Page No:4.63" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable declaration\nl = 0.5*10**-9; # width of one dimensional box in m \nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn = 1; # for ground state\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nE = (h**2 * n**2)/(8*m*l**2 *e ) # Energy of electron in eV \n\n# Result\nprint 'Least Energy of an electron = %3.4f' %E,' eV';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Least Energy of an electron = 1.5056 eV\n" } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 1, Page No:4.64" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# variable declaration\nh = 6.625*10**-34 # plancks constant\nc = 3*10**8; # vel. of light\nlamda = 5893*10**-10; # wavelength in m\nP = 100 # power of sodium vapour lamp\n\n# Calculations\nE = (h*c)/lamda; # Energy in joules\nN = P/E # Number of photons emitted\n\n# Result\nprint 'Number of Photons emitted = %3.4e' %N,' per second';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Number of Photons emitted = 2.9650e+20 per second\n" } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 2, Page No:4.64" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable declaration\nlamda1 = 0.022*10**-10; # wavelength of scatterd X-rays in m\ntheta = 45; # scatterring angle in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.11*10**-31 # mass in Kg\nc = 3*10**8; # vel. of light \n\n# Calculatioms\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\n\ntheta_r = theta*math.pi/180; # degree to radian conversion\nlamda = lamda1-( (h/(mo*c))*(1-math.cos(theta_r))) # incident Wavelength\n\n# Result\nprint 'Wavelength of incident beam = %3.4f' %(lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Wavelength of incident beam = 0.0149 \u00c5\n" } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 3 , Page No:4.65" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nEi = 1.02*10**6 # photon energy in eV\ntheta = 90; # scattered angle in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.1*10**-31 # mass of electron in Kg\ne = 1.6*10**-19 # charge of electron\nc = 3*10**8; # vel. of light in m/s\n\n# Calculations\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\ntheta_r = theta*math.pi/180; # degree to radian conversion\nc_lamda = ( (h/(mo*c))*(1-math.cos(theta_r))) #Change in wavelength in m\ndv = c/c_lamda; # change in frequency of the scattered photon\ndE = (h*dv)/e # change in energy of scattered photon in eV\n# This change in energy is transferred as the KE of the recoil electron\nEr = dE; # Energy of recoil electron\nEs = Ei - Er # Energy of scattered photon\n\n\n# Result\nprint 'Energy of the recoil electron = %3.4f' %(Er*10**-6),' MeV','\\n','Energy of the Scattered photon = %3.4f' %(Es*10**-6),'MeV';\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Energy of the recoil electron = 0.5119 MeV \nEnergy of the Scattered photon = 0.5081 MeV\n" } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 4, Page No:4.65" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nlamda = 0.124*10**-10; # wavelength of X-rays in m\ntheta = 180; # Scattering angle in degrees\nh = 6.625*10**-34 # plancks constant\nmo = 9.11*10**-31 # mass in Kg\nc = 3*10**8; # vel. of light \n\n# Calculatioms\n# from Compton theory ,Compton shift is given by\n# lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\n\ntheta_r = theta*math.pi/180; # degree to radian conversion\nlamda1 = lamda+( (h/(mo*c))*(1-math.cos(theta_r))) # wavelength of scattered X-rays\n\n# Result\nprint 'Wavelength of Scattered X-rays = %3.4f' %(lamda1*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Wavelength of Scattered X-rays = 0.1725 \u00c5\n" } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 5, Page No:4.65" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\ne = 1.6*10**-19 # charge of electron\nV = 2000; # potential in volts\n\n# Calculations\n\nlamda = h/(math.sqrt(2*m*e*V)) # de Broglie wavelength\n\n# Result\nprint 'The de-Broglie wavelength of electron = %3.4f' %(lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength of electron = 0.2744 \u00c5\n" } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 6, Page No:4.66" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# variable Declaration \nh = 6.625*10**-34 # plancks constant\nm = 1.678*10**-27 # mass of proton in Kg\ne = 1.6*10**-19 # charge of electron\nKb = 1.38*10**-23; # boltzmann constant\nT = 300 # Temperature in kelvin\n\n#Calculations\nlamda = h/(math.sqrt(3*m*Kb*T)) #de Broglie wavelength\n\n#Result\nprint 'The de-Broglie wavelength = %3.4f' %(lamda*10**10),' \u00c5';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "The de-Broglie wavelength = 1.4512 \u00c5\n" } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 7, Page No:4.66" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\nlamda = 3*10**-2; # wavelength of electron wave\ne = 1.6*10**-19; # charge of electron\n\n# Calculations\nE = (h**2)/(2*m*lamda**2); # Energy in Joules\nE1 = E/e;\n\n# Result\nprint 'Energy of the electron E = %3.4e' %E1,'eV';\nprint 'Note: Calculation mistake in textbook'", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Energy of the electron E = 1.6729e-15 eV\nNote: Calculation mistake in textbook\n" } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 8, Page No:4.67" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable declaration\nh = 6.625*10**-34 # plancks constant\nm = 9.11*10**-31 # mass of electron in Kg\nc = 3*10**8; # velocity of light in m/s\n\n# Calculations\nve = 0.7071*c # velocity of electron\nlamda = h/(m*ve*math.sqrt(1-(ve/c)**2)) #de Broglie wavelength\n\n# we know Compton wavelength ,lamda' - lamda = (h/(mo*c))*(1-cos\u03b8)\n# maximum shift \u03b8 = 180\ntheta = 180\ntheta1 = theta*math.pi/180;\nd_lamda = (h/(m*c))*(1-math.cos(theta1))\nprint 'de Broglie wavelength = %e' %lamda,' m';\nprint 'compton wavelength = %e' %d_lamda,'m';\nprint 'The de-Broglie wacelength is equal to the compton wavelength';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "de Broglie wavelength = 4.848152e-12 m\ncompton wavelength = 4.848152e-12 m\nThe de-Broglie wacelength is equal to the compton wavelength\n" } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 9, Page no:4.68" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nl = 10**-10; # side of one dimensional box \nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn1 = 1; # for 1st eigen value\nn2 = 2; # for 2nd eigen value\nn3 = 3; # for 3rd eigen value\nn4 = 4; # for 4th eigen value\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nE1 = (h**2 * n1**2)/(8*m*l**2 *e ) #first Eigen value\nE2 = (h**2 * n2**2)/(8*m*l**2 *e ) # second Eigen value\nE3 = (h**2 * n3**2)/(8*m*l**2 *e ) # third Eigen value\nE4 = (h**2 * n4**2)/(8*m*l**2 *e ) # fourth Eigen value\n \n# Result\nprint '1st Eigen value = %3.1f' %E1,'eV';\nprint '2nd Eigen value = %3.1f' %E2,'eV';\nprint '3rd Eigen value = %3.1f' %E3,'eV';\nprint '4th Eigen value = %3.1f' %E4,'eV';\n\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "1st Eigen value = 37.6 eV\n2nd Eigen value = 150.6 eV\n3rd Eigen value = 338.8 eV\n4th Eigen value = 602.2 eV\n" } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 10 , Page No:4.68" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nl = 10**-10 ; # length of one dimensional box in m \nh = 6.625*10**-34 # plancks constant in Jsec\nm = 9.11*10**-31 # mass of electron in Kg\nn = 1; # for ground state\ne = 1.6*10**-19 # charge of electron in columbs\n\n# Calculations\nE = 2*(h**2 * n**2)/(8*m*l**2 *e ) #Energy of system having two electrons\n\n# Result\nprint 'Energy of the system having two electrons = %3.4f' %E,' eV';", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Energy of the system having two electrons = 75.2789 eV\n" } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Addl_Example 11 , Page No:4.69" }, { "cell_type": "code", "collapsed": false, "input": "import math;\n\n# Variable Declaration\nb = 40; # angle subtended by final images at eye in degrees\na = 10 # angle subtended by the object at the eye kept at near point in degrees\n\n# Calculations\nb_r = b*math.pi/180; # degree to radian conversion\na_r = a*math.pi/180; # degree to radian conversion\nM = math.tan(b_r)/math.tan(a_r); # magnifying power\n\n#Result\nprint 'Magnifying power = %3.3f' %M;", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Magnifying power = 4.759\n" } ], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": "", "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }