brianjp93/Physics 353 HW 7.ipynb

## Physics 353 HW 7.ipynb
{
 "metadata": {
  "name": "Physics 353 HW 7"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "7.33 C"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = 298 #K\nm = 9.109e-31 #mass of electron\nV = 1e-6 #m^3\nl = 1.11*1.602e-19 #Joules\nk = 1.381e-23 #J/K\nh = 6.626e-34 #J*s\n\nN = (((8*pi*m*k*T)**(3/2))/(4*h**3))*exp((-l)/(2*k*T))*V\nN",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 56,
       "text": "10294909873.571798"
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = 300 #K\nm = 9.109e-31 #mass of electron\nV = 1 #m^3\nl = 1.11*1.602e-19 #Joules\nk = 1.381e-23 #J/K\nh = 6.626e-34 #J*s\n\nN1 = (((8*pi*m*k*T)**(3/2))/(4*h**3))*exp((-l)/(2*k*T))*V\nN1",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": "12009686231927736.0"
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = 400 #K\nm = 9.109e-31 #mass of electron\nV = 1 #m^3\nl = 1.11*1.602e-19 #Joules\nk = 1.381e-23 #J/K\nh = 6.626e-34 #J*s\n\nN2 = (((8*pi*m*k*T)**(3/2))/(4*h**3))*exp((-l)/(2*k*T))*V\nN2",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": "3.9535555005996892e+18"
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "N2/N1",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": "329.19723498597045"
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "7.33 e"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def con(l_ev):\n    l_J = l_ev*1.602e-19\n    return (((8*pi*m*k*T)**(3/2))/(4*h**3))*exp((-l_J)/(2*k*T))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "con(3.33)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": "41371.321785415275"
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "7.35"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = linspace(.1,300,1000)\ne_f = (h**2/8)\nI = .044 * 1.602e-19\nNd = 1e23\nvq = ((h/(sqrt(2*pi*m*k*T)))**3)\nNc = (-1 + sqrt(1 + 4*(Nd*vq*exp(I/(k*T)))))/(2*vq*exp(I/(k*T)))\nmu = -k*T*log((2)/((Nc)*vq))\nplot(T,mu/1.602e-19)\nxlabel('Temperature ($K$)')\nylabel('$\\mu$ (eV)')\ntitle('$\\mu$ vs Temp')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": "<matplotlib.text.Text at 0xa2278d0>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2sW/fPpYsWVLjINq0acPRo0cBc920tm3bOl6fr6pEU93PK9GIeKecHBg3zhyh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\nQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x9def0b8>"
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = linspace(50,300,1000)\ne_f = (h**2/8)\nI = .044 * 1.602e-19\nNd = 1e23\nvq = ((h/(sqrt(2*pi*m*k*T)))**3)\nNc = (-1 + sqrt(1 + 4*(Nd*vq*exp(I/(k*T)))))/(2*vq*exp(I/(k*T)))\nmu = -k*T*log((2)/((Nc)*vq))\nplot(T, (1/Nc)/vq)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 98,
       "text": "[<matplotlib.lines.Line2D at 0xb0e4198>]"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aatbWP/rIbGPvCncwg3zu3O5wnz3bHPFRAkM3VQXJ739v1vb/7u/gySfN261F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\n+gAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0xa249128>"
      }
     ],
     "prompt_number": 98
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "min((1/Nc)/vq)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 99,
       "text": "63.886683248968311"
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "((1/Nc)/vq)[-1]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 100,
       "text": "130.77548653198309"
      }
     ],
     "prompt_number": 100
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = linspace(700,1000,10000)\nm = 9.109e-31 #mass of electron\nV = 1 #m^3\nl = 1.11*1.602e-19 #Joules\nk = 1.381e-23 #J/K\nh = 6.626e-34 #J*s\n\nN = (((8*pi*m*k*T)**(3/2))/(4*h**3))*exp((-l)/(2*k*T))*V",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 101
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "e_f = (h**2/8)\nI = .044 * 1.602e-19\nNd = 1e23\nvq = ((h/(sqrt(2*pi*m*k*T)))**3)\nNc = (-1 + sqrt(1 + 4*(Nd*vq*exp(I/(k*T)))))/(2*vq*exp(I/(k*T)))\nmu = -k*T*log((2)/((Nc)*vq))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 102
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plot(T, N/Nc)\ntitle(\"Conduction Band Electrons/Donor Electrons vs Temp\")\nxlabel(\"Temperature (K)\")\nylabel(\"Si vs P electrons\")\nplot(T, linspace(1,1,10000))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 103,
       "text": "[<matplotlib.lines.Line2D at 0xb3d1080>]"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XLkXr1q01sm0iqrni46UBdV99Bbz4or6jqf7KTBQFBQXw9fVFjx498Pvvv0Oh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\nTEwURERUJiYKIiIqExMFERGV6f8ATrUjY26IQpsAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0xa8c5b70>"
      }
     ],
     "prompt_number": 103
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "line = list(abs((N/Nc)-1))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x = line.index(min(line))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T[x]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 71,
       "text": "897.65976597659767"
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "7.38"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T1 = 3000\nT2 = 6000\nc = 3e8\n\n\neps = linspace(.0001,10,1000) #eV\neps = eps*1.602e-19 #convert to J\nu1 = ((8*pi)/(h*c)**3)*((eps**3)/(exp(eps/(k*T1))-1)) #in J/Volume?\nu2 = ((8*pi)/(h*c)**3)*((eps**3)/(exp(eps/(k*T2))-1)) #in J/Volume?\n\nplot(eps/1.602e-19, u1, label=\"T = 3000\")\nplot(eps/1.602e-19, u2, label=\"T = 6000\")\nxlabel('eV')\nylabel('u($\\epsilon$)')\ntitle('Photon spectrum')\nlegend()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": "<matplotlib.legend.Legend at 0x9588630>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IIUQiKhCEEEIkogJBCCFEInW+A6ia4mfFuP/kPgy0DOBo5AgBRzWaECKfqEDIyF/3/8Kn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\nhEhEBYIQQohEVCAIIYRIRAWCEEKIRP8P4oGjaBRpiOYAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x9377240>"
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "7.40"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "eps = linspace(.0001, 10, 1000)*1.602e-19 #J\nV = 1\ng = (8*pi*V*eps**2)/((h*c)**3)\n\nplot(eps/1.602e-19, g*1.602e-19)\nxlabel('eV')\nylabel('g($\\epsilon$)')\ntitle('Photon Gas Density of States for V=$1m^3$')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": "<matplotlib.text.Text at 0x9c94f28>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lxmPBY8FjUfGtqn9Y67QFERgYiAMHDiA7Oxu2trZYsGABCgsLAQDTp0/XZSlERPQUOg2I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\ntGJAEBGRVv8HTCa34rYbEJ0AAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x9355da0>"
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = linspace(.001, 10000, 1000)\nV = 1\nU = (8*(pi**5)*(k*T)**4)/((15*(h*c)**3))\n\nplot(T, U)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": "[<matplotlib.lines.Line2D at 0x9dd2978>]"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XU1pais/nY//+/fTp04f27dvTokULduzYgTGGJUuWVP5OqJg5cya5ubn4fD6W\nL1/OT3/6U5YsWRKR56J9+/bExsayb98+ADIzM0lKSmLYsGERdy66devG9u3bOXnyJMYYMjMzSUxM\njMhzcZo//k6MGDHirH2tWLGCgQMH1lxA/S8PGPPOO++YLl26mLi4ODNz5swL2VVQev/9901UVJTp\n0aOHSUlJMSkpKWb16tXmm2++MQMHDjTx8fFm8ODB5tixY5W/8/jjj5u4uDjTtWtXs2bNmsrXd+3a\nZbp3727i4uLMb37zGze+jt94vd7K0S+Rei4++ugjk5aWZq688kozcuRIU1BQELHnYvbs2SYxMdF0\n797dTJgwwZSWlkbMuRg7dqzp0KGDady4sYmJiTEvv/yyX797cXGx+cUvfmE6d+5s+vbta3w+X401\n6eYjEZEwckE3H4mISHBRqIuIhBGFuohIGFGoi4iEEYW6iEgYUaiLiIQRhbqISBhRqIuIhJH/BydI\nhu4t8EkeAAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x937bc88>"
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "T = 5800\nU = (8*(pi**5)*(k*T)**4)/((15*(h*c)**3))\nU",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": "0.8552965518757857"
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "U/1.602e-19",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": "5.338929786989923e+18"
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "b"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "eps = linspace(.001, 10, 1000)*1.602e-19\n\nu = ((8*pi)/(h*c)**3)*((eps**3)/(exp(eps/(k*T))-1))\n\nplot(eps/1.602e-19, u)\nxlabel('eV')\nylabel('u($\\epsilon$)')\ntitle('Density of States for photons on Sun')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 77,
       "text": "<matplotlib.text.Text at 0x9b410f0>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OANCxY0dER0ejXbt2cHJywo0bN/Dxxx/jX//6F+zs7PDaa68hKiqq0v7nzZuHmJgYODo6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\n",
       "text": "<matplotlib.figure.Figure at 0x9de9588>"
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "((h*c)/400e-9)/1.602e-19",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 78,
       "text": "3.102059925093633"
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "((h*c)/700e-9)/1.602e-19",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 79,
       "text": "1.772605671482076"
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "e2 = ((h*c)/400e-9)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "e1 = ((h*c)/700e-9)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x1 = e1/(k*T)\nx2 = e2/(k*T)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x1",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": "3.5452998648084666"
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x2",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 84,
       "text": "6.2042747634148165"
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(19.09*pi*(k*T)**4)/((h*c)**3)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 85,
       "text": "0.3142855623508224"
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": ".314/U",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 86,
       "text": "0.36712412707774145"
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "blah = array([1,2,3])",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 113
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "la = list(blah)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 116
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "print(la)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "[1, 2, 3]\n"
      }
     ],
     "prompt_number": 117
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "la.pop(-1)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 118,
       "text": "3"
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "la",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 119,
       "text": "[1, 2]"
      }
     ],
     "prompt_number": 119
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}