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+{

+ "metadata": {

+  "name": "",

+  "signature": "sha256:881432a5cd98267b92bdfa11e021925fdef61ae98abdadccafbf254c6f9ca038"

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "12: Band theory of solids"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.1, Page number 243"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "EF=8;     #fermi energy(eV)\n",

+      "e=1.6*10**-19;   #conversion factor from J to eV\n",

+      "m=9.1*10**-31;    #mass of electron(kg)\n",

+      "\n",

+      "#Calculation\n",

+      "E0bar=3*EF/5;   \n",

+      "v=math.sqrt(2*E0bar*e/m);     #speed of electron(m/s)\n",

+      "\n",

+      "#Result\n",

+      "print \"speed of electron is\",round(v/10**6,1),\"*10**6 m/s\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "speed of electron is 1.3 *10**6 m/s\n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.2, Page number 244"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "I=8;    #current(ampere)\n",

+      "r=9*10**-4;   #radius(m)\n",

+      "V=5;   #potential difference(V)\n",

+      "L=1;   #length(m)\n",

+      "\n",

+      "#Calculation\n",

+      "A=math.pi*r**2;    #area of wire(m**2)\n",

+      "E=V/L;\n",

+      "J=I/A;   #current density(V/m)\n",

+      "rho=E/J;    #resistivity(ohm m)\n",

+      "\n",

+      "#Result\n",

+      "print \"current density is\",round(J/10**6,3),\"*10**6 V/m\"\n",

+      "print \"resistivity is\",round(rho*10**6,2),\"*10**-6 ohm m\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "current density is 3.144 *10**6 V/m\n",

+        "resistivity is 1.59 *10**-6 ohm m\n"

+       ]

+      }

+     ],

+     "prompt_number": 6

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.3, Page number 245"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "n=1;\n",

+      "a=4*10**-10;   #lattice parameter(m)\n",

+      "N=1.56*10**28;  \n",

+      "e=1.6*10**-19;   #conversion factor from J to eV\n",

+      "tow=10**-15;    #collision time(s)\n",

+      "m=9.1*10**-31;    #mass of electron(kg)\n",

+      "\n",

+      "#Calculation\n",

+      "N=n/(a**3);    #number of electrons per unit volume(per m**3)\n",

+      "sigma=N*e**2*tow/m;   #conductivity(per ohm m)\n",

+      "rho=1/sigma;   #resistivity(ohm m)\n",

+      "\n",

+      "#Result\n",

+      "print \"conductivity is\",round(sigma/10**6,2),\"*10**6 ohm m\"\n",

+      "print \"resistivity is\",rho,\"ohm m\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "conductivity is 0.44 *10**6 ohm m\n",

+        "resistivity is 2.275e-06 ohm m\n"

+       ]

+      }

+     ],

+     "prompt_number": 8

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.4, Page number 247"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "k=1.38*10**-23;   #boltzmann constant(J/K)\n",

+      "NA=6.02*10**26;   #avagadro number(k/mole)\n",

+      "T=300;     #temperature(K)\n",

+      "EF=2;   #fermi energy(eV)\n",

+      "e=1.6*10**-19;   #conversion factor from J to eV\n",

+      "\n",

+      "#Calculation\n",

+      "C=math.pi**2*k**2*NA*T/(2*EF*e);    #electronic specific heat(J/kmol/K)\n",

+      "\n",

+      "#Result\n",

+      "print \"electronic specific heat is\",int(C),\"J/kmol/K\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "electronic specific heat is 530 J/kmol/K\n"

+       ]

+      }

+     ],

+     "prompt_number": 10

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.5, Page number 247"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "K=327;    #thermal conductivity(W/mK)\n",

+      "T=300;   #temperature(K)\n",

+      "rho=7.13*10**3;    #density(kg/m**3)\n",

+      "NA=6.02*10**26;   #avagadro number(k/mole)\n",

+      "w=65.38;   #atomic weight\n",

+      "e=1.6*10**-19;   #conversion factor from J to eV\n",

+      "tow=2.5*10**-14;   #relaxation time(s)\n",

+      "m=9.1*10**-31;    #mass of electron(kg)\n",

+      "\n",

+      "#Calculation\n",

+      "N=2*rho*NA/w;     #number of electrons per unit volume(per m**3)\n",

+      "sigma=N*e**2*tow/m;   #conductivity(per ohm m)\n",

+      "L=K/(sigma*T);    #lorentz number(W ohm/K**2)\n",

+      "\n",

+      "#Result\n",

+      "print \"lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "lorentz number is 1.1804 *10**-8 W ohm/K**2\n"

+       ]

+      }

+     ],

+     "prompt_number": 12

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 12.6, Page number 248"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "e=1.6*10**-19;   #conversion factor from J to eV\n",

+      "n=5*10**28;    #number of atoms(/m**3)\n",

+      "\n",

+      "#Calculation\n",

+      "RH=-1/(n*e);    #hall coefficient(m**3/C)\n",

+      "\n",

+      "#Result\n",

+      "print \"hall coefficient is\",round(RH*10**9,3),\"*10**-9 m**3/C\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "hall coefficient is -0.125 *10**-9 m**3/C\n"

+       ]

+      }

+     ],

+     "prompt_number": 14

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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