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+{

+ "cells": [

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "#4: Electron Theory of Solids"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.1, Page number 4.57"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 10,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "de broglie wavelength is 0.00286 angstrom\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "E=10**4*1.6*10**-19;      #kinetic energy(J)\n",

+    "m=1.675*10**-27;     #mass(kg)\n",

+    "h=6.625*10**-34;     #planck's constant\n",

+    "\n",

+    "#Calculation\n",

+    "v=math.sqrt(2*E/m);     #velocity(m/s)\n",

+    "lamda=h/(m*v);          #de broglie wavelength(m)\n",

+    "\n",

+    "#Result\n",

+    "print \"de broglie wavelength is\",round(lamda*10**10,5),\"angstrom\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.2, Page number 4.58"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 11,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "energy difference is 1.81 *10**-37 J\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

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

+    "nx=ny=nz=1;\n",

+    "n=6;\n",

+    "a=1;     #edge(m)\n",

+    "h=6.63*10**-34;     #planck's constant\n",

+    "\n",

+    "#Calculation\n",

+    "E1=h**2*(nx**2+ny**2+nz**2)/(8*m*a**2);\n",

+    "E2=h**2*n/(8*m*a**2);\n",

+    "E=E2-E1;               #energy difference(J)\n",

+    "\n",

+    "#Result\n",

+    "print \"energy difference is\",round(E*10**37,2),\"*10**-37 J\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.3, Page number 4.58"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 15,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "temperature is 1261 K\n",

+      "answer varies due to rounding off errors\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "y=1/100;    #percentage of probability\n",

+    "x=0.5*1.6*10**-19;     #energy(J)\n",

+    "k=1.38*10**-23;       #boltzmann constant\n",

+    "\n",

+    "#Calculation\n",

+    "xbykT=math.log((1/y)-1);\n",

+    "T=x/(k*xbykT);       #temperature(K)\n",

+    "\n",

+    "#Result\n",

+    "print \"temperature is\",int(T),\"K\"\n",

+    "print \"answer varies due to rounding off errors\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.4, Page number 4.58"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 16,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "fermi energy is 3.15 eV\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "d=970;    #density(kg/m**3)\n",

+    "Na=6.02*10**26;    #avagadro number\n",

+    "w=23;    #atomic weight\n",

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

+    "h=6.62*10**-34;     #planck's constant\n",

+    "\n",

+    "#Calculation\n",

+    "N=d*Na/w;    #number of atoms/m**3\n",

+    "x=h**2/(8*m);\n",

+    "y=(3*N/math.pi)**(2/3);\n",

+    "EF=x*y;     #fermi energy(J)\n",

+    "\n",

+    "#Result\n",

+    "print \"fermi energy is\",round(EF/(1.6*10**-19),2),\"eV\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.5, Page number 4.59"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 18,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "work function is 4.14 eV\n",

+      "maximum kinetic energy is 0.758 eV\n",

+      "answer varies due to rounding off errors\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "h=6.625*10**-34;     #planck's constant\n",

+    "c=3*10**8;     #velocity of light(m/s)\n",

+    "lamda0=3000*10**-10;   #wavelength(m)\n",

+    "e=1.6*10**-19;    #charge(coulomb)\n",

+    "lamda=2536*10**-10;      #wavelength(m)\n",

+    "\n",

+    "#Calculation\n",

+    "hf0=c*h/(lamda0*e);    #work function(eV)\n",

+    "E=c*h*((1/lamda)-(1/lamda0))/e;            #maximum kinetic energy(eV)\n",

+    "\n",

+    "#Result\n",

+    "print \"work function is\",round(hf0,2),\"eV\"\n",

+    "print \"maximum kinetic energy is\",round(E,3),\"eV\"\n",

+    "print \"answer varies due to rounding off errors\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.6, Page number 4.59"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 19,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "lowest energy of neutron is 2.05 MeV\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "n=1;\n",

+    "hbar=1.054*10**-34;    \n",

+    "m=1.67*10**-27;    #mass of neutron(kg)\n",

+    "a=10**-14;      #size(m)\n",

+    "\n",

+    "#Calculation\n",

+    "E=n**2*math.pi**2*hbar**2/(2*m*a**2);     #lowest energy of neutron(J)\n",

+    "\n",

+    "#Result\n",

+    "print \"lowest energy of neutron is\",round(E/(1.6*10**-13),2),\"MeV\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.7, Page number 4.59"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 20,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "probability of particle is 0.0158\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "from scipy.integrate import quad\n",

+    "\n",

+    "#Variable declaration\n",

+    "k=1;\n",

+    "\n",

+    "#Calculation\n",

+    "def zintg(x):\n",

+    "\treturn math.exp(-2*k*x)\n",

+    "\n",

+    "a=quad(zintg,2/k,3/k)[0];        #probability of particle\n",

+    "\n",

+    "#Result\n",

+    "print \"probability of particle is\",round(2*a,4)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example number 4.8, Page number 4.60"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 22,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "voltage appeared is 1.83 mV\n"

+     ]

+    }

+   ],

+   "source": [

+    "#importing modules\n",

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#Variable declaration\n",

+    "i=10**-2;    #current(ampere)\n",

+    "A=0.01*0.001;     #area(m**2)\n",

+    "RH=3.66*10**-4;   #hall coefficient(m**3/coulomb)\n",

+    "Bz=0.5;     #magnetic induction(weber/m**2)\n",

+    "\n",

+    "#Calculation\n",

+    "Jx=i/A;     \n",

+    "Ey=RH*Bz*Jx;    \n",

+    "Vy=Ey*i;      #voltage appeared(V)\n",

+    "\n",

+    "#Result\n",

+    "print \"voltage appeared is\",Vy*10**3,\"mV\""

+   ]

+  }

+ ],

+ "metadata": {

+  "kernelspec": {

+   "display_name": "Python 2",

+   "language": "python",

+   "name": "python2"

+  },

+  "language_info": {

+   "codemirror_mode": {

+    "name": "ipython",

+    "version": 2

+   },

+   "file_extension": ".py",

+   "mimetype": "text/x-python",

+   "name": "python",

+   "nbconvert_exporter": "python",

+   "pygments_lexer": "ipython2",

+   "version": "2.7.9"

+  }

+ },

+ "nbformat": 4,

+ "nbformat_minor": 0

+}