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authorkinitrupti2017-05-12 18:53:46 +0530
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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#5: Elements of statistical mechanics"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 5.1, Page number 5.10"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "average thermal energy is 0.039 eV\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "k=1.38*10**-23; #boltzmann constant(J)\n",
- "T=300; #temperature(K)\n",
- "e=1.6*10**-19; #charge(c)\n",
- "\n",
- "#Calculation\n",
- "E=3*k*T/(2*e); #average thermal energy(eV)\n",
- "\n",
- "#Result\n",
- "print \"average thermal energy is\",round(E,3),\"eV\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 5.3, Page number 5.18"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fermi function is 0.269\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "kT=1; #assume\n",
- "E_Ef=kT;\n",
- "\n",
- "#Calculation\n",
- "FE=1/(1+math.exp(1)); #fermi function\n",
- "\n",
- "#Result\n",
- "print \"fermi function is\",round(FE,3)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 5.4, Page number 5.18"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " temperature is 290.2 K\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "FE=10/100; #fermi function\n",
- "EF=5.5; #energy function(eV)\n",
- "e=1.6*10**-19; #charge(c)\n",
- "k=1.38*10**-23; #boltzmann constant(J)\n",
- "\n",
- "#Calculation\n",
- "E=EF+(EF/100); #energy(eV)\n",
- "x=math.log((1/FE)-1);\n",
- "T=(E-EF)*e/(k*x); #temperature(K)\n",
- "\n",
- "#Result\n",
- "print \"temperature is\",round(T,1),\"K\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 5.5, Page number 5.19"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "fermi velocity is 0.86 *10**6 m s-1\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "k=1.38*10**-23; #boltzmann constant(J)\n",
- "T=24600; #temperature(K)\n",
- "m=9.108*10**-31; #mass(kg)\n",
- "\n",
- "#Calculation\n",
- "vF=math.sqrt(2*k*T/m); #fermi velocity(m s-1)\n",
- "\n",
- "#Result\n",
- "print \"fermi velocity is\",round(vF/10**6,2),\"*10**6 m s-1\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 5.6, Page number 5.21"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "number of states is 1.1877 *10**26\n",
- "answer given in the book is wrong\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "from scipy.integrate import quad\n",
- "\n",
- "#Variable declaration\n",
- "EF=3.0; #fermi energy(eV)\n",
- "e=1.6*10**-19; #charge(c)\n",
- "m=9.14*10**-31; #mass(kg)\n",
- "h=6.62*10**-34; #planck's constant\n",
- "\n",
- "#Calculation\n",
- "E1=EF*e; #energy(J)\n",
- "E2=(EF+0.01)*e; #energy(J)\n",
- "def zintg(E):\n",
- "\treturn (4*math.pi*(2*m)**(3/2)*math.sqrt(E))/h**3;\n",
- "\n",
- "n=quad(zintg,E1,E2)[0]; #number of states\n",
- "\n",
- "#Result\n",
- "print \"number of states is\",round(n/10**26,4),\"*10**26\"\n",
- "print \"answer given in the book is wrong\""
- ]
- }
- ],
- "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
-}