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diff --git a/Applied_Physics_by_S._Mani_Naidu/Chapter5.ipynb b/Applied_Physics_by_S._Mani_Naidu/Chapter5.ipynb new file mode 100644 index 00000000..40c994ca --- /dev/null +++ b/Applied_Physics_by_S._Mani_Naidu/Chapter5.ipynb @@ -0,0 +1,569 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5: Electron Theory of Metals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 1, Page number 5-27" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "temperature is 1259.93 K\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "E_EF=0.5; #fermi energy(eV)\n", + "FE=1/100; #probability\n", + "Kb=1.381*10**-23; #boltzmann constant(J/k)\n", + "x=6.24*10**18; \n", + "\n", + "#Calculation\n", + "KB=Kb*x;\n", + "y=E_EF/KB;\n", + "T=y/math.log(1/FE); #temperature(K)\n", + "\n", + "#Result\n", + "print \"temperature is\",round(T,2),\"K\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 2, Page number 5-28" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "total number of free electrons is 8.3954 *10**28 electrons/m**3\n", + "answer in the book varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e=1.602*10**-19; #charge(c)\n", + "m=9.11*10**-31; #mass(kg)\n", + "h=6.63*10**-34; #plancks constant(Js)\n", + "Ef=7*e; #fermi energy(J)\n", + "\n", + "#Calculation\n", + "x=Ef*8*m/h**2;\n", + "n23=x/((3/math.pi)**(2/3));\n", + "n=n23**(3/2); #total number of free electrons(electrons/m**3)\n", + "\n", + "#Result\n", + "print \"total number of free electrons is\",round(n/10**28,4),\"*10**28 electrons/m**3\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 3, Page number 5-28" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "relaxation time is 39.742 *10**-15 s\n", + "answer in the book varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "rho=1.54*10**-8; #resistivity(ohm m)\n", + "n=5.8*10**28; #number of electrons\n", + "e=1.602*10**-19; #charge(c)\n", + "m=9.11*10**-31; #mass(kg)\n", + "\n", + "#Calculation\n", + "tow=m/(n*e**2*rho); #relaxation time(s)\n", + "\n", + "#Result\n", + "print \"relaxation time is\",round(tow*10**15,3),\"*10**-15 s\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 4, Page number 5-29" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "relaxation time is 3.82 *10**-14 s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "rho=1.43*10**-8; #resistivity(ohm m)\n", + "n=6.5*10**28; #number of electrons\n", + "e=1.6*10**-19; #charge(c)\n", + "m=9.1*10**-31; #mass(kg)\n", + "\n", + "#Calculation\n", + "tow=m/(n*e**2*rho); #relaxation time(s)\n", + "\n", + "#Result\n", + "print \"relaxation time is\",round(tow*10**14,2),\"*10**-14 s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 5, Page number 5-29" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of conduction electrons is 1.8088 *10**29 /m**3\n", + "mobility is 0.00128 m**2/Vs\n", + "drift velocity is 2.3 *10**-4 m/s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "D=2.7*10**3; #density(kg/m**3)\n", + "rho=2.7*10**-8; #resistivity(ohm m)\n", + "w=26.98; #atomic weight\n", + "Na=6.025*10**26; #avagadro number\n", + "e=1.6*10**-19; #charge(c)\n", + "L=5; #length(m)\n", + "R=0.06; #resistance(ohm)\n", + "I=15; #current(A)\n", + "n=3; #number of electrons\n", + "\n", + "#Calculation\n", + "N=n*D*Na/w; #number of conduction electrons(/m**3)\n", + "mew=1/(rho*N*e); #mobility(m**2/Vs)\n", + "vd=I*R/(L*rho*N*e); #drift velocity(m/s)\n", + "\n", + "#Result\n", + "print \"number of conduction electrons is\",round(N/10**29,4),\"*10**29 /m**3\"\n", + "print \"mobility is\",round(mew,5),\"m**2/Vs\"\n", + "print \"drift velocity is\",round(vd*10**4,1),\"*10**-4 m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6, Page number 5-30" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mobility is 0.00427 m**2/Vs\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "D=8.92*10**3; #density(kg/m**3)\n", + "rho=1.73*10**-8; #resistivity(ohm m)\n", + "W=63.5; #atomic weight\n", + "Na=6.02*10**26; #avagadro number\n", + "e=1.6*10**-19; #charge(c)\n", + "\n", + "#Calculation\n", + "n=D*Na/W;\n", + "mew=1/(rho*n*e); #mobility(m**2/Vs)\n", + "\n", + "#Result\n", + "print \"mobility is\",round(mew,5),\"m**2/Vs\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 7, Page number 5-31" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mobility is 0.00428 m**2/Vs\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "D=8.95*10**3; #density(kg/m**3)\n", + "rho=1.721*10**-8; #resistivity(ohm m)\n", + "W=63.54; #atomic weight\n", + "Na=6.025*10**26; #avagadro number\n", + "e=1.6*10**-19; #charge(c)\n", + "\n", + "#Calculation\n", + "n=D*Na/W;\n", + "mew=1/(rho*n*e); #mobility(m**2/Vs)\n", + "\n", + "#Result\n", + "print \"mobility is\",round(mew,5),\"m**2/Vs\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 8, Page number 5-31" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "relaxation time is 3.64 *10**-14 s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "rho=1.50*10**-8; #resistivity(ohm m)\n", + "n=6.5*10**28; #conduction electrons(per m**3)\n", + "e=1.602*10**-19; #charge(c)\n", + "m=9.11*10**-31; #mass(kg)\n", + "\n", + "#Calculation\n", + "tow=m/(n*e**2*rho); #relaxation time(sec)\n", + "\n", + "#Result\n", + "print \"relaxation time is\",round(tow*10**14,2),\"*10**-14 s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 9, Page number 5-32" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "relaxation time is 3.97 *10**-14 s\n", + "drift velocity is 0.7 m/s\n", + "mobility is 0.7 *10**-2 m**2/Vs\n", + "thermal velocity is 1.17 *10**5 m/s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "m=9.11*10**-31; #mass(kg)\n", + "rho=1.54*10**-8; #resistivity(ohm m)\n", + "e=1.602*10**-19; #charge(c)\n", + "E=10**2; #electric field(V/m)\n", + "n=5.8*10**28; #number of electrons\n", + "Kb=1.381*10**-23; #boltzmann constant\n", + "T=300; #temperature(K)\n", + "\n", + "#Calculation\n", + "tow=m/(n*e**2*rho); #relaxation time(s)\n", + "vd=e*E*tow/m; #drift velocity(m/s)\n", + "mew=vd/E; #mobility(m**2/Vs)\n", + "Vth=math.sqrt(3*Kb*T/m); #thermal velocity(m/s)\n", + "\n", + "#Result\n", + "print \"relaxation time is\",round(tow*10**14,2),\"*10**-14 s\"\n", + "print \"drift velocity is\",round(vd,1),\"m/s\"\n", + "print \"mobility is\",round(mew*10**2,1),\"*10**-2 m**2/Vs\"\n", + "print \"thermal velocity is\",round(Vth/10**5,2),\"*10**5 m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 10, Page number 5-32" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fermi velocity is 1.39 *10**6 m/s\n", + "mean free path is 5.52 *10**-8 m\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "m=9.11*10**-31; #mass(kg)\n", + "e=1.602*10**-19; #charge(c)\n", + "E=5.5; #fermi energy(V/m)\n", + "tow=3.97*10**-14; #relaxation time(s)\n", + "\n", + "#Calculation\n", + "Vf=math.sqrt(2*E*e/m); #fermi velocity(m/s)\n", + "lamda=Vf*tow; #mean free path(m)\n", + "\n", + "#Result\n", + "print \"fermi velocity is\",round(Vf/10**6,2),\"*10**6 m/s\"\n", + "print \"mean free path is\",round(lamda*10**8,2),\"*10**-8 m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 11, Page number 5-33" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "electronic concentration is 5.863 *10**28 per m**3\n", + "fermi energy is 8.83 *10**-19 J\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n=1; #number of electrons\n", + "NA=6.025*10**26; #avagadro number\n", + "D=10500; #density(kg/m**3)\n", + "M=107.9; #atomic weight(kg)\n", + "m=9.11*10**-31; #mass(kg)\n", + "h=6.63*10**-34; #plancks constant(Js)\n", + "\n", + "#Calculation\n", + "n=n*NA*D/M; #electronic concentration(per m**3)\n", + "x=(3*n/math.pi)**(2/3);\n", + "Ef=h**2*x/(8*m); #fermi energy(J)\n", + "\n", + "#Result\n", + "print \"electronic concentration is\",round(n/10**28,3),\"*10**28 per m**3\"\n", + "print \"fermi energy is\",round(Ef*10**19,2),\"*10**-19 J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 12, Page number 5-33" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "current density is 1 *10**7 amp/m**2\n", + "drift velocity is 0.7391 *10**-3 m/s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "D=8.92*10**3; #density(kg/m**3)\n", + "w=63.5; #atomic weight\n", + "Na=6.02*10**26; #avagadro number\n", + "e=1.6*10**-19; #charge(c)\n", + "I=100; #current(A)\n", + "A=10*10**-6; #area(m**2)\n", + "n=1;\n", + "\n", + "#Calculation\n", + "J=I/A; #current density(amp/m**2)\n", + "n=n*Na*D/w;\n", + "vd=J/(n*e); #drift velocity(m/s)\n", + "\n", + "#Result\n", + "print \"current density is\",int(J/10**7),\"*10**7 amp/m**2\"\n", + "print \"drift velocity is\",round(vd*10**3,4),\"*10**-3 m/s\"" + ] + } + ], + "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": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |