From 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../Chapter4_1.ipynb | 390 +++++++++++++++++++++ 1 file changed, 390 insertions(+) create mode 100755 Applied_Physics_by_P._K._Palanisamy/Chapter4_1.ipynb (limited to 'Applied_Physics_by_P._K._Palanisamy/Chapter4_1.ipynb') diff --git a/Applied_Physics_by_P._K._Palanisamy/Chapter4_1.ipynb b/Applied_Physics_by_P._K._Palanisamy/Chapter4_1.ipynb new file mode 100755 index 00000000..d55516d5 --- /dev/null +++ b/Applied_Physics_by_P._K._Palanisamy/Chapter4_1.ipynb @@ -0,0 +1,390 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:7ccac901d3d7a8c9dde630e169f5e7e52a039a9eb5d4b37586cb97d5a7fe1fca" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "4: Electron Theory of Metals" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.1, Page number 4.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "rho_s = 10.5*10**3 #density of silver(kg/m^3)\n", + "NA = 6.02*10**26 #avagadro number(per k-mol)\n", + "MA = 107.9 #atomic weight of silver\n", + "sigma = 6.8*10**7; #conductivity of silver(ohm-1 m-1)\n", + "e = 1.6*10**-19\n", + "\n", + "#Calculation\n", + "n = rho_s*NA/MA #molar volume of silver\n", + "mew = sigma/(n*e) #mobility of electrons(m^2/Vs)\n", + "mew = mew*10**2\n", + "mew = math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print \"density of electrons in silver is\",round(n/1e28,2),\"*10^28\"\n", + "print \"mobility of electrons is\",mew,\"*10**-2 m**2/Vs\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "density of electrons in silver is 5.86 *10^28\n", + "mobility of electrons is 0.7255 *10**-2 m**2/Vs\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.2, Page number 4.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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", + "e = 1.6*10**-19\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "N = 6.02*10**26 #avagadro's number(per k-mol)\n", + "AW = 63.5 #atomic weight\n", + "rho = 1.73*10**-8 #resistivity of copper, ohm-m\n", + "\n", + "#Calculation\n", + "n = d*N/AW #number of cu atoms(per m^3)\n", + "mew = 1/(rho*n*e) #mobility of electrons(m/Vs)\n", + "mew = mew*10**2\n", + "mew = math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n", + "tow = m/(n*e**2*rho) #relaxation time(s)\n", + "\n", + "#Result\n", + "print \"mobility of electrons is\",round(mew,3),\"*10**-2 m/Vs\"\n", + "print \"relaxation time is\",round(tow/1e-14,3),\"*10^-14 sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mobility of electrons is 0.427 *10**-2 m/Vs\n", + "relaxation time is 2.43 *10^-14 sec\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.3, Page number 4.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#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 #conduction electrons(per m^3)\n", + "m = 9.108*10**-31 #mass of electron(kg)\n", + "e = 1.602*10**-19\n", + "\n", + "#Calculation\n", + "tow = m/(n*(e**2)*rho) #relaxation time(sec)\n", + "\n", + "#Result\n", + "print \"relaxation time of conduction electrons is\",round(tow/1e-14,2),\"*10^-14 sec\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "relaxation time of conduction electrons is 3.97 *10^-14 sec\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.4, Page number 4.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "R = 0.06 #resistance(ohm)\n", + "D = 5 #length of Al wire(m)\n", + "e = 1.602*10**-19\n", + "rho = 2.7*10**-8 #resistivity of Al(ohm-m)\n", + "MA = 26.98 #atomic weight\n", + "NA = 6.025*10**26 #avagadro number(k/mol)\n", + "rho_s = 2.7*10**3 #density(kg/m^3)\n", + "I = 15 #current(A)\n", + "\n", + "#Calculation\n", + "n = 3*rho_s*NA/MA #free electron concentration(electrons/m^3)\n", + "mew = 1/(n*e*rho) #mobility(m/Vs)\n", + "E = I*R/D #electric field(V/m)\n", + "vd = mew*E #drift velocity(m/s)\n", + "vd = vd*10**3\n", + "mew = mew*10**3\n", + "mew = math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n", + "vd = math.ceil(vd*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print \"free electron concentration is\",round(n/1e29,4),\"*10^29 electrons/m^2\"\n", + "print \"mobility is\",round(mew,3),\"*10^-3 m/Vs\"\n", + "print \"drift velocity is\",round(vd,2),\"*10^-3 m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "free electron concentration is 1.8088 *10^29 electrons/m^2\n", + "mobility is 1.278 *10^-3 m/Vs\n", + "drift velocity is 0.23 *10^-3 m/s\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.5, Page number 4.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n1 = 1\n", + "n2 = 1\n", + "n3 = 1 #for lowest energy\n", + "h = 6.62*10**-34 #planck's constant(Js)\n", + "e = 1.6*10**-19\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "L = 0.1 #side of box(nm)\n", + "\n", + "#Calculation\n", + "L = L*10**-9 #side of box(m)\n", + "E1 = (h**2)*(n1**2+n2**2+n3**2)/(8*m*L**2) #lowest energy(J)\n", + "E1 = E1/e #lowest energy(eV)\n", + "E1 = math.ceil(E1*10)/10 #rounding off to 1 decimal\n", + "\n", + "#Result\n", + "print \"lowest energy of electron is\",E1,\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "lowest energy of electron is 112.9 eV\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.6, Page number 4.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "\n", + "#Calculation\n", + "#Fermi function F(E) = 1/(1+exp((E-Ef)/(kT)))\n", + "#given E-Ef = kT. therefore F(E) = 1/(1+exp(1))\n", + "F_E = 1/(1+math.exp(1))\n", + "F_E = math.ceil(F_E*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"fermi function is\",F_E" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "fermi function is 0.269\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.7, Page number 4.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "F_E = 10 #probability in percent\n", + "k = 1.38*10**-23\n", + "EF = 5.5 #fermi energy(eV)\n", + "\n", + "#Calculation\n", + "E = EF+(EF/100) #energy(eV)\n", + "X = E-EF #E-EF(eV)\n", + "X = X*e #E-EF(J)\n", + "T = X/(k*math.log(F_E-1)) #temperature(K)\n", + "T = math.ceil(T*10**2)/10**2 #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"temperature is\",round(T,1),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "temperature is 290.2 K\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.8, Page number 4.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "F_E = 0.01 #probability in percent\n", + "k = 1.38*10**-23\n", + "e = 1.6*10**-19\n", + "#let E-EF be X\n", + "X = 0.5 #E-EF(eV)\n", + "\n", + "#Calculation\n", + "kT = X/(2.303*math.log10((1-F_E)*100)) #value of kT(eV)\n", + "T = kT*e/k #temperature(K)\n", + "T = math.ceil(T*10)/10 #rounding off to 1 decimal\n", + "\n", + "#Result\n", + "print \"temperature is\",T,\"K\"\n", + "print \"answer given in the book is wrong by a decimal point\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "temperature is 1261.4 K\n", + "answer given in the book is wrong by a decimal point\n" + ] + } + ], + "prompt_number": 23 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit