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diff --git a/Engineering_Physics_by_Dr._K._Vijaya_Kumar/chapter2_2.ipynb b/Engineering_Physics_by_Dr._K._Vijaya_Kumar/chapter2_2.ipynb new file mode 100755 index 00000000..2ff5590c --- /dev/null +++ b/Engineering_Physics_by_Dr._K._Vijaya_Kumar/chapter2_2.ipynb @@ -0,0 +1,814 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:04561aafd347865fa8c83acfb9b60eb84db275f85862655b442f546023cadd1e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Electron Theory of Metals" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.1, Page number 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#import module\n", + "import math\n", + "\n", + "#Calculation\n", + "# given that E-Ef = kT\n", + "# fermi function FE = 1/(1+exp((E-Ef)/kT)\n", + "# therefore FE = 1/(1+exp(kT/kT));\n", + "# FE = 1/(1+exp(1))\n", + "FE=1/(1+math.exp(1));\n", + "FE=math.ceil(FE*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"fermi function is\",FE);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('fermi function is', 0.27)\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.2, Page number 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "\n", + "#Calculation\n", + "# given that E-Ef = kT\n", + "# fermi function FE = 1/(1+exp((E-Ef)/kT)\n", + "# therefore FE = 1/(1+exp(kT/kT));\n", + "# FE = 1/(1+exp(1))\n", + "FE=1/(1+math.exp(1));\n", + "FE=math.ceil(FE*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"fermi function is\",FE);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('fermi function is', 0.269)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.3, Page number 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "FE=10/100; #fermi function is 10%\n", + "Ef=5.5; #fermi energy of silver in eV\n", + "k=1.38*10**-23;\n", + "\n", + "#Calculation\n", + "E=Ef+(Ef/100);\n", + "#FE=1/(1+math.exp((E-Ef)/(k*T)))\n", + "#therefore 1/FE = 1+math.exp((E-Ef)/(k*T))\n", + "#therefore (1/FE)-1 = math.exp((E-Ef)/(k*T))\n", + "#therefore log((1/FE)-1) = (E-Ef)/(k*T)\n", + "#therefore T = (E-Ef)/(k*math.log((1/FE)-1))\n", + "#let X=E-Ef; \n", + "X=E-Ef; #energy in eV\n", + "X=X*1.6*10**-19; #energy in J\n", + "T = (X/(k*math.log((1/FE)-1)));\n", + "T=math.ceil(T*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"temperature in K is\",T);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('temperature in K is', 290.23)\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.4, Page number 70 **************************************" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "#let X=E-Ef\n", + "X=0.5; #E-Ef=0.5 in eV\n", + "\n", + "#Calculation\n", + "X=X*1.6*10**-19; #X in J\n", + "FE=1/100; #fermi function is 1% \n", + "k=1.38*10**-23;\n", + "#FE=1/(1+exp(X/(k*T)))\n", + "#therefore 1/FE = 1+math.exp(X/(k*T))\n", + "#therefore (1/FE)-1 = math.exp(X/(k*T))\n", + "#therefore log((1/FE)-1) = X/(k*T)\n", + "#but log(x) = 2.303*math.log10(x)\n", + "#therefore T = X/(k*math.log((1/FE)-1))\n", + "#but log(x)=2.303*math.log10(x)\n", + "#therefore T = X/(k*2.303*math.log10((1/FE)-1))\n", + "T = X/(k*2.303*math.log10((1/FE)-1));\n", + "\n", + "#Result\n", + "print(\"temperature in K is\",T);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('temperature in K is', 1261.3505710887953)\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.5, Page number 71 *******" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "rho_s=10.5*10**3; #density in kg/m^3\n", + "NA=6.02*10**26; #avagadro number per kmol\n", + "MA=107.9; \n", + "\n", + "#Calculation\n", + "n=(rho_s*NA)/MA;\n", + "sigma=6.8*10**7;\n", + "e=1.6*10**-19; #charge in coulomb\n", + "mew=sigma/(n*e);\n", + "mew=math.ceil(mew*10**6)/10**6; #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"density of electrons is\",n);\n", + "print(\"mobility of electrons in silver in m^2/Vs is\",mew);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('density of electrons is', 5.85820203892493e+28)\n", + "('mobility of electrons in silver in m^2/Vs is', 0.007255)\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.6, Page number 71 ***" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "d=8.92*10**3; #density in kg/m^3\n", + "rho=1.73*10**-8; #resistivity in ohm-m\n", + "m=9.1*10**-31; #mass in kg\n", + "w=63.5; #atomic weight\n", + "e=1.6*10**-19; #charge in coulomb\n", + "A=6.02*10**26; #avagadro number\n", + "\n", + "#Calculation\n", + "n=(d*A)/w;\n", + "mew=1/(rho*n*e);\n", + "tow=m/(n*(e**2)*rho);\n", + "mew=math.ceil(mew*10**6)/10**6; #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"mobility of electrons in Copper in m/Vs is\",mew);\n", + "print(\"average time of collision of electrons in copper in sec is\",tow);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('mobility of electrons in Copper in m/Vs is', 0.004273)\n", + "('average time of collision of electrons in copper in sec is', 2.4297841992299697e-14)\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.7, Page number 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "rho=1.54*10**-8; #resistivity in ohm-m\n", + "n=5.8*10**28; #electron/m^3\n", + "m=9.108*10**-31; #mass in kg\n", + "e=1.602*10**-19; #charge in coulomb\n", + "\n", + "#Calculation\n", + "tow=m/(n*(e**2)*rho);\n", + "\n", + "#Result\n", + "print(\"relaxation time of conduction electrons in sec is\",tow);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('relaxation time of conduction electrons in sec is', 3.973281032516849e-14)\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.8, Page number 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "FE=10/100; #fermi function is 10%\n", + "Ef=5.5; #fermi energy of silver in eV\n", + "k=1.38*10**-23;\n", + "\n", + "#Calculation\n", + "E=Ef+(Ef/100);\n", + "#FE=1/(1+math.exp((E-Ef)/(k*T)))\n", + "#therefore 1/FE = 1+math.exp((E-Ef)/(k*T))\n", + "#therefore (1/FE)-1 = math.exp((E-Ef)/(k*T))\n", + "#therefore log((1/FE)-1) = (E-Ef)/(k*T)\n", + "#therefore T = (E-Ef)/(k*math.log((1/FE)-1))\n", + "#let X=E-Ef; \n", + "X=E-Ef; #energy in eV\n", + "X=X*1.6*10**-19; #energy in J\n", + "T = (X/(k*math.log((1/FE)-1)));\n", + "T=math.ceil(T*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"temperature in K is\",T);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('temperature in K is', 290.23)\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.9, Page number 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "\n", + "#Calculation\n", + "# given that E-Ef = kT\n", + "# fermi function FpE = 1/(1+exp((E-Ef)/kT)\n", + "# therefore FpE = 1/(1+exp(kT/kT));\n", + "# FpE = 1/(1+exp(1))\n", + "FpE=1/(1+math.exp(1));\n", + "FpE=math.ceil(FpE*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"fermi function is\",FpE);\n", + "#the presence of electron at that energy level is not certain" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('fermi function is', 0.27)\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.10, Page number 74 ****************************" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "m=9.1*10**-31; #mass in kg\n", + "h=6.626*10**-34;\n", + "A=(8*m)**(3/2);\n", + "\n", + "#Calculation\n", + "B=math.pi/(2*h**3);\n", + "EfeV=3.10; #fermi energy in eV\n", + "Ef=EfeV*1.6*10**-19; #fermi energy in J\n", + "EFeV=EfeV+0.02; #energy after interval in eV\n", + "EF=EFeV*1.6*10**-19; #energy after interval in J\n", + "def f(E):\n", + " Q=A*B*math.sqrt(E)\n", + " \n", + "I=(Ef,EF,f)\n", + "\n", + "#Result\n", + "print(\"number of energy states per unit volume is\",I);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('number of energy states per unit volume is', (4.960000000000001e-19, 4.992000000000001e-19, <function f at 0x7f1495202848>))\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.11, Page number 74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "T=300; #temperature in K\n", + "n=8.5*10**28; #density per m^3\n", + "rho=1.69*10**-8; #resistivity in ohm/m^3\n", + "me=9.11*10**-31; #mass of electron in kg\n", + "e=1.6*10**-19; #charge in coulomb\n", + "KB=1.38*10**-23; #boltzmann constant in J/k\n", + "\n", + "#Calculation\n", + "lamda=math.sqrt(3*KB*me*T)/(n*(e**2)*rho);\n", + "\n", + "#Result\n", + "print(\"mean free path of electron in m is\",lamda);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('mean free path of electron in m is', 2.892506814374228e-09)\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.12, Page number 75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "rho=1.43*10**-8; #resistivity in ohm-m\n", + "n=6.5*10**28; #electron/m^3\n", + "m=9.11*10**-34; #mass in kg\n", + "e=1.6*10**-19; #charge in coulomb\n", + "\n", + "#Calculation\n", + "tow=m/(n*(e**2)*rho);\n", + "\n", + "#Result\n", + "print(\"relaxation time of conduction electrons in sec is\",tow);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('relaxation time of conduction electrons in sec is', 3.8285032275416887e-17)\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.13, Page number 75 ******" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "d=8.92*10**3; #density in kg/m^3\n", + "rho=1.73*10**-8; #resistivity in ohm-m\n", + "m=9.1*10**-31; #mass in kg\n", + "M=63.5; #atomic weight\n", + "e=1.6*10**-19; #charge in coulomb\n", + "A=6.02*10**26; #avagadro number\n", + "\n", + "#Calculation\n", + "n=(d*A)/M;\n", + "mew=1/(rho*n*e);\n", + "tow=m/(n*(e**2)*rho);\n", + "mew=math.ceil(mew*10**6)/10**6; #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"mobility of electrons in Copper in m/Vs is\",mew);\n", + "print(\"average time of collision of electrons in copper in sec is\",tow);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('mobility of electrons in Copper in m/Vs is', 0.004273)\n", + "('average time of collision of electrons in copper in sec is', 2.4297841992299697e-14)\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.14, Page number 76" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "MH=1.008*2*1.67*10**-27; #mass in kg\n", + "T=30; #temperature in C\n", + "\n", + "#Calculation\n", + "T=T+273; #temperature in K\n", + "KB=1.38*10**-23; #boltzmann constant in J/k\n", + "KE=(3/2)*KB*T; #kinetic energy in J\n", + "KEeV=KE*6.24*10**18; #kinetic energy in eV\n", + "cbar=math.sqrt((3*KB*T)/MH);\n", + "\n", + "#Result\n", + "print(\"average kinetic energy in J is\",KE);\n", + "print(\"average kinetic energy in eV is\",KEeV);\n", + "print(\"velocity of molecules in m/s is\",cbar);\n", + "\n", + "#answers for average kinetic energy in eV and velocity of electrons given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('average kinetic energy in J is', 6.2720999999999986e-21)\n", + "('average kinetic energy in eV is', 0.039137903999999994)\n", + "('velocity of molecules in m/s is', 1930.269663853336)\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.15, Page number 77 ****" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "Ee=10; #electron kinetic energy in eV\n", + "Ep=10; #proton kinetic energy in eV\n", + "me=9.1*10**-31; #mass of electron in kg\n", + "mp=1.67*10**-27; #mass of proton in kg\n", + "\n", + "#Calculation\n", + "EeeV=Ee*1.6*10**-19; #electron kinetic energy in J\n", + "EpeV=Ep*1.6*10**-19; #proton kinetic energy in J\n", + "cebar=math.sqrt((2*EeeV)/me);\n", + "cpbar=math.sqrt((2*EpeV)/mp);\n", + "\n", + "#Result\n", + "print(\"velocity of electron in m/s is\",cebar);\n", + "print(\"velocity of proton in m/s is\",cpbar);\n", + "\n", + "#answers given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('velocity of electron in m/s is', 1875228.9237539817)\n", + "('velocity of proton in m/s is', 43774.05241316662)\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.16, Page number 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "A=10; #area of cross section in mm^2\n", + "A=A*10**-6; #area of cross section in m^2\n", + "i=100; #current in amp\n", + "n=8.5*10**28; #number of electrons per mm^3\n", + "e=1.6*10**-19; #electron charge in coulumb\n", + "\n", + "#Calculation\n", + "vd=1/(n*A*e);\n", + "\n", + "#Result\n", + "print(\"drift velocity in m/s is\",vd);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('drift velocity in m/s is', 7.3529411764705884e-06)\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.17, Page number 78" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "tow=3*10**-14; #relaxation time in sec\n", + "n=8*10**28; #density of electrons per m^3\n", + "KB=1.38*10**-23; #boltzmann constant in J/k\n", + "T=0; #temperature in C\n", + "\n", + "#Calculation\n", + "T=T+273; #temperature in K\n", + "m=9.1*10**-31; #mass of electron in kg\n", + "sigma_T=((3*n*tow*(KB**2)*T)/(2*m));\n", + "sigma_T=math.ceil(sigma_T*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"thermal conductivity of copper in ohm-1 is\",sigma_T);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('thermal conductivity of copper in ohm-1 is', 205.68)\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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