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-{
- "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",
- "function Q=f(E),Q=A*B*math.sqrt(E),endfunction\n",
- "I=intg(Ef,EF,f)\n",
- "\n",
- "#Result\n",
- "print(\"number of energy states per unit volume is\",I);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "ename": "SyntaxError",
- "evalue": "invalid syntax (<ipython-input-25-15d658985351>, line 18)",
- "output_type": "pyerr",
- "traceback": [
- "\u001b[1;36m File \u001b[1;32m\"<ipython-input-25-15d658985351>\"\u001b[1;36m, line \u001b[1;32m18\u001b[0m\n\u001b[1;33m function Q=f(E),Q=A*B*math.sqrt(E),endfunction\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "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": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-08 19:45:23 +0000