{ "metadata": { "name": "", "signature": "sha256:ef6d9a0d23fffdb9f7c392e83ea5acb91eccb75cc2e53a11277239fd4fc34966" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter05:Electron Theory of Metals" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.1.i:pg-110" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.1.i: probability for diamond\n", " \n", "# given :\n", "\n", "Eg=5.6; # in eV\n", "k=86.2*10**-6; # in eVk**-1\n", "T=273+25.0; # in K\n", "E_Ef=Eg/2;\n", "f_E=1/(1+math.exp(E_Ef/(k*T)));\n", "print f_E,\" is probability for diamond\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.58172567644e-48 is probability for diamond\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.1.ii:pg-110" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.1.ii: probability for silicon\n", " \n", "# given :\n", "Eg=1.07; # in eV\n", "k=86.2*10**-6; # in eVk**-1\n", "T=273+25.0; # in K\n", "E_Ef=Eg/2;\n", "f_E=1/(1+math.exp(E_Ef/(k*T)));\n", "print f_E,\"is probability for diamond \"\n", "# answer is wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "9.01312095705e-10 is probability for diamond \n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.2:pg-119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.2: resistance\n", " \n", "# given :\n", "l=1; # length in m\n", "A=4*10**-4; # area of cross section in m**2\n", "p=0.01*10**-2; # resistivity in ohm-m\n", "R=p*(l/A);\n", "print R,\"is resistance of wire,R(ohm) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.25 is resistance of wire,R(ohm) \n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.3:pg-120" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.3: resistance\n", " \n", "# given :\n", "\n", "p=1.7*10**-8; # resistivity i ohm-m\n", "d=0.0005; # diameter of the wire in m\n", "l=31.4; # length in m\n", "A=(math.pi*d**2)/4;\n", "R=p*(l/A);\n", "print round(R,2),\"is resistance of wire,R(ohm) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.72 is resistance of wire,R(ohm) \n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.4:pg-120" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.4: conductivity\n", " \n", "# given :\n", "\n", "V=.432; # voltage drop across the wire in volts\n", "I=10; # current through the wire in A\n", "l=1; # length in m\n", "d=1*10**-3; # diameter in m\n", "R=V/I;\n", "A=(math.pi*d**2)/4;\n", "p=(R*A)/l;\n", "b=1/p;\n", "print round(b,2),\" is conductivitty,b(ohm**-1.m**-1) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "29473137.61 is conductivitty,b(ohm**-1.m**-1) \n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.5:pg-124" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.5: drift velocity\n", " \n", "# given :\n", "\n", "n=10**19; # in m**3\n", "b=0.01; # conductivity in ohm**-1. m**-1\n", "V=0.17; # in volts\n", "d=.27*10**-3; # in m\n", "e=1.602*10**-19; # in C\n", "m=9.1*10**-31; # in kg\n", "E=V/d; # in volt/m\n", "v=((b*E)/(n*e));\n", "print round(v,2),\"is drift velocity of electron,v (m/sec) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "3.93 is drift velocity of electron,v (m/sec) \n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.6:pg-124" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.6: conductivity\n", " \n", "# given :\n", "e=1.6*10**-19; # in C\n", "T=300; # temerature in K\n", "t=2*10**-14; # time in sec\n", "c=63.54; # atomic weight of copper in a.m.u\n", "m=9.1*10**-31; # mass in kg\n", "# we know that 63.45 grams of copper contains 6.023*10**23 free electrons since one atom contributes one electron.the volume of 63.54 gram of copper is 8.9 cubic centimetre(c.c).\n", "n=6.023*10**23/(c/8.9); #number of electrons per unit volume(c.c)\n", "n1=n*10**6; # the number of electrons per m**3\n", "b=(e**2*n1*t)/m;\n", "print round(b,2),\"is conductivity,b(mho/m) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "47466174.12 is conductivity,b(mho/m) \n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.7:pg-125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.7: mobility of electrons\n", " \n", "# given :\n", "\n", "e=1.602*10**-19; # in C\n", "m=9.1*10**-31; # in kg\n", "t=10**-14; # time in sec\n", "mu=(e*t)/m;\n", "print mu,\"is mobility of electrons,mu(m**2/volts.sec) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.00176043956044 is mobility of electrons,mu(m**2/volts.sec) \n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.8:pg-125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.8: mobility \n", " \n", "# given :\n", "\n", "d=10.5; # density of silver in gm/c.c\n", "w=107.9; # atomic weight\n", "b=6.8*10**5; # conductivity in mhos/cm\n", "e=1.602*10**-19; # in C\n", "N=6.023*10**23;\n", "n=(N*d)/w;\n", "mu=b/(e*n);\n", "print round(mu,2),\"is mobility of electron,mu(m**2/volt-sec) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "72.42 is mobility of electron,mu(m**2/volt-sec) \n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.9:pg-126" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 5.9: mobility and drift velocity\n", " \n", "# given :\n", "b=6.5*10**7; # conductivity in ohm**-1.m**-1\n", "e=1.602*10**-19; # in C\n", "n=6*10**23; #\n", "E=1; # in V/m\n", "mu=b/(e*n);\n", "v=mu*E;\n", "print round(mu,2),\"is mobility ,mu(m**2/volt-sec) \"\n", "print round(v,2),\"is drift velocity,v(m/sec) \"\n", "# mobility and drift is calculated wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "676.24 is mobility ,mu(m**2/volt-sec) \n", "676.24 is drift velocity,v(m/sec) \n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.10:pg-126" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.10 : density and drift velocity \n", " \n", "#given data :\n", "\n", "e=1.602 *10**-19;\n", "b=58*10**6;# in ohm**-1 m**-1\n", "mu_n=3.5*10**-3;# in m**2/V s\n", "E=0.5; # in V/m\n", "n=b/(e*mu_n);\n", "print n,\"is density,n(m**-3) \"\n", "v=mu_n*E;\n", "print v,\"is drift velocity,v(m/s) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.03442125914e+29 is density,n(m**-3) \n", "0.00175 is drift velocity,v(m/s) \n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.11:pg-127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.11 : velocity\n", "import math\n", "#given data :\n", "m=9.109*10**-31; # in kg\n", "e=1.602 *10**-19;\n", "Ef=2.1# in ev\n", "Wf=e*Ef;# in J\n", "vf=math.sqrt((2*Wf)/m);\n", "print vf,\"is velocity,vf(m/s) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "859449.869617 is velocity,vf(m/s) \n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.12.a:pg-127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.12.a : velocity\n", " \n", "#given data :\n", "m=9.1*10**-31; # in kg\n", "e=1.602 *10**-19;\n", "Ef=3.75;# in ev\n", "Wf=(e*Ef);# in J\n", "vf=math.sqrt(((2*Wf)/m));\n", "print vf,\" is velocity,vf(m/s) \"\n", "# answer is wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1149055.99095 is velocity,vf(m/s) \n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.12.b:pg-127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Example 5.12.b : mobility of electron\n", " \n", "#given data :\n", "m=9.1*10**-31; # in kg\n", "e=1.602 *10**-19;\n", "Ef=3.75;# in ev\n", "t=10**-14;# in sec\n", "mu=(e*t)/m;\n", "print mu,\"is mobility,mu(m**2/V-sec) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.00176043956044 is mobility,mu(m**2/V-sec) \n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.13:pg-127" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.13 : the mean free path\n", "import math\n", "#given data :\n", "\n", "t=10**-9; # in sec\n", "m=9.109*10**-31; # in kg\n", "e=1.602 *10**-19;\n", "Ef=7# in ev\n", "Wf=e*Ef;# in J\n", "vf=math.sqrt((2*Wf)/m);\n", "lamda=vf*t*10**3;\n", "print round(lamda,2),\"is the mean free path,lamda(mm) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.57 is the mean free path,lamda(mm) \n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.14:pg-128" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.14 : mobility and average time\n", " \n", "#given data :\n", "\n", "m=9.109*10**-31; # in kg\n", "e=1.602 *10**-19;\n", "d=8.92*10**3;# in kg/m**3\n", "p=1.73*10**-8;# ohm-m\n", "A=63.5;#atomic weight\n", "N=6.023*10**22; # avogadro's number\n", "n=(N*d)/A;\n", "b=1/p;# conductivity\n", "mu=b/(n*e);\n", "print round(mu,1),\"= mobility,mu(m**2/V-s) \"\n", "t=(mu*m)/e;\n", "print round(t*10**9,3),\"= average time,t(ns) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "42.6 = mobility,mu(m**2/V-s) \n", "0.242 = average time,t(ns) \n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.15:pg-129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 5.15 : electrical resistivity\n", "import math\n", "#given data :\n", "\n", "r=1.86*10**-10;# in m\n", "t=3*10**-14;# in sec\n", "a=2;\n", "m=9.1*10**-31; # in kg\n", "e=1.602 *10**-9;\n", "A=23*10**-3;#in kg/m\n", "N=6.023*10**23; # avogadro's number\n", "M=(a*A)/N;\n", "V=((4/math.sqrt(3))*r)**3;\n", "d=M/V;\n", "mu=((e*t)/m);\n", "n=(N*d)/A;\n", "b=1.602 *10**-19*n*mu;\n", "p=(1/b);\n", "print p,\"= resistivity,p(ohm-m) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.68383991207e-18 = resistivity,p(ohm-m) \n" ] } ], "prompt_number": 43 } ], "metadata": {} } ] }