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diff --git a/Engineering_Physics_by_S._Mani_Naidu/Chapter5.ipynb b/Engineering_Physics_by_S._Mani_Naidu/Chapter5.ipynb new file mode 100755 index 00000000..f11e05ff --- /dev/null +++ b/Engineering_Physics_by_S._Mani_Naidu/Chapter5.ipynb @@ -0,0 +1,566 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#5: Electron theory of metals"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.1, Page number 5.27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "temperature is 1260.84 K\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "fE=1/100; #probability(%)\n",
+ "E_EF=0.5; #fermi energy(eV)\n",
+ "Kb=1.38*10**-23; #boltzmann constant\n",
+ "e=6.24*10**18; #conversion faction from J to eV\n",
+ "\n",
+ "#Calculation\n",
+ "x=E_EF/(Kb*e);\n",
+ "y=math.log(1/fE);\n",
+ "T=x/y; #temperature(K)\n",
+ "\n",
+ "#Result\n",
+ "print \"temperature is\",round(T,2),\"K\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.2, Page number 5.28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total number of free electrons is 8.3954 **10**28 per m**3\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Ef=7*1.602*10**-19; #fermi energy(J)\n",
+ "h=6.63*10**-34; #planck's constant\n",
+ "m=9.11*10**-31; #mass(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "x=h**2/(8*m);\n",
+ "y=(3/math.pi)**(2/3);\n",
+ "n23=Ef/(x*y);\n",
+ "n=n23**(3/2); #total number of free electrons(per m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"total number of free electrons is\",round(n/10**28,4),\"**10**28 per m**3\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.3, Page number 5.28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "relaxation time is 39.742 *10**-15 s\n",
+ "answer 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 of metal(ohm m)\n",
+ "n=5.8*10**28; #number of free 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(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"relaxation time is\",round(tow*10**15,3),\"*10**-15 s\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.4, Page number 5.29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "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 of metal(ohm m)\n",
+ "n=6.5*10**28; #number of free electrons(per m**3)\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 5.5, Page number 5.29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of conduction electrons is 1.8088 *10**29 per m**3\n",
+ "mobility of electrons 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",
+ "L=5; #length(m)\n",
+ "R=0.06; #resistance(ohm)\n",
+ "I=15; #current(A)\n",
+ "ne=3; #number of electrons\n",
+ "rho=2.7*10**-8; #resistivity(ohm m)\n",
+ "w=26.98; #atomic weight\n",
+ "D=2.7*10**3; #density(kg/m**3)\n",
+ "Na=6.025*10**26; #avagadro number(per k mol)\n",
+ "\n",
+ "#Calculation\n",
+ "n=ne*Na*D/w; #number of conduction electrons(per m**3)\n",
+ "mew=1/(n*e*rho); #mobility of electrons(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 per m**3\"\n",
+ "print \"mobility of electrons 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 5.6, Page number 5.30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "mobility of electrons is 0.00427 m**2/Vs\n",
+ "answer in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ne=1; #number of electrons\n",
+ "rho=1.73*10**-8; #resistivity(ohm m)\n",
+ "w=63.5; #atomic weight\n",
+ "e=1.6*10**-19; #charge(c)\n",
+ "D=8.92*10**3; #density(kg/m**3)\n",
+ "Na=6.02*10**26; #avagadro number(per k mol)\n",
+ "\n",
+ "#Calculation\n",
+ "n=ne*Na*D/w;\n",
+ "mew=1/(n*e*rho); #mobility of electrons(m**2/Vs)\n",
+ "\n",
+ "#Result\n",
+ "print \"mobility of electrons is\",round(mew,5),\"m**2/Vs\"\n",
+ "print \"answer in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.7, Page number 5.31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "mobility of electrons is 0.00428 m**2/Vs\n",
+ "answer in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ne=1; #number of electrons\n",
+ "rho=1.721*10**-8; #resistivity(ohm m)\n",
+ "w=63.54; #atomic weight\n",
+ "e=1.6*10**-19; #charge(c)\n",
+ "D=8.95*10**3; #density(kg/m**3)\n",
+ "Na=6.025*10**26; #avagadro number(per k mol)\n",
+ "\n",
+ "#Calculation\n",
+ "n=ne*Na*D/w;\n",
+ "mew=1/(n*e*rho); #mobility of electrons(m**2/Vs)\n",
+ "\n",
+ "#Result\n",
+ "print \"mobility of electrons is\",round(mew,5),\"m**2/Vs\"\n",
+ "print \"answer in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.8, Page number 5.31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "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=1.5*10**-8; #resistivity of metal(ohm m)\n",
+ "n=6.5*10**28; #number of free 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(s)\n",
+ "\n",
+ "#Result\n",
+ "print \"relaxation time is\",round(tow*10**14,2),\"*10**-14 s\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.9, Page number 5.32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "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",
+ "rho=1.54*10**-8; #resistivity of metal(ohm m)\n",
+ "n=5.8*10**28; #number of free electrons(per m**3)\n",
+ "e=1.602*10**-19; #charge(c)\n",
+ "m=9.11*10**-31; #mass(kg)\n",
+ "E=1*10**2; #electric field(V/m)\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 5.10, Page number 5.32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "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",
+ "EF=5.5*1.602*10**-19; #fermi energy of silver(J)\n",
+ "tow=3.97*10**-14; #relaxation time(s)\n",
+ "m=9.11*10**-31; #mass(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "vf=math.sqrt(2*EF/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 5.11, Page number 5.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "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",
+ "ne=1; #number of electrons\n",
+ "M=107.9; #atomic weight\n",
+ "D=10500; #density(kg/m**3)\n",
+ "Na=6.025*10**26; #avagadro number(per k mol)\n",
+ "m=9.11*10**-31; #mass(kg)\n",
+ "h=6.63*10**-34; #planck's constant\n",
+ "\n",
+ "#Calculation\n",
+ "n=ne*Na*D/M; \n",
+ "x=h**2/(8*m);\n",
+ "y=(3/math.pi)**(2/3);\n",
+ "Ef=x*y*n**(2/3); #fermi energy(eV) \n",
+ "\n",
+ "#Result\n",
+ "print \"fermi energy is\",round(Ef*10**19,2),\"*10**-19 J\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 5.12, Page number 5.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "drift velocity of free electrons is 0.7391 *10**-3 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "A=10*10**-6; #area(m**2)\n",
+ "ne=1; #number of electrons\n",
+ "I=100; #current(amperes)\n",
+ "w=63.5; #atomic weight\n",
+ "e=1.6*10**-19; #charge(c)\n",
+ "D=8.92*10**3; #density(kg/m**3)\n",
+ "Na=6.02*10**26; #avagadro number(per k mol)\n",
+ "\n",
+ "#Calculation\n",
+ "n=ne*Na*D/w;\n",
+ "J=I/A;\n",
+ "vd=J/(n*e); #drift velocity of free electrons(m/s)\n",
+ "\n",
+ "#Result\n",
+ "print \"drift velocity of free electrons 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": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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