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diff --git a/Applied_Physics_by_S._Mani_Naidu/Chapter4.ipynb b/Applied_Physics_by_S._Mani_Naidu/Chapter4.ipynb new file mode 100644 index 00000000..1b0ca557 --- /dev/null +++ b/Applied_Physics_by_S._Mani_Naidu/Chapter4.ipynb @@ -0,0 +1,668 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4: Elements of Statistical Mechanics and Principles of Quantum Mechanics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 1, Page number 4-41" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average energy of oscillator is 2.948 *10**-21 joule\n", + "answer given in the book varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "new=5.6*10**12; #frequency(Hz)\n", + "h=6.625*10**-34; #plank constant\n", + "kB=1.38*10**-23; #boltzmann constant\n", + "T=330; #temperature(K) \n", + "\n", + "#Calculation\n", + "x=h*new/(kB*T); \n", + "E=h*new/(math.exp(x)-1); #average energy of oscillator(joule)\n", + "\n", + "#Result\n", + "print \"average energy of oscillator is\",round(E*10**21,3),\"*10**-21 joule\"\n", + "print \"answer given in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 2, Page number 4-41" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy density per unit wavelength is 7.13 Jm-4\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h=6.63*10**-34; #plank constant\n", + "kB=1.38*10**-23; #boltzmann constant\n", + "T=1500; #temperature(K) \n", + "c=3*10**8; #velocity of light(m/sec)\n", + "lamda=6000*10**-10; #wavelength(m)\n", + "\n", + "#Calculation\n", + "new=c/lamda;\n", + "x=h*new/(kB*T); \n", + "y=math.exp(x)-1; #average energy of oscillator(joule)\n", + "Ulamda=8*math.pi*h*new/(y*lamda**4); #energy density per unit wavelength(Jm-4)\n", + "\n", + "#Result\n", + "print \"energy density per unit wavelength is\",round(Ulamda,2),\"Jm-4\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 3, Page number 4-41" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength is 0.0275 nm\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e=1.6*10**-19; #charge(c)\n", + "m=9.1*10**-31; #mass(kg)\n", + "h=6.63*10**-34; #plank constant\n", + "E=2000; #energy(eV)\n", + "\n", + "#Calculation\n", + "lamda=h/math.sqrt(2*m*E*e); #wavelength(m)\n", + "\n", + "#Result\n", + "print \"wavelength is\",round(lamda*10**9,4),\"nm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 4, Page number 4-42" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "velocity is 438.9 *10**4 m/s\n", + "kinetic energy is 54.78 eV\n", + "answer for energy given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda=1.66*10**-10; #wavelength(m)\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E=h**2/(2*m*e*lamda**2); #kinetic energy(eV)\n", + "v=h/(m*lamda); #velocity(m/s)\n", + "\n", + "#Result\n", + "print \"velocity is\",round(v*10**-4,1),\"*10**4 m/s\"\n", + "print \"kinetic energy is\",round(E,2),\"eV\"\n", + "print \"answer for energy given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 5, Page number 4-42" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ground state energy is 37.7377 eV\n", + "energy of 1st excited state is 150.95 eV\n", + "energy of 2nd excited state is 339.6395 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=1*10**-10; #length(m)\n", + "n2=2;\n", + "n3=3;\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #ground state energy(eV)\n", + "E2=n2**2*E1; #energy of 1st excited state(eV)\n", + "E3=n3**2*E1; #energy of 2nd excited state(eV)\n", + "\n", + "#Result\n", + "print \"ground state energy is\",round(E1,4),\"eV\"\n", + "print \"energy of 1st excited state is\",round(E2,2),\"eV\"\n", + "print \"energy of 2nd excited state is\",round(E3,4),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6, Page number 4-43" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum energy is 2.3586 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=4*10**-10; #length(m)\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #minimum energy(eV)\n", + "\n", + "#Result\n", + "print \"minimum energy is\",round(E1,4),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 7, Page number 4-43" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of electron waves is 0.01 nm\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V=15*10**3; #accelerated voltage(V)\n", + "\n", + "#Calculation\n", + "lamda=1.227/math.sqrt(V); #wavelength of electron waves(nm)\n", + "\n", + "#Result\n", + "print \"wavelength of electron waves is\",round(lamda,2),\"nm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 8, Page number 4-43" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum energy is 150.95 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=0.05*10**-9; #length(m)\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #minimum energy(eV)\n", + "\n", + "#Result\n", + "print \"minimum energy is\",round(E1,2),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 9, Page number 4-44" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum energy is 4.2 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=3*10**-10; #length(m)\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #minimum energy(eV)\n", + "\n", + "#Result\n", + "print \"minimum energy is\",round(E1,1),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 10, Page number 4-44" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de broglie wavelength is 8488 nm\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "me=9.1*10**-31; #mass(kg)\n", + "h=6.63*10**-34; #plank constant\n", + "mn=1.676*10**-27; #mass(kg)\n", + "\n", + "#Calculation\n", + "lamdan=h*10**9/math.sqrt(4*mn*me); #de broglie wavelength(nm) \n", + "\n", + "#Result\n", + "print \"de broglie wavelength is\",int(lamdan),\"nm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 11, Page number 4-44" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ground state energy is 9.43 eV\n", + "energy of 1st excited state is 37.738 eV\n", + "energy of 2nd excited state is 150.95 eV\n", + "answers for energy of 1st and 2nd states given in the book are wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=2*10**-10; #length(m)\n", + "n2=2;\n", + "n4=4;\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #minimum energy(eV)\n", + "E2=n2**2*E1; #energy of 1st excited state(eV)\n", + "E4=n4**2*E1; #energy of 2nd excited state(eV)\n", + "\n", + "#Result\n", + "print \"ground state energy is\",round(E1,2),\"eV\"\n", + "print \"energy of 1st excited state is\",round(E2,3),\"eV\"\n", + "print \"energy of 2nd excited state is\",round(E4,2),\"eV\"\n", + "print \"answers for energy of 1st and 2nd states given in the book are wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 12, Page number 4-45" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "spacing of crystal is 0.382 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n=1;\n", + "e=1.6*10**-19; #charge(c)\n", + "m=9.1*10**-31; #mass(kg)\n", + "h=6.63*10**-34; #plank constant\n", + "V=344; #energy(eV)\n", + "theta=60*math.pi/180; #angle(radian)\n", + "\n", + "#Calculation\n", + "d=h*10**10/(2*math.sin(theta)*math.sqrt(2*m*V*e)); #spacing of crystal(angstrom)\n", + "\n", + "#Result\n", + "print \"spacing of crystal is\",round(d,3),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 13, Page number 4-45" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ground state energy is 37.696 eV\n", + "energy of 2nd excited state is 339.27 eV\n", + "energy required to pump an electron is 301.57 eV\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=1*10**-10; #length(m)\n", + "n3=3;\n", + "m=9.11*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #ground state energy(eV)\n", + "E3=n3**2*E1; #energy of 2nd excited state(eV)\n", + "E=E3-E1; #energy required to pump an electron(eV) \n", + "\n", + "#Result\n", + "print \"ground state energy is\",round(E1,3),\"eV\"\n", + "print \"energy of 2nd excited state is\",round(E3,2),\"eV\"\n", + "print \"energy required to pump an electron is\",round(E,2),\"eV\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 14, Page number 4-46" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum energy is 9.43 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L=2*10**-10; #length(m)\n", + "m=9.1*10**-31; #mass(kg)\n", + "e=1.6*10**-19; #charge(c)\n", + "h=6.63*10**-34; #plank constant\n", + "\n", + "#Calculation\n", + "E1=h**2/(8*m*e*L**2); #minimum energy(eV)\n", + "\n", + "#Result\n", + "print \"minimum energy is\",round(E1,2),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 15, Page number 4-46" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of electron waves is 0.31 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V=1600; #accelerated voltage(V)\n", + "\n", + "#Calculation\n", + "lamda=1.227*10/math.sqrt(V); #wavelength of electron waves(angstrom)\n", + "\n", + "#Result\n", + "print \"wavelength of electron waves is\",round(lamda,2),\"angstrom\"" + ] + } + ], + "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": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |