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diff --git a/Engineering_Physics_By_G_Vijayakumari/Chapter8.ipynb b/Engineering_Physics_By_G_Vijayakumari/Chapter8.ipynb new file mode 100755 index 00000000..e403d61e --- /dev/null +++ b/Engineering_Physics_By_G_Vijayakumari/Chapter8.ipynb @@ -0,0 +1,669 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#8: Quantum Physics"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.1, Page number 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The energy of photon is 12412.5 eV\n",
+ "The momentum of the photon is 6.62e-24 Kg m s^-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "W=0.1*10**-9; #wavelength of photon(m)\n",
+ "h=6.62*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "E=h*c/(W*e); #energy of photon(eV)\n",
+ "P=h/W; #momentum of the photon(Kgms^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"The energy of photon is\",E,\"eV\"\n",
+ "print \"The momentum of the photon is\",P,\"Kg m s^-1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.2, Page number 205"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The total number of photons emitted per second is 2.965 *10**20 per sec\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",
+ "w=5893*10**-10; #wavelength of emitted light(m)\n",
+ "e=100; #total energy emitted per sec\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "E=h*c/w; #energy of one photon(J)\n",
+ "N=e/E; #The total numberof photons emitted(sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"The total number of photons emitted per second is\",round(N/10**20,3),\"*10**20 per sec\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.3, Page number 205"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The energy density per unit wavelength in a black body cavity is 0.018349 J/m^4\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",
+ "w=4000*10**-10; #wavelength in black body(m)\n",
+ "t=1500; #temperature of black body(K)\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "Kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
+ "\n",
+ "#Calculation\n",
+ "Edw=(8*math.pi*h*c/w**5)*(1/(math.exp(h*c/(w*Kb*t))-1)); #The energy density per unit wavelength in a black body cavity(J/m^4)\n",
+ "\n",
+ "#Result\n",
+ "print \"The energy density per unit wavelength in a black body cavity is\",round(Edw,6),\"J/m^4\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.4, Page number 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The compton wavelength for an electron is 0.0242 Angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "\n",
+ "#Calculation\n",
+ "w=h/(c*m)*10**10; #The compton wavelength for an electron(Armstrong)\n",
+ "\n",
+ "#Result\n",
+ "print \"The compton wavelength for an electron is\",round(w,4),\"Angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.5, Page number 212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The change in wavelength for X ray photon is 0.0242 Angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=90; #x ray photon scattered at a angle(degrees)\n",
+ "h=6.625*10**-34; #Planck's constant(J-sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "deltalamda=((h/(c*m))*(1-math.cos(x)))/10**-10; #The change in wavelength for Xray photon(Angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The change in wavelength for X ray photon is\",round(deltalamda,4),\"Angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.6, Page number 212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The wavelength of X-rays carbon is 1.72 Angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=180; #x ray carbon scattered at a angle(degrees)\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "m=9.11*10**-31; #mass of electron(kg)\n",
+ "v=1.8*10**18; #frequency of incident rays(s^-1)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "w=c/v; #wavelength(m)\n",
+ "tw=(h/(c*m))*(1-math.cos(theta)); #The change wavelength for Xray carbon(m)\n",
+ "lamda_dash=(w+tw)/10**-10; #The wavelength of X-rays carbon(Angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The wavelength of X-rays carbon is\",round(lamda_dash,2),\"Angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.7, Page number 212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The wavelength of scattered photons is 3.012 Angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "w=3*10**-10; #wavelength of incident photons(m)\n",
+ "theta=60; #angle of view(degrees)\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "c=3*10**8; #velocity of light(m/sec)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "lamda_dash=(w+((h/(c*m))*(1-math.cos(theta))))/10**-10; #The wavelength of scattered photons(Angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The wavelength of scattered photons is\",round(lamda_dash,3),\"Angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.8, Page number 213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The Velocity of moving electron is 2.9047 *10**8 m/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "x=4; #Total energy increase to 4 times of its initial rest energy\n",
+ "c=3*10**8; #velocity of light(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "v=math.sqrt(c**2*(1-(1/x**2))); #The Velocity of moving electron(m/sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"The Velocity of moving electron is\",round(v/10**8,4),\"*10**8 m/sec\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.9, Page number 224"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The least energy of the particle can be obtained is 37.639 eV\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",
+ "a=0.1*10**-9; #width of high potential box(m)\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "n=1; #take n equal to one\n",
+ "\n",
+ "#Calculation\n",
+ "E=(n**2*h**2)/(8*m*a**2*e); #The least energy of the particle can be obtained(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The least energy of the particle can be obtained is\",round(E,3),\"eV\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.10, Page number 224"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The least energy of the neutron can be obtained is 2.053 MeV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=10**-14; #length of impenerable box(m)\n",
+ "m=1.67*10**-27; #mass of neutron(Kg)\n",
+ "n=1; #for lowest energy\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "E=(n**2*h**2)/(8*m*a**2); #The least energy of the neutron can be obtained(J)\n",
+ "\n",
+ "#Result\n",
+ "print \"The least energy of the neutron can be obtained is\",round(E/(1.6*10**-19*10**6),3),\"MeV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.11, Page number 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The first permitted energy level by taking n=1 is 2.352 eV\n",
+ "The second permitted energy level by taking n=2 is 9.41 eV\n",
+ "The third permitted energy level by taking n=3 is 21.172 eV\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",
+ "a=4*10**-10; #width of electron box(m)\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "n=1; #first permitted level\n",
+ "\n",
+ "#Calculation\n",
+ "E1=((n**2*h**2)/(8*m*a**2*e)); #The first permitted energy level by taking n=1(eV)\n",
+ "E2=4*E1; #The second permitted energy level by taking n=2(eV)\n",
+ "E3=9*E1; #The third permitted energy level by taking n=3(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The first permitted energy level by taking n=1 is\",round(E1,3),\"eV\"\n",
+ "print \"The second permitted energy level by taking n=2 is\",round(E2,2),\"eV\"\n",
+ "print \"The third permitted energy level by taking n=3 is\",round(E3,3),\"eV\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.12, Page number 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lowest energy of electron in a cubical box is 50.186 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=1.5*10**-10; #each side of cubical box(m)\n",
+ "n1=1; #for lowest energy\n",
+ "n2=1; #for lowest energy\n",
+ "n3=1; #for lowest energy\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "n=(n1**2+n2**2+n3**2); #total value of n\n",
+ "E=((n*h**2)/(8*m*a**2*e)); #The lowest energy of electron ina cubical box(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lowest energy of electron in a cubical box is\",round(E,3),\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.13, Page number 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lowest energy of electron in deep potential well is 0.02352 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=4*10**-9; #width of potential well(m)\n",
+ "n=1; #For minimum energy n value\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "E=((n**2*h**2)/(8*m*a**2*e)); #The lowest energy of electron in deep potential well(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lowest energy of electron in deep potential well is\",round(E,5),\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.14, Page number 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The energy required the electron from its ground state to the fifth exited state is 1317 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=0.1*10**-9; #length of one dimensional box(m)\n",
+ "n=1; #first permitted level\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "E1=((n**2*h**2)/(8*m*a**2*e)); #The ground state of electron in an one dimensional box(eV)\n",
+ "E6=36*E1; #The fifth exited state of electron(eV)\n",
+ "E=E6-E1; #The energy required the electron from its ground state to the fifth exited state(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The energy required the electron from its ground state to the fifth exited state is\",int(E),\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 8.15, Page number 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lowest energy of the system consisting of three electron ia a one dimensional box is 112.9184 eV\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",
+ "a=0.1*10**-9; #length of one dimensional box(m)\n",
+ "n=1; #first permitted level\n",
+ "h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
+ "m=9.11*10**-31; #mass of electron(Kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "ne=3; #the number of electrons\n",
+ "\n",
+ "#Calculation\n",
+ "E=((n**2*h**2)/(8*m*a**2*e))*ne; #The lowest energy of the system consisting of three electron ia a one dimensional box(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lowest energy of the system consisting of three electron ia a one dimensional box is\",round(E,4),\"eV\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ }
+ ],
+ "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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