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diff --git a/Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter4.ipynb b/Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter4.ipynb new file mode 100644 index 00000000..e840f21f --- /dev/null +++ b/Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter4.ipynb @@ -0,0 +1,861 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4: Matter Waves" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 1, Page number 153" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-Broglie wavelength in 1st case is 6.625e-34 m\n", + "de-Broglie wavelength in 2nd case is 1.8 angstrom\n", + "de-Broglie wavelength in 3rd case is 3.9 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "e=1.602*10**-19; #charge(coulomb)\n", + "me=9.11*10**-31; #mass(kg)\n", + "h=6.625*10**-34; #planks constant(Js)\n", + "M=0.05; #mass(kg)\n", + "v=20; #velocity(m/sec)\n", + "vp=2200; #velocity of proton(m/sec)\n", + "mp=1.67*10**-27; #mass of proton(kg)\n", + "E=10; #energy(eV)\n", + "\n", + "#Calculations\n", + "lamda1=h/(M*v); #de-Broglie wavelength in 1st case(m)\n", + "lamda2=h/(mp*vp); #de-Broglie wavelength in 2nd case(m)\n", + "lamda3=h/math.sqrt(2*me*e*E); #de-Broglie wavelength in 3rd case(m)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength in 1st case is\",lamda1,\"m\"\n", + "print \"de-Broglie wavelength in 2nd case is\",round(lamda2*10**10,1),\"angstrom\"\n", + "print \"de-Broglie wavelength in 3rd case is\",round(lamda3*10**10,1),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 2, Page number 154" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-Broglie wavelength in 1st case is 1.225 angstrom\n", + "de-Broglie wavelength in 2nd case is 0.1225 angstrom\n", + "de-Broglie wavelength in 3rd case is 0.15313 angstrom\n", + "answer given in the book is wrong\n", + "de-Broglie wavelength in 4th case is 0.1225 angstrom\n", + "de-Broglie wavelength in 5th case is 0.3963 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planks constant(Js)\n", + "vp=10**4; #velocity of proton(m/sec)\n", + "mp=1.673*10**-27; #mass of proton(kg)\n", + "V1=100; #potential difference in 1st case(V)\n", + "V2=10000; #potential difference in 2nd case(V)\n", + "V3=6400; #potential difference in 3rd case(V)\n", + "\n", + "#Calculations\n", + "lamda1=12.25/math.sqrt(V1); #de-Broglie wavelength in 1st case(angstrom)\n", + "lamda2=12.25/math.sqrt(V2); #de-Broglie wavelength in 2nd case(angstrom)\n", + "lamda3=12.25/math.sqrt(V3); #de-Broglie wavelength in 3rd case(angstrom)\n", + "lamda4=12.25/math.sqrt(V2); #de-Broglie wavelength in 4th case(angstrom)\n", + "lamda5=h*10**10/(mp*vp); #de-Broglie wavelength in 5th case(angstrom)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength in 1st case is\",lamda1,\"angstrom\"\n", + "print \"de-Broglie wavelength in 2nd case is\",lamda2,\"angstrom\"\n", + "print \"de-Broglie wavelength in 3rd case is\",round(lamda3,5),\"angstrom\"\n", + "print \"answer given in the book is wrong\"\n", + "print \"de-Broglie wavelength in 4th case is\",lamda4,\"angstrom\"\n", + "print \"de-Broglie wavelength in 5th case is\",round(lamda5,4),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 3, Page number 154" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-Broglie wavelength of proton is 2.64 *10**-14 m\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "c=3*10**8; #velocity of light(m/sec)\n", + "mp=1.67*10**-27; #mass of proton(kg)\n", + "h=6.62*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "v=c/20; #velocity of proton(m/sec)\n", + "lamda=h/(mp*v); #de-Broglie wavelength of proton(m)\n", + "\n", + "#Result\n", + "print \"de-Broglie wavelength of proton is\",round(lamda*10**14,2),\"*10**-14 m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 4, Page number 155" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy of neutron is 8.13 *10**-2 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "m=1.674*10**-27; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "lamda=10**-10; #wavelength(m)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "E=h**2/(2*e*m*lamda**2); #energy of neutron(eV)\n", + "\n", + "#Result\n", + "print \"energy of neutron is\",round(E*10**2,2),\"*10**-2 eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 5, Page number 155" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy of neutron is 167217.6 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", + "m=9.1*10**-31; #mass of proton(kg)\n", + "h=6.62*10**-34; #planks constant(Js)\n", + "lamda=3*10**-12; #wavelength(m)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "E=h**2/(2*e*m*lamda**2); #energy of neutron(eV)\n", + "\n", + "#Result\n", + "print \"energy of neutron is\",round(E,1),\"eV\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6, Page number 155" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "voltage is 934.9 V\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", + "m=9.1*10**-31; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "lamda=0.4*10**-10; #wavelength(m)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "V=h**2/(2*m*e*lamda**2); #voltage(V)\n", + "\n", + "#Result\n", + "print \"voltage is\",round(V,1),\"V\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 7, Page number 156" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "velocity is 3.97 *10**3 m/sec\n", + "kinetic energy of particle is 0.08225 eV\n", + "answer 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", + "m=1.67*10**-27; #mass of proton(kg)\n", + "h=6.63*10**-34; #planks constant(Js)\n", + "lamda=10**-10; #wavelength(m)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "v=h/(m*lamda); #velocity(m/sec)\n", + "E=m*v**2/(2*e); #kinetic energy of particle(eV)\n", + "\n", + "#Result\n", + "print \"velocity is\",round(v/10**3,2),\"*10**3 m/sec\"\n", + "print \"kinetic energy of particle is\",round(E,5),\"eV\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 8, Page number 156" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of photon is 12.4 angstrom\n", + "wavelength of electron is 0.39 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "c=3*10**8; #velocity of light(m/sec)\n", + "E=1000; #energy(eV) \n", + "m=9.1*10**-31; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "lamdap=h*c/(E*e); #wavelength of photon(m)\n", + "lamdae=h/math.sqrt(2*m*e*E); #wavelength of electron(m)\n", + "\n", + "#Result\n", + "print \"wavelength of photon is\",round(lamdap*10**10,1),\"angstrom\"\n", + "print \"wavelength of electron is\",round(lamdae*10**10,2),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 9, Page number 157" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy is 2.4 *10**-15 J\n", + "wavelength of photo-electron is 0.1 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "c=3*10**8; #velocity of light(m/sec)\n", + "m=9.1*10**-31; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "lamda=0.82*10**-10; #wavelength(m)\n", + "\n", + "#Calculations\n", + "E=h*c/lamda; #energy(J)\n", + "lamda=h/math.sqrt(2*m*E); #wavelength of photo-electron(m)\n", + "\n", + "#Result\n", + "print \"energy is\",round(E*10**15,1),\"*10**-15 J\"\n", + "print \"wavelength of photo-electron is\",round(lamda*10**10,1),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 10, Page number 157" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of quantum is 0.0242 angstrom\n", + "answer 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", + "c=3*10**8; #velocity of light(m/sec)\n", + "m=9.1*10**-31; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "lamda=h/(m*c); #wavelength of quantum(m)\n", + "\n", + "#Result\n", + "print \"wavelength of quantum is\",round(lamda*10**10,4),\"angstrom\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 11, Page number 158" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 2.86 *10**-18 m\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "E=10**14; #kinetic energy(eV)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "m=1.675*10**-27; #mass of proton(kg)\n", + "h=6.625*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "v=math.sqrt(2*e*E/m); #velocity(m/sec) \n", + "lamda=h/(m*v); #de-broglie wavelength(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda*10**18,2),\"*10**-18 m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 12, Page number 158" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 7.998 *10**-15 m\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", + "E=12.8*10**6; #kinetic energy(eV)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "m=1.675*10**-27; #mass of proton(kg)\n", + "h=6.625*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "v=math.sqrt(2*e*E/m); #velocity(m/sec) \n", + "lamda=h/(m*v); #de-broglie wavelength(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda*10**15,3),\"*10**-15 m\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 13, Page number 158" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 0.0004 angstrom\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", + "E=12.8*10**6; #kinetic energy(eV)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "mp=1836*m; #mass of proton(kg) \n", + "h=6.625*10**-34; #planks constant(Js)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "E=m*c**2; #energy(J)\n", + "v=math.sqrt(2*E/mp); #velocity(m/sec) \n", + "lamda=h/(mp*v); #de-broglie wavelength(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda*10**10,4),\"angstrom\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 14, Page number 159" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength is 1.777 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "T=300; #temperature(K)\n", + "m=1.67*10**-27; #mass of electron(kg)\n", + "h=6.60*10**-34; #planks constant(Js)\n", + "k=8.6*10**-5; #boltzmann constant(eV deg-1)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "\n", + "#Calculations\n", + "lamda=h/math.sqrt(2*m*e*k*T); #wavelength(m)\n", + "\n", + "#Result\n", + "print \"wavelength is\",round(lamda*10**10,3),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 16, Page number 160" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 4.047 *10**11 angstrom\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", + "E=0.512*10**6; #kinetic energy(eV)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "m=1.673*10**-27; #mass of proton(kg)\n", + "h=6.63*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "v=2*e*E/m; #velocity(m/sec) \n", + "lamda=h*10**10/(m*v); #de-broglie wavelength(angstrom)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda*10**11,3),\"*10**11 angstrom\"\n", + "print \"answer given in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 17, Page number 160" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 0.006348 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "E=0.512*10**6; #rest mass energy(eV)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "KE=1.512*10**6; #kinetic energy(eV) \n", + "c=3*10**8; #velocity of light(m/sec)\n", + "m0=9.1*10**-31; #mass of proton(kg)\n", + "h=6.63*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "E1=(E+KE)*e; #energy(J)\n", + "m=E1/c**2; #mass(kg)\n", + "v=math.sqrt(c**2*(1-(m0/m)**2)); #velocity(m/sec)\n", + "lamda=h*10**10/(m*v); #de-broglie wavelength(angstrom)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda,6),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 18, Page number 161" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength is 1.45 *10**-10 metre\n", + "answer 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", + "k=1.38*10**-23; #boltzmann constant\n", + "T=300; #temperature(K)\n", + "m0=1.67*10**-27; #mass of proton(kg)\n", + "h=6.6*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "lamda=h/math.sqrt(3*m0*k*T); #de-broglie wavelength(metre)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength is\",round(lamda*10**10,2),\"*10**-10 metre\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 19, Page number 162" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "interplanar spacing is 1.78 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "k=1.38*10**-23; #boltzmann constant\n", + "T=300; #temperature(K)\n", + "mn=1.67*10**-27; #mass of proton(kg)\n", + "h=6.62*10**-34; #planks constant(Js)\n", + "\n", + "#Calculations\n", + "E=k*T; #energy(J)\n", + "p=math.sqrt(2*mn*E); \n", + "d=h*10**10/p; #interplanar spacing(angstrom)\n", + "\n", + "#Result\n", + "print \"interplanar spacing is\",round(d,2),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 20, Page number 162" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "interplanar spacing is 0.4 angstrom\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", + "m=9*10**-31; #mass of proton(kg)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "V=344; #voltage(V)\n", + "h=6.62*10**-34; #planks constant(Js)\n", + "theta=60*math.pi/180; #angle(radian)\n", + "\n", + "#Calculations\n", + "d=h*10**10/(2*math.sin(theta)*math.sqrt(2*m*e*V)); #spacing of crystal(angstrom)\n", + "\n", + "#Result\n", + "print \"interplanar spacing is\",round(d,1),\"angstrom\"\n", + "print \"answer given in the book is wrong\"" + ] + } + ], + "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 +} |