diff options
Diffstat (limited to 'Engineering_Physics_by_S.L.Gupta,_Sanjeev_Gupta/Chapter6_1.ipynb')
| -rw-r--r-- | Engineering_Physics_by_S.L.Gupta,_Sanjeev_Gupta/Chapter6_1.ipynb | 1649 |
1 files changed, 1649 insertions, 0 deletions
diff --git a/Engineering_Physics_by_S.L.Gupta,_Sanjeev_Gupta/Chapter6_1.ipynb b/Engineering_Physics_by_S.L.Gupta,_Sanjeev_Gupta/Chapter6_1.ipynb new file mode 100644 index 00000000..d39bb9e9 --- /dev/null +++ b/Engineering_Physics_by_S.L.Gupta,_Sanjeev_Gupta/Chapter6_1.ipynb @@ -0,0 +1,1649 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6: Principles of Quantum Mechanics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.1, Page number 157" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength of ball is 6.625e-34 m\n", + "de-broglie wavelength of proton is 1.8 angstrom\n", + "de-broglie wavelength of electron is 2.27 *10**14 m\n", + "answer for de-broglie wavelength of electron in the book is wrong\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(J-sec)\n", + "m=0.05; #mass(kg)\n", + "v=20; #velocity(m/sec)\n", + "mp=1.67*10**-27; #mass of proton(kg)\n", + "vp=2200; #velocity of proton(m/sec)\n", + "me=9.11*10**-31; #mass of electron(kg)\n", + "E=10*1.602*10**-19; #kinetic energy(J)\n", + "\n", + "#Calculations\n", + "lamda_ball=h/(m*v); #de-broglie wavelength of ball(m)\n", + "lamda_p=h*10**10/(mp*vp); #de-broglie wavelength of proton(angstrom)\n", + "lamda_e=h/(2*me*E); #de-broglie wavelength of electron(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength of ball is\",lamda_ball,\"m\"\n", + "print \"de-broglie wavelength of proton is\",round(lamda_p,2),\"angstrom\"\n", + "print \"de-broglie wavelength of electron is\",round(lamda_e/10**14,2),\"*10**14 m\"\n", + "print \"answer for de-broglie wavelength of electron in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.2, Page number 158" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "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 0.153 angstrom\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; #planck's constant(J-sec)\n", + "m=1.673*10**-27; #mass of proton(kg)\n", + "v=10**4; #velocity of proton(m/sec)\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", + "\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/(m*v); #de-broglie wavelength of proton(m)\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(lamda3,3),\"angstrom\"\n", + "print \"de-broglie wavelength in 4th case is\",lamda4,\"angstrom\"\n", + "print \"de-broglie wavelength of proton is\",round(lamda5*10**10,4),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.3, Page number 158" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "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", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m=1.67*10**-27; #mass of proton(kg)\n", + "vc=3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculations\n", + "v=vc/20; #velocity of proton(m/sec)\n", + "lamda=h/(m*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 6.4, Page number 159" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "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", + "h=6.60*10**-34; #planck's constant(J-sec)\n", + "m=1.674*10**-27; #mass of proton(kg)\n", + "lamda=10**-10; #de-broglie wavelength(m)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "E=h**2/(2*m*lamda**2); #energy of neutron(J)\n", + "E=E/e; #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 6.5, Page number 159" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy of electron is 167217.6 eV\n", + "answer in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "lamda=3*10**-12; #de-broglie wavelength(m)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "E=h**2/(2*m*lamda**2); #energy of electron(J)\n", + "E=E/e; #energy of electron(eV)\n", + "\n", + "#Result\n", + "print \"energy of electron is\",round(E,1),\"eV\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.6, Page number 159" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kinetic energy of electron is 4.34 *10**-6 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "lamda=5896*10**-10; #de-broglie wavelength(m)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "K=h**2/(2*m*lamda**2); #energy of electron(J)\n", + "K=K/e; #kinetic energy of electron(eV)\n", + "\n", + "#Result\n", + "print \"kinetic energy of electron is\",round(K*10**6,2),\"*10**-6 eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.7, Page number 160" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "voltage is 934.9 V\n", + "answer in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "lamda=0.4*10**-10; #de-broglie wavelength(m)\n", + "e=1.6*10**-19; #charge of electron(c)\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 in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.8, Page number 160" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "velocity of neutron is 3.97 *10**3 m/sec\n", + "kinetic energy of neutron is 0.08225 eV\n", + "answer for kinetic energy 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; #planck's constant(J-sec)\n", + "m=1.67*10**-27; #mass of neutron(kg)\n", + "lamda=10**-10; #de-broglie wavelength(m)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "v=h/(m*lamda); #velocity of neutron(m/sec)\n", + "E=m*v**2/(2*e); #kinetic energy of neutron(eV)\n", + "\n", + "#Result\n", + "print \"velocity of neutron is\",round(v/10**3,2),\"*10**3 m/sec\"\n", + "print \"kinetic energy of neutron is\",round(E,5),\"eV\"\n", + "print \"answer for kinetic energy in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.9, Page number 161" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "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", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "E=1000; #energy of electron(eV)\n", + "\n", + "#Calculations\n", + "lamda_p=h*c*10**10/(E*e); #wavelength of photon(angstrom)\n", + "lamda_e=h*10**10/math.sqrt(2*m*E*e); #wavelength of electron(angstrom)\n", + "\n", + "#Result\n", + "print \"wavelength of photon is\",round(lamda_p,1),\"angstrom\"\n", + "print \"wavelength of electron is\",round(lamda_e,2),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.10, Page number 161" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "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", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "lamda=0.82*10**-10; #wavelength(m)\n", + "\n", + "#Calculations\n", + "E=h*c/lamda; #energy(J)\n", + "lamda=h*10**10/math.sqrt(2*m*E); #wavelength of photo-electron(angstrom)\n", + "\n", + "#Result\n", + "print \"wavelength of photo-electron is\",round(lamda,1),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.11, Page number 162" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of electron 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", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculations\n", + "lamda=h*10**10/(m*c); #wavelength of electron(angstrom)\n", + "\n", + "#Result\n", + "print \"wavelength of electron is\",round(lamda,4),\"angstrom\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.12, Page number 162" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength of neutron is 2.86 *10**-18 m\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(J-sec)\n", + "m=1.675*10**-27; #mass of neutron(kg)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "E=10**14; #energy of neutron(eV)\n", + "\n", + "#Calculations\n", + "v=math.sqrt(2*E*e/m); #velocity(m/sec)\n", + "lamda=h/(m*v); #de-broglie wavelength of neutron(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength of neutron is\",round(lamda*10**18,2),\"*10**-18 m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.13, Page number 162" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength of neutron is 7.998 *10**-15 m\n", + "answer in the book is wrong\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(J-sec)\n", + "m=1.675*10**-27; #mass of neutron(kg)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "E=12.8*10**6; #energy of neutron(eV)\n", + "\n", + "#Calculations\n", + "v=math.sqrt(2*E*e/m); #velocity(m/sec)\n", + "lamda=h/(m*v); #de-broglie wavelength of neutron(m)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength of neutron is\",round(lamda*10**15,3),\"*10**-15 m\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.14, Page number 163" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de-broglie wavelength of proton is 0.0004 angstrom\n", + "answer in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "mp=1836*m; #mass of photon(kg)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "E=m*c**2; #energy(J)\n", + "v=math.sqrt(2*E/mp); #velocity(m/sec)\n", + "lamda=h*10**10/(mp*v); #de-broglie wavelength of proton(angstrom)\n", + "\n", + "#Result\n", + "print \"de-broglie wavelength of proton is\",round(lamda,4),\"angstrom\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.15, Page number 163" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength of thermal neutron is 1.777 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.60*10**-34; #planck's constant(J-sec)\n", + "m=1.67*10**-27; #mass of neutron(kg)\n", + "k=8.6*10**-5; #boltzmann constant(eV/deg)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "T=300; #temperature(K)\n", + "\n", + "#Calculations\n", + "lamda=h*10**10/math.sqrt(2*m*k*e*T); #wavelength of thermal neutron(angstrom)\n", + "\n", + "#Result\n", + "print \"wavelength of thermal neutron is\",round(lamda,3),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.16, Page number 164" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "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", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "mn=1.67*10**-27; #mass of neutron(kg)\n", + "k=1.38*10**-23; #boltzmann constant(eV/deg)\n", + "T=300; #temperature(K)\n", + "\n", + "#Calculations\n", + "E=k*T; #energy(J)\n", + "p=math.sqrt(2*mn*E); #momentum\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 6.17, Page number 164" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "interplanar spacing is 0.38 angstrom\n", + "answer in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m=9*10**-31; #mass of neutron(kg)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "V=344; #potential difference(V)\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)); #interplanar spacing(angstrom)\n", + "\n", + "#Result\n", + "print \"interplanar spacing is\",round(d,2),\"angstrom\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.18, Page number 171" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in momentum is 1.65e-24 kg m/sec\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "deltax=4*10**-10; #uncertainity in position of electron(m)\n", + "\n", + "#Calculations\n", + "delta_px=h/deltax; #uncertainity in momentum(kg m/sec)\n", + "\n", + "#Result\n", + "print \"uncertainity in momentum is\",delta_px,\"kg m/sec\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.19, Page number 171" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in position of electron is 0.02418 m\n", + "answer in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "v=600; #speed(m/sec)\n", + "a=0.005/100; #accuracy(%)\n", + "\n", + "#Calculations\n", + "deltav=v*a; #uncertainity in speed(kg m/sec)\n", + "delta_px=m*deltav; #uncertainity in momentum(kg m/sec)\n", + "deltax=h/delta_px; #uncertainity in position of electron(m)\n", + "\n", + "#Result\n", + "print \"uncertainity in position of electron is\",round(deltax,5),\"m\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.20, Page number 172 Theoritical " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.21, Page number 172" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in momentum is 6.63e-23 kg m/sec\n", + "uncertainity in velocity is 7.286 *10**7 m/sec\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "m0=9.1*10**-31; #mass of electron(kg)\n", + "deltax=0.1*10**-10; #uncertainity in position of electron(m)\n", + "\n", + "#Calculations\n", + "delta_p=h/deltax; #uncertainity in momentum(kg m/sec)\n", + "delta_v=delta_p/m0; #uncertainity in velocity(m/sec)\n", + "\n", + "#Result\n", + "print \"uncertainity in momentum is\",delta_p,\"kg m/sec\"\n", + "print \"uncertainity in velocity is\",round(delta_v/10**7,3),\"*10**7 m/sec\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.22, Page number 172" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in velocity is 1835\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "me=9.10*10**-31; #mass of electron(kg)\n", + "mp=1.67*10**-27; #mass of electron(kg)\n", + "\n", + "#Calculations\n", + "uv=mp/me; #uncertainity in velocity\n", + "\n", + "#Result\n", + "print \"uncertainity in velocity is\",int(uv)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.23, Page number 172" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "smallest possible uncertainity in position of electron is 0.019 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m0=9*10**-31; #mass of electron(kg)\n", + "v=3*10**7; #velocity of electron(m/sec)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculations\n", + "deltax_min=h*10**10*math.sqrt(1-(v**2/c**2))/(4*math.pi*m0*v); #smallest possible uncertainity in position of electron(angstrom)\n", + "\n", + "#Result\n", + "print \"smallest possible uncertainity in position of electron is\",round(deltax_min,3),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.24, Page number 173" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum uncertainity in velocity of electron is 7.3 *10**5 m/s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "m=9*10**-31; #mass of electron(kg)\n", + "deltax_max=10*10**-10; #length of box(m)\n", + "\n", + "#Calculations\n", + "deltavx_min=h/(deltax_max*m); #minimum uncertainity in velocity of electron(m/s)\n", + "\n", + "#Result\n", + "print \"minimum uncertainity in velocity of electron is\",round(deltavx_min/10**5,1),\"*10**5 m/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.25 Page number 173" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time required is 1.9 *10**-8 second\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "dlamda=10**-4*10**-10; #width(m)\n", + "lamda=6000*10**-10; #wavelength(m)\n", + "c=3*10**8; #velocity of light(m/sec)\n", + "\n", + "#Calculations\n", + "delta_t=lamda**2/(2*math.pi*c*dlamda); #time required(second)\n", + "\n", + "#Result\n", + "print \"time required is\",round(delta_t*10**8,1),\"*10**-8 second\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.26 Page number 174" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in position of electron is 1.6903 *10**-8 m\n", + "answer 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; #planck's constant(J-sec)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "v=3.5*10**7; #speed(cm/sec)\n", + "a=0.0098/100; #accuracy(%)\n", + "\n", + "#Calculations\n", + "deltav=v*a; #uncertainity in speed(kg m/sec)\n", + "delta_p=m*deltav; #uncertainity in momentum(kg m/sec)\n", + "deltax=h/(4*math.pi*delta_p); #uncertainity in position of electron(m)\n", + "\n", + "#Result\n", + "print \"uncertainity in position of electron is\",round(deltax*10**8,4),\"*10**-8 m\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.27 Page number 174" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in position of dust particle is 9.58 *10**-10 m\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.62*10**-34; #planck's constant(J-sec)\n", + "m=10**-6; #mass of electron(kg)\n", + "deltav=5.5*10**-20; #speed(m/sec)\n", + "\n", + "#Calculations\n", + "delta_p=m*deltav; #uncertainity in momentum(kg m/sec)\n", + "deltax=h/(4*math.pi*delta_p); #uncertainity in position of dust particle(m)\n", + "\n", + "#Result\n", + "print \"uncertainity in position of dust particle is\",round(deltax*10**10,2),\"*10**-10 m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.28 Page number 175" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uncertainity in energy is 3.3 *10**-4 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "delta_t=10**-12; #life time(s)\n", + "hby2pi=1.054*10**-34; \n", + "e=1.6*10**-19; #charge of electron(c)\n", + "\n", + "#Calculations\n", + "deltaE=hby2pi/(2*e*delta_t); #uncertainity in energy(eV)\n", + "\n", + "#Result\n", + "print \"uncertainity in energy is\",round(deltaE*10**4,1),\"*10**-4 eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.29 Page number 175" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum uncertainity in frequency is 8.0 *10**6 s-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "delta_t=10**-8; #life time(s)\n", + "\n", + "#Calculations\n", + "deltav=1/(4*math.pi*delta_t); #minimum uncertainity in frequency(s-1)\n", + "\n", + "#Result\n", + "print \"minimum uncertainity in frequency is\",round(deltav/10**6),\"*10**6 s-1\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.30 Page number 175" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum energy is 13.18997 keV\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", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "delta_t=2.5*10**-14*10**-6; #life time(s)\n", + "\n", + "#Calculations\n", + "deltaE=h*10**-3/(4*math.pi*delta_t*e); #minimum energy(keV)\n", + "\n", + "#Result\n", + "print \"minimum energy is\",round(deltaE,5),\"keV\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.31 Page number 183" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "least energy is 37.649 eV\n", + "answer 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; #planck's constant(J-sec)\n", + "e=1.602*10**-19; #charge of electron(c)\n", + "L=10**-10; #width(m)\n", + "m=9.11*10**-31; #mass of electron(kg)\n", + "\n", + "\n", + "#Calculations\n", + "E1=h**2/(8*m*e*L**2); #least energy(eV)\n", + "\n", + "#Result\n", + "print \"least energy is\",round(E1,3),\"eV\"\n", + "print \"answer in the book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.32 Page number 184" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1st least energy is 6 eV\n", + "2nd least energy is 24 eV\n", + "3rd least energy is 54 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "L=2.5*10**-10; #width(m)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "n1=1;\n", + "n2=2;\n", + "n3=3;\n", + "\n", + "#Calculations\n", + "E=h**2/(8*m*e*L**2); #energy(eV)\n", + "E1=n1**2*h**2/(8*m*e*L**2); #1st least energy(eV)\n", + "E2=n2**2*h**2/(8*m*e*L**2); #2nd least energy(eV)\n", + "E3=n3**2*h**2/(8*m*e*L**2); #3rd least energy(eV)\n", + "\n", + "#Result\n", + "print \"1st least energy is\",int(E1),\"eV\"\n", + "print \"2nd least energy is\",int(E2),\"eV\"\n", + "print \"3rd least energy is\",int(E3),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.33 Page number 184" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wavelength in 1st energy state is 20 angstrom\n", + "wavelength in 2nd energy state is 10 angstrom\n", + "wavelength in 3rd energy state is 6.67 angstrom\n", + "1st least energy is 0.38 eV\n", + "2nd least energy is 1.5095 eV\n", + "3rd least energy is 3.396 eV\n", + "answers for 2nd and 3rd least energies varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "L=10**-9; #width(m)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "n1=1;\n", + "n2=2;\n", + "n3=3;\n", + "\n", + "#Calculations\n", + "lamda1=2*L*10**10/n1; #wavelength in 1st energy state(angstrom)\n", + "lamda2=2*L*10**10/n2; #wavelength in 2nd energy state(angstrom)\n", + "lamda3=2*L*10**10/n3; #wavelength in 3rd energy state(angstrom)\n", + "E=h**2/(8*m*e*L**2); #energy(eV)\n", + "E1=n1**2*h**2/(8*m*e*L**2); #1st least energy(eV)\n", + "E2=n2**2*h**2/(8*m*e*L**2); #2nd least energy(eV)\n", + "E3=n3**2*h**2/(8*m*e*L**2); #3rd least energy(eV)\n", + "\n", + "#Result\n", + "print \"wavelength in 1st energy state is\",int(lamda1),\"angstrom\"\n", + "print \"wavelength in 2nd energy state is\",int(lamda2),\"angstrom\"\n", + "print \"wavelength in 3rd energy state is\",round(lamda3,2),\"angstrom\"\n", + "print \"1st least energy is\",round(E1,2),\"eV\"\n", + "print \"2nd least energy is\",round(E2,4),\"eV\"\n", + "print \"3rd least energy is\",round(E3,3),\"eV\"\n", + "print \"answers for 2nd and 3rd least energies varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.34 Page number 185" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1st least energy is 37.69 eV\n", + "2nd least energy is 150 eV\n", + "energy difference between ground state and 1st excited state is 113.08 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", + "h=6.626*10**-34; #planck's constant(J-sec)\n", + "e=1.60*10**-19; #charge of electron(c)\n", + "L=10**-10; #width(m)\n", + "m=9.1*10**-31; #mass of electron(kg)\n", + "n1=1;\n", + "n2=2;\n", + "\n", + "#Calculations\n", + "E=h**2/(8*m*e*L**2); #energy(eV)\n", + "E1=n1**2*h**2/(8*m*e*L**2); #1st least energy(eV)\n", + "E2=n2**2*h**2/(8*m*e*L**2); #2nd least energy(eV)\n", + "Ed=E2-E1; #energy difference between ground state and 1st excited state(eV)\n", + "\n", + "#Result\n", + "print \"1st least energy is\",round(E1,2),\"eV\"\n", + "print \"2nd least energy is\",int(E2),\"eV\"\n", + "print \"energy difference between ground state and 1st excited state is\",round(Ed,2),\"eV\"\n", + "print \"answer in the book varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.35 Page number 185" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1st least energy is 3.4 *10**-45 eV\n", + "2nd least energy is 13.6 *10**-45 eV\n", + "3rd least energy is 30.6 *10**-45 eV\n", + "energy levels are so close to each other that the energy states cannot be observed\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.6*10**-34; #planck's constant(J-sec)\n", + "e=1.6*10**-19; #charge of electron(c)\n", + "L=10**-1; #width(m)\n", + "m=10**-2; #mass of electron(kg)\n", + "n1=1;\n", + "n2=2;\n", + "n3=3;\n", + "\n", + "#Calculations\n", + "E=h**2/(8*m*e*L**2); #energy(eV)\n", + "E1=n1**2*h**2/(8*m*e*L**2); #1st least energy(eV)\n", + "E2=n2**2*h**2/(8*m*e*L**2); #2nd least energy(eV)\n", + "E3=n3**2*h**2/(8*m*e*L**2); #3rd least energy(eV)\n", + "\n", + "#Result\n", + "print \"1st least energy is\",round(E1*10**45,1),\"*10**-45 eV\"\n", + "print \"2nd least energy is\",round(E2*10**45,1),\"*10**-45 eV\"\n", + "print \"3rd least energy is\",round(E3*10**45,1),\"*10**-45 eV\"\n", + "print \"energy levels are so close to each other that the energy states cannot be observed\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.36 Page number 186" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mass of particle is 9.3 *10**-31 kg\n", + "quantum state is 10.4\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "h=6.63*10**-34; #planck's constant(J-sec)\n", + "e=1.602*10**-19; #charge of electron(c)\n", + "L=0.2*10**-9; #width(m)\n", + "n5=5;\n", + "En=10**3; #energy(eV)\n", + "E5=230; #energy of particle(eV)\n", + "\n", + "#Calculations2\n", + "E5=230*e; #energy(J)\n", + "E1=E5/n5**2; #energy in 1st state(J)\n", + "m=h**2/(8*E1*L**2); #mass of particle(kg)\n", + "n=math.sqrt(En*e/E1); #quantum state\n", + "\n", + "#Result\n", + "print \"mass of particle is\",round(m*10**31,1),\"*10**-31 kg\"\n", + "print \"quantum state is\",round(n,1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.37 Page number 186" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probability of finding the particle is 0.4\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration \n", + "L=25*10**-10; #width(m)\n", + "deltax=5*10**-10; #interval(m)\n", + "\n", + "#Calculations2\n", + "P=2*deltax/L; #probability of finding the particle\n", + "\n", + "#Result\n", + "print \"probability of finding the particle is\",P" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 6.38 Page number 187" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probability of finding the particle is 0.0161 a**2\n", + "expectation value of position of particle is 0.25 a**2\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "from scipy.integrate import quad\n", + "\n", + "#Variable declaration \n", + "a=1; #assume\n", + "\n", + "#Calculations2\n", + "def zintg(x):\n", + " return (a*x)**2 \n", + "\n", + "P=quad(zintg,0.35,0.45)[0] #probability of finding the particle\n", + "\n", + "def zintg(x):\n", + " return x*(a*x)**2 \n", + "\n", + "X=quad(zintg,0,1)[0] #expectation value of position of particle\n", + "\n", + "#Result\n", + "print \"probability of finding the particle is\",round(P,4),\"a**2\"\n", + "print \"expectation value of position of particle is\",X,\"a**2\"" + ] + } + ], + "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 +} |