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Diffstat (limited to 'Introduction_To_Modern_Physics_Volume_1')
16 files changed, 5852 insertions, 0 deletions
diff --git a/Introduction_To_Modern_Physics_Volume_1/README.txt b/Introduction_To_Modern_Physics_Volume_1/README.txt new file mode 100755 index 00000000..53b29955 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/README.txt @@ -0,0 +1,10 @@ +Contributed By: Nisha Raj +Course: btech +College/Institute/Organization: IAF +Department/Designation: Flying Officer +Book Title: Introduction To Modern Physics Volume 1 +Author: R. B. Singh +Publisher: New Age International, New Delhi +Year of publication: 2009 +Isbn: 9788122429220 +Edition: 2
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/UNIT_1,Chapter_1.ipynb b/Introduction_To_Modern_Physics_Volume_1/UNIT_1,Chapter_1.ipynb new file mode 100755 index 00000000..cc6e8d64 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/UNIT_1,Chapter_1.ipynb @@ -0,0 +1,889 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:The special theory of relativity"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "x=50.0\n",
+ "y=20.0\n",
+ "z=10.0 #x,y,z cordinates in meters(frame s)\n",
+ "t=5.0*10**(-8) #time in seconds(frame s)\n",
+ "velocity=0.6*3*10**8 #velocity of observer in s' frame relative to s in meter/second\n",
+ "c=3.0*10.0**8 #speed of light in meter/second\n",
+ "Beta=0.6 \n",
+ "Gamma=1.0/((1.0-Beta**2)**(1.0/2.0)) \n",
+ "\n",
+ "#Calculation \n",
+ "xdash=Gamma*(x-(velocity*t)) #value of x cordinate in frame s' in meters\n",
+ "ydash=y #value of y cordinate in frame s' in meters\n",
+ "zdash=z #value of z cordinate in frame s' in meters\n",
+ "tdash=Gamma*(t-((velocity*x)/(c**2))) #value of t in frame s' in seconds\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nValue of space time cordinates in frame s`:\\n\\t x`=\",xdash,\" m\\n\\t y`=\",ydash,\"m\\n\\t z`=\",zdash,\"m\\n\\t t`=\",tdash,\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Value of space time cordinates in frame s`:\n",
+ "\t x`= 51.25 m\n",
+ "\t y`= 20.0 m\n",
+ "\t z`= 10.0 m\n",
+ "\t t`= -6.25e-08 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "x1=20.0 #position of event 1 in meters(frame s)\n",
+ "t1=2.0*10**(-8) #time of event 1 in seconds(frame s)\n",
+ "x2=60.0 #position of event 2 in meters(frame s)\n",
+ "t2=3.0*10**(-8) #time of event 2 in seconds(frame s)\n",
+ "c=3.0*10**8 #speed of light in meter/second\n",
+ "v=0.6*c #speed of frame s' relative to frame s (meter/second)\n",
+ "Beta=0.6\n",
+ "Gamma=1.0/((1.0-Beta**2.0)**(1.0/2.0)) \n",
+ "\n",
+ "#Calculation\n",
+ "#part(i)\n",
+ "separation=Gamma*((x2-x1)-v*(t2-t1)) #spatial separation of the events in frame s' (meter)\n",
+ "#part(ii)\n",
+ "interval=Gamma*((t2-t1)-(v*(x2-x1))/(c**2)) #time interval between the two events in frame s' (second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nIn frame s`:\\n\\t (i)spatial separation=\",separation,\"m\\n\\t (ii)time interval=\",interval,\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "In frame s`:\n",
+ "\t (i)spatial separation= 47.75 m\n",
+ "\t (ii)time interval= -8.75e-08 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "x1=24.0 #position of event 1 in meters(frame s)\n",
+ "t1=8.0*10**(-8) #time of event 1 in seconds(frame s)\n",
+ "x2=48.0 #position of event 2 in meters(frame s)\n",
+ "t2=4.0*10**(-8) #time of event 2 in seconds(frame s)\n",
+ "c=3.0*10**8 #speed of light in meter/second\n",
+ "\n",
+ "#calculation \n",
+ "v=((c**2)*(t2-t1))/(x2-x1) #velocity of the frame s' (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nvelocity of the frame s` =\",v/(3*10**8),\"c\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "velocity of the frame s` = -0.5 c\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import numpy\n",
+ "#variable declaration\n",
+ "interval_s=1.0 #time difference between two events in frame s (second)\n",
+ "interval_sdash=4.0 #time difference between two events in frame s' (second)\n",
+ "separation_s=0.0 #spatial separation of two events in frame s (meter)\n",
+ "c=3.0*10**8 #speed of light (meter/second)\n",
+ "v=numpy.random.rand() #assign a random value to unknown velocity(meter/second)\n",
+ "import math\n",
+ "#calculation \n",
+ "Gamma=interval_sdash/(interval_s-(v*(separation_s))/(c**2)) #calculating gamma\n",
+ "separation=-2.0*(((Gamma**2.0)-1)**(1.0/2.0))*c #spatial separation in s' (meter)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nspatial separation of the events in frame s` =\",separation/(3*10**8*math.sqrt(15)),\"c sqrt(15)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "spatial separation of the events in frame s` = -2.0 c sqrt(15)\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import numpy\n",
+ "#variable declaration\n",
+ "interval_s=0.0 #time difference between two events in frame s (second)\n",
+ "separation_s=1.0 #spatial separation of two events in frame s (meter)\n",
+ "separation_sdash=2.0 #spatial separation of two events in frame s' (meter)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "v=numpy.random.rand() #assign a random value to unknown velocity of frame s' with respect to frame s (meter/second)\n",
+ "\n",
+ "#calculation \n",
+ "Gamma=separation_sdash/(separation_s-(v*interval_s)) #calculating value of Gamma\n",
+ "Beta=(1-1/(Gamma**2))**(1/2) #calculating value of Beta\n",
+ "v=Beta*c #velocity of s' with respect to s (meter/second)\n",
+ "interval_sdash=Gamma*(interval_s-((v*separation_s)/(c**2))) #time interval between the events in frame s' (second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe time interval between the events in frame s` =\",interval_sdash/(3*10**8),\"X0\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The time interval between the events in frame s` = -2.22222222222e-17 X0\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "IbyI_not=.99 #ratio of moving length and rest length\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "\n",
+ "#calculation\n",
+ "Beta=(1-IbyI_not**2)**(1/2.0) #calculating value of Beta\n",
+ "v=Beta*c #velocity of rocket ship (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe velocity of the rocket ship = %.2e\"%(v/(3*10**8)),\"c\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The velocity of the rocket ship = 1.41e-01 c\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "l_dash=1.0 #length of the rod in frame s' (meter)\n",
+ "Theta_dash_degree=45.0 #angle of the rod with x-axis in frame s' (degree)\n",
+ "Beta=1/2.0 #value of Beta\n",
+ "import math\n",
+ "\n",
+ "#calculation \n",
+ "Theta_dash_radian=Theta_dash_degree*(math.pi/180.0) #conversion of angle Theta in radian from degree (radian)\n",
+ "l=((l_dash**2)*((math.sin(Theta_dash_radian))**2+((1-(Beta**2))*((math.cos(Theta_dash_radian))**2))))**(1.0/2.0) #length of the rod in frame s (meter)\n",
+ "tan_theta=math.tan(Theta_dash_radian)/((1.0-Beta**2)**(1.0/2.0)) #tan of angle of rod with x-axis in frame s\n",
+ "theta=math.atan(tan_theta) #angle of rod with x-axis in frame s (degree)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe length of the rod =\",round(l,2),\"m\\nInclination of rod with x-axis =\",round(math.degrees(theta)),\" degree\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The length of the rod = 0.94 m\n",
+ "Inclination of rod with x-axis = 49.0 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 89
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "\n",
+ "#calculation \n",
+ "Beta=(1-((1/1.25)**2))**(1.0/2.0) #calculating Beta (1.25 comes from the fact that in frame s' density of bloc is 25% greater than frame s)\n",
+ "v=Beta*c #velocity of the reference frame s'\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nBeta =\",Beta\n",
+ "print\"NOTE solved in book:\\nThe velocity of the frame s` = %.1e\"%v,\" m/s\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Beta = 0.6\n",
+ "NOTE solved in book:\n",
+ "The velocity of the frame s` = 1.8e+08 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 93
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:11,Page no:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "del_tao=1436.0 #min\n",
+ "del_t=1440.0 #min\n",
+ "\n",
+ "#Calculation\n",
+ "def f(b):\n",
+ " return(del_t-del_tao/(math.sqrt(1-b**2)))\n",
+ "\n",
+ "from scipy.optimize import fsolve\n",
+ "be=fsolve(f,0.5)\n",
+ "\n",
+ "#Result\n",
+ "print\"Beta=\",be[0],\"=1/(sqrt(180))\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Beta= 0.0744838204322 =1/(sqrt(180))\n"
+ ]
+ }
+ ],
+ "prompt_number": 107
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "deltaTow=1*10**(-6) #mean proper lifetime of particle (second)\n",
+ "Beta=0.9 #value of Beta\n",
+ "v=2.7*10**8 #velocity of particle (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "#part(i)\n",
+ "deltaT=deltaTow/((1-Beta**2)**(1.0/2.0)) #lifetime of the particle in the laboratory frame (second)\n",
+ "#part(ii)\n",
+ "d=v*deltaT #distance traversed by the particle in the laboratory before disintegration (meter)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nIn laboratory frame:\\n\\t(i)Lifetime of the particle = %.2e\"%deltaT,\"s\\n\"\n",
+ "print\"\\t(ii)Distance traversed by the particle = %.2g\"%d,\" m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "In laboratory frame:\n",
+ "\t(i)Lifetime of the particle = 2.29e-06 s\n",
+ "\n",
+ "\t(ii)Distance traversed by the particle = 6.2e+02 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "d=3.0 #km\n",
+ "d=d*1000.0 #[m]\n",
+ "c=3.0*10**8 #m/s speed of light\n",
+ "\n",
+ "#Calculation\n",
+ "v=0.99*c #muon velocity\n",
+ "b=(v**2)/(c**2)\n",
+ "\n",
+ "del_t=d/v\n",
+ "del_tao=del_t*math.sqrt(1-0.99**2)\n",
+ "#In moun's frame,\n",
+ "d_dash=d*math.sqrt(1-0.99**2)\n",
+ "\n",
+ "#Result\n",
+ "print\"(i)Proper lifetime of the muon= %.1e\"%del_tao,\"s\"\n",
+ "print\"(ii)In muon's frame,distance travelled by it is %.3e\"%d_dash,\"m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)Proper lifetime of the muon= 1.4e-06 s\n",
+ "(ii)In muon's frame,distance travelled by it is 4.232e+02 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 130
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:14,Page no:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "import sympy\n",
+ "c=sympy.Symbol(\"c\")\n",
+ "u1=0.6*c #speed of Beta particle 1 in lab frame (meter/second)\n",
+ "u2=-0.8*c #speed of Beta particle 2 in lab frame (meter/second)\n",
+ "v=u1 #velocity of frame s' where frame s' is attached to the first Beta particle (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "u2_dash=(u2-v)/(1-((u2*v)/c**2)) #velocity of 2nd Beta particle relative to the 1st Beta particle (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"The velocity of 2nd Beta particle relative to the 1st Beta particle =\",round(u2_dash/c,3)*c\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity of 2nd Beta particle relative to the 1st Beta particle = -0.946*c\n"
+ ]
+ }
+ ],
+ "prompt_number": 140
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:15,Page no:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#variable declaration\n",
+ "m0=1.0 #let rest mass of particle to be 1 (kg)\n",
+ "m=3.0*m0 #moving mass of particle (kg)\n",
+ "import sympy #speed of light (meter/second)\n",
+ "c=sympy.Symbol(\"c\")\n",
+ "\n",
+ "#calculation \n",
+ "Beta=(1-(m0/m)**2)**(1.0/2.0) #Calculation fo Beta\n",
+ "v=Beta*c #speed of particle (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"The speed of The particle =\",round(v/c,3)*c,\"=((2*sqrt 2)/3)c\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The speed of The particle = 0.943*c =((2*sqrt 2)/3)c\n"
+ ]
+ }
+ ],
+ "prompt_number": 142
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:23,Page no:38"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "RestEnergy=0.51 #energy of electron if the electron is at rest (Mev)\n",
+ "T=2 #kinetic energy of electron (Bev)\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "#E=T=pc\n",
+ "\n",
+ "from sympy import Symbol\n",
+ "c=Symbol(\"c\") #speed of light (meter/second)\n",
+ "p=(T/c) #momentum of electron neglecting rest energy relative to kinetic energy (Bev*second/meter)\n",
+ "\n",
+ "#Result\n",
+ "print\"The momentum of the electron =\",p,\"BeV/c\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The momentum of the electron = 2/c BeV/c\n"
+ ]
+ }
+ ],
+ "prompt_number": 57
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:24,Page no:38"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "n=0.01 #fractional increase in momentum\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "Beta=(n*(2-n))**(1.0/2.0) #calculation of Beta\n",
+ "v=Beta*c #velocity of particle (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nBeta =\",round(Beta,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Beta = 0.14\n"
+ ]
+ }
+ ],
+ "prompt_number": 58
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:26,Page no:39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "RestEnergy=0.51 #rest energy of electron (Mev)\n",
+ "T=1.0 #potential difference i.e. kinetic energy (Mev)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "Beta=(1-(RestEnergy/(T+RestEnergy))**2)**(1.0/2.0) #calculation of Beta\n",
+ "v=Beta*c #speed of electron (meter/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"The speed of the electron,Beta =\",round(Beta,4)\n",
+ "print\"Note: In the book answer of Beta is wrong\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The speed of the electron,Beta = 0.9412\n",
+ "Note: In the book answer of Beta is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 59
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:27,Page no:39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "RestEnergy=0.51 #rest energy of electron (Mev)\n",
+ "T=2000.0 #potential difference i.e. kinetic energy (Mev)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#part(i)effective mass of electron in terms of its rest mass\n",
+ "EffectiveMass=1+(T/RestEnergy) #ratio of effective mass of electron and rest mass\n",
+ "#part(ii)speed of electron in terms of the speed of light\n",
+ "Beta=(1-(1/EffectiveMass)**2)**(1.0/2.0) #Calculatio of Beta\n",
+ "import sympy\n",
+ "eff_mass=sympy.Symbol(\"3923\")\n",
+ "beta=((1-(1/eff_mass)**2))**(1.0/2.0) #Calculatio of Beta\n",
+ "\n",
+ "#Result\n",
+ "print\"The effective mass of electron in terms of its rest mass is\",round(EffectiveMass)\n",
+ "print\"The speed of electron =\",beta,\"c is speed of light\" \n",
+ "print\"OR after solving:\"\n",
+ "print\"Speed of electron=%.2f\"%Beta,\"c\"\n",
+ "print\"\\nNote: Wrong answer in book\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The effective mass of electron in terms of its rest mass is 3923.0\n",
+ "The speed of electron = (1 - 1/3923**2)**0.5 c is speed of light\n",
+ "OR after solving:\n",
+ "Speed of electron=1.00 c\n",
+ "\n",
+ "Note: Wrong answer in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 60
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:28,Page no:39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "c=3*10**8 #speed of light(meter/second)\n",
+ "v1=0.6*c #initial velocity of particle (meter/second)\n",
+ "v2=0.8*c #final velocity of particle (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "#Classically\n",
+ "W_Classic=0.5*((v2/c)**2-(v1/c)**2) #ratio of work and m0*c**2 (mo is the rest mass of particle and c is the speed of light)\n",
+ "#Relativistically\n",
+ "W_Relative=(1/(1-(v2/c)**2)**(1.0/2.0))-(1/(1-(v1/c)**2)**(1.0/2.0)) #ratio of work and m0*c**2 (mo is the rest mass of particle and c is the speed of light)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nWork required:\\n\\t Classically: Work =\",W_Classic,\"*m0*c**2\\n\\t Relativistically: Work =\",round(W_Relative,3),\"*m0*c**2\\nWhere m0:rest mass of particle & c:speed of light\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Work required:\n",
+ "\t Classically: Work = 0.14 *m0*c**2\n",
+ "\t Relativistically: Work = 0.417 *m0*c**2\n",
+ "Where m0:rest mass of particle & c:speed of light\n"
+ ]
+ }
+ ],
+ "prompt_number": 61
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:29,Page no:40"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.63*10**-34 #planck's constant (joule*second)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "lambda1=5000*10**-10 #wavelength (meter)\n",
+ "lambda2=0.1*10**-10 #wavelength (meter)\n",
+ "\n",
+ "#Calculation\n",
+ "#part(i): wavelength=5000 \u00c5\n",
+ "m1=h/(lambda1*c) #effective mass of photon of wavelength 5000 \u00c5\n",
+ "#part(ii): wavelength=0.1 \u00c5\n",
+ "m2=h/(lambda2*c) #effective mass of photon of wavelength 0.1 \u00c5\n",
+ "\n",
+ "#Result\n",
+ "print\"Effective mass of photon:\\n\\t(i) mass =\",m1,\"kg\\n\\t(ii) mass =\",m2,\"kg\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effective mass of photon:\n",
+ "\t(i) mass = 4.42e-36 kg\n",
+ "\t(ii) mass = 2.21e-31 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 62
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:30,Page no:40"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "RestEnergy=0.51 #rest energy of electron (Mev)\n",
+ "\n",
+ "#Calculation\n",
+ "E=2*RestEnergy #minimum energy of gamma ray photon (Mev)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nMinimum energy required =\",E,\"Mev\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Minimum energy required = 1.02 Mev\n"
+ ]
+ }
+ ],
+ "prompt_number": 63
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:33,Page no:41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "c=3*10**8 #Speed of sound (meter/second)\n",
+ "M=1.97*10**30 #Mass of sun (kg)\n",
+ "R=1.5*10**11 #Mean radius of the earth orbit (meter)\n",
+ "sigma=1.4*10**3 #Solar energy received by the earth (joule/meter**2*second)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "loss=(4*math.pi*R**2*sigma)/(M*c**2) #Fractional loss of mass of the sun per second\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe fractional loss of mass of the sun= %.e\"%loss,\"s**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The fractional loss of mass of the sun= 2e-21 s**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 64
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_1.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_1.ipynb new file mode 100755 index 00000000..57a00802 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_1.ipynb @@ -0,0 +1,734 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:Origin of Quantum Concepts"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "c1=0.01\n",
+ "c2=0.1\n",
+ "c3=1\n",
+ "c4=10\n",
+ "b=2.898*10**-3 #Wien's constant (meter-kelvin)\n",
+ "h=(6.625*10**-34)/(2*math.pi) #Planck's constant (joule-second)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "k=1.38*10**-23 #Boltzmann constant (joule/kelvin)\n",
+ "T=3000 #Temperature of black body (kelvin)\n",
+ "Delta_lembda=1*10**-9 #wavelength interval (meter)\n",
+ "\n",
+ "#Calculation\n",
+ "from sympy import *\n",
+ "kT=Symbol('kT')\n",
+ "#(a)Average energy of Planck's oscillator:\n",
+ "E1=round(c1/(math.exp(c1)-1))*kT #Average energy of Planck's oscillator\n",
+ "E2=round(c2/(math.exp(c2)-1),2)*kT #Average energy of Planck's oscillator\n",
+ "E3=round(c3/(math.exp(c3)-1),2)*kT #Average energy of Planck's oscillator\n",
+ "E4=round(c4/(math.exp(c4)-1),5)*kT #Average energy of Planck's oscillator\n",
+ "#(b)Power radiated by a unit area of a black body\n",
+ "P=(4*(math.pi**2)*h*(c**2)*(T**5)*Delta_lembda)/((b**5)*((math.exp((2*math.pi*h*c)/(b*k)))-1.0)) #The power radiated per unit area (watt/meter**2)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The average energy of Planck`s oscillator:\"\n",
+ "print\"(i) Energy =\",E1\n",
+ "print\"Energy =\",E2\n",
+ "print\"Energy = \",E3\n",
+ "print\"Energy =\",E4\n",
+ "print\"(b) The power radiated per unit area =%.f\"%P,\"W/m**2\"\n",
+ "print\"NOTE:Approximate values are used in book,that's why different answer\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The average energy of Planck`s oscillator:\n",
+ "(i) Energy = 1.0*kT\n",
+ "Energy = 0.95*kT\n",
+ "Energy = 0.58*kT\n",
+ "Energy = 0.00045*kT\n",
+ "(b) The power radiated per unit area =3115 W/m**2\n",
+ "NOTE:Approximate values are used in book,that's why different answer\n"
+ ]
+ }
+ ],
+ "prompt_number": 87
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v=2*10**-2 #side of the cube (meter)\n",
+ "lembda=5000*10**-10 #wavelength (meter)\n",
+ "delta_lembda=10*10**-10 #range of wavelength (meter)\n",
+ "k=1.38*10**-23 #Boltzmann constant (joule/kelvin)\n",
+ "T=1500 #Temperature of the cavity (kelvin)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(i)Number of modes:\n",
+ "N=(8*math.pi*v**3*delta_lembda)/lembda**4 #number of modes\n",
+ "#(ii)Total radiant energy in the cavity:\n",
+ "U=N*k*T #energy density (joule)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) Number of modes =%.3e\"%N,\"joule\\n(b) Energy density =%.2e\"%U ,\"J\"\n",
+ "print\"Note: In book the answers of both the parts are WRONG by one order of magnitude in powers\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Number of modes =3.217e+12 joule\n",
+ "(b) Energy density =6.66e-08 J\n",
+ "Note: In book the answers of both the parts are WRONG by one order of magnitude in powers\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=0.1 #mass of a spring-mass system (kg)\n",
+ "k=10 #spring constant of a spring-mass system (newton/meter)\n",
+ "A=0.1 #Amplitude of system oscillation (meter)\n",
+ "h=(6.625*10**-34)/(2*math.pi) #Planck's constant (joule-second)\n",
+ "delta_n=1 #change in quantum number\n",
+ "\n",
+ "#Calculation\n",
+ "#(a) Quantum number n associated with the energy of the oscillator\n",
+ "f=(k/m)**(1.0/2.0) #frequency of oscillator (radian/second)\n",
+ "E=0.5*f*A**2 #Energy of oscillator (joule)\n",
+ "n=E/(h*f) #Quantum number of the oscillator\n",
+ "#(b) Fractional change in energy\n",
+ "change_E=delta_n/n #fractional change in energy\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) Quantum number of the oscillator =%.e\"%n\n",
+ "print\"(b) Fractional change in energy =%.g\"%change_E\n",
+ "print\"(c) This example illustrates that the energy levels of macroscopic oscillators are so close together that even most delicate instruments cannot reveal the quantized nature of energy levels. All this is due to smallness of Planck\u2019s constant h. In the limit h->0, the energy levels become continuous.\"\n",
+ "print\"WRONG ANSWER NOTE:The answer given in the book for quantum number is just the order of it as it is a very large number. But the answer generated by the code is the exact value of it.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Quantum number of the oscillator =5e+31\n",
+ "(b) Fractional change in energy =2e-32\n",
+ "(c) This example illustrates that the energy levels of macroscopic oscillators are so close together that even most delicate instruments cannot reveal the quantized nature of energy levels. All this is due to smallness of Planck\u2019s constant h. In the limit h->0, the energy levels become continuous.\n",
+ "WRONG ANSWER NOTE:The answer given in the book for quantum number is just the order of it as it is a very large number. But the answer generated by the code is the exact value of it.\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "h=(6.625*10**-34)/(2*math.pi) #Planck's constant (joule-second)\n",
+ "c=3*10**8 #Speed of light (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "ch=(2*math.pi*h*c*10**9)/e #Value of ch (eV nm)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nch =\",round(ch),\"eV nm\"\n",
+ "print\"WRONG ANSWER:Approximate answer is given in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "ch = 1242.0 eV nm\n",
+ "WRONG ANSWER:Approximate answer is given in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "h=(6.625*10**-34)/(2*math.pi) #Planck's constant (joule-second)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "lembda=2000 #Wavelength of the light (\u00c5)\n",
+ "phi=4.2 #work function of aluminium surface (eV)\n",
+ "ch=12400 #constant (eV \u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "#(a) maximum kinetic energy of photoelectrons\n",
+ "Tmax=(ch/lembda)-phi #maximum kinetic energy of photoelectrons (eV)\n",
+ "\n",
+ "#(b) minimum kinetic energy of photoelectrons\n",
+ "Tmin=0\n",
+ "\n",
+ "#(c) cut-off wavelength\n",
+ "lembda_cut=ch/phi # cut-off wavelength (\u00c5)\n",
+ "\n",
+ "#(d) stopping potential\n",
+ "v=2 #stopping potential (volt)\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) Maximum kinetic energy of photoelectrons =\",round(Tmax),\"eV\"\n",
+ "print\"(b) Minimum kinetic energy of photoelectrons =\",Tmin\n",
+ "print\"(c) Cut-off(Threshold) wavelength =\",round(lembda_cut),\"\u00c5\\n\"\n",
+ "print\"(d) Stopping potential =\",v,\"volt\" \n",
+ "print\"Note: In book answer of cut_off wavelength is wrong\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Maximum kinetic energy of photoelectrons = 2.0 eV\n",
+ "(b) Minimum kinetic energy of photoelectrons = 0\n",
+ "(c) Cut-off(Threshold) wavelength = 2952.0 \u00c5\n",
+ "\n",
+ "(d) Stopping potential = 2 volt\n",
+ "Note: In book answer of cut_off wavelength is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:64"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda1=4000.0 #wavelength of light (\u00c5)\n",
+ "V1=2.0 #stopping potential (volt)\n",
+ "lembda2=6000.0 #wavelength of light (\u00c5)\n",
+ "V2=1.0 #stopping potential (volt)\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "c=3.0*10**8 #speed of light (meter/second)\n",
+ "ch=12400.0 #constant (eV \u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) Planck's constant\n",
+ "h=(e*(V1-V2)*lembda1*10**-10*lembda2*10**-10)/(c*((lembda2*10**-10)-(lembda1*10**-10))) #Planck's constant (joule-second)\n",
+ "#(ii) Work function\n",
+ "phi=(ch/lembda1)-V1 #work function of the material (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\" Planck`s constant = h =\",h,\"J-s\\n\"\n",
+ "print\" Work function of the material =\",phi,\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Planck`s constant = h = 6.4e-34 J-s\n",
+ "\n",
+ " Work function of the material = 1.1 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:64"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12400 #constant (eV \u00c5)\n",
+ "phi_Tantalum=4.2 #work function of Tantalum (eV)\n",
+ "phi_Tungsten=4.5 #work function of Tungsten (eV)\n",
+ "phi_Aluminium=4.2 #work function of Aluminium (eV)\n",
+ "phi_Barium=2.5 #work function of Barium (eV)\n",
+ "phi_Lithium=2.3 #work function of Lithium (eV)\n",
+ "\n",
+ "#Calculation\n",
+ "lembda_Tantalum=ch/phi_Tantalum #Threshold wavelength of Tantalum (\u00c5)\n",
+ "lembda_Tungsten=ch/phi_Tungsten #Threshold wavelength of Tungsten (\u00c5)\n",
+ "lembda_Aluminium=ch/phi_Aluminium #Threshold wavelength of Aluminium (\u00c5)\n",
+ "lembda_Barium=ch/phi_Barium #Threshold wavelength of Barium (\u00c5)\n",
+ "lembda_Lithium=ch/phi_Lithium #Threshold wavelength of Lithium (\u00c5)\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Tantalum %d\"%lembda_Tantalum,\"\u00c5\"\n",
+ "print\"Tungsten %d\"%lembda_Tungsten,\"\u00c5\"\n",
+ "print\"Aluminium %d\"%lembda_Aluminium,\"\u00c5\"\n",
+ "print\"Barium %d\"%lembda_Barium,\"\u00c5\"\n",
+ "print\"Lithium %d\"%lembda_Lithium,\"\u00c5\"\n",
+ "if(lembda_Tantalum<8000 and lembda_Tantalum>4000): \n",
+ " print\"Tantalum can be used for designing photocell\"\n",
+ "\n",
+ "\n",
+ "if(lembda_Tungsten<8000 and lembda_Tungsten>4000): #Checking whether Threshold wavelength of Tungsten lies in visible range or not\n",
+ " print\"Tungsten can be used for designing photocell\"\n",
+ "\n",
+ "\n",
+ "if(lembda_Aluminium<8000 and lembda_Aluminium>4000): #Checking whether Threshold wavelength of Aluminium lies in visible range or not\n",
+ " print\"Aluminium can be used for designing photocell\"\n",
+ "\n",
+ "\n",
+ "if(lembda_Barium<8000 and lembda_Barium>4000): #Checking whether Threshold wavelength of Barium lies in visible range or not\n",
+ " print\"Barium can be used for designing photocell\"\n",
+ "\n",
+ "\n",
+ "if(lembda_Lithium<8000 and lembda_Lithium>4000): #Checking whether Threshold wavelength of Lithium lies in visible range or not\n",
+ " print\"Lithium can be used for designing photocell\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tantalum 2952 \u00c5\n",
+ "Tungsten 2755 \u00c5\n",
+ "Aluminium 2952 \u00c5\n",
+ "Barium 4960 \u00c5\n",
+ "Lithium 5391 \u00c5\n",
+ "Barium can be used for designing photocell\n",
+ "Lithium can be used for designing photocell\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "lembda_c=0.024 #Compton wavelength of electron (\u00c5)\n",
+ "lembda=1 #Wavelength of X-rays (\u00c5)\n",
+ "Theta1=(60*math.pi)/180 #angle (radian)\n",
+ "Theta2=(90*math.pi)/180 #angle (radian)\n",
+ "Theta3=(180*math.pi)/180 #angle (radian)\n",
+ "ch=12400 #constant (eV \u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "#(a) Compton shift\n",
+ "shift1=lembda_c*(1-math.cos(Theta1)) #Compton shift (\u00c5)\n",
+ "shift2=lembda_c*(1-math.cos(Theta2)) #Compton shift (\u00c5)\n",
+ "shift3=lembda_c*(1-math.cos(Theta3)) #Compton shift (\u00c5)\n",
+ "#(b) Kinetic energy imparted to the recoil electron\n",
+ "T1=(ch*shift1)/(lembda*(lembda+shift1)) #Kinetic energy imparted to the electron (eV)\n",
+ "T2=(ch*shift2)/(lembda*(lembda+shift2)) #Kinetic energy imparted to the electron (eV)\n",
+ "T3=(ch*shift3)/(lembda*(lembda+shift3)) #Kinetic energy imparted to the electron (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) Compton shift:\\n\\t (i)\",shift1,\" \u00c5\\n\\t (ii)\",shift2,\" \u00c5\\n\\t (iii)\",shift3,\" \u00c5\\n\"\n",
+ "print\"(b) Kinetic energy imparted to the recoil electron:\\n\\t (i)\",round(T1),\" eV\\n\\t (ii) %d\"%T2,\" eV\\n\\t (iii)\",round(T3),\" eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Compton shift:\n",
+ "\t (i) 0.012 \u00c5\n",
+ "\t (ii) 0.024 \u00c5\n",
+ "\t (iii) 0.048 \u00c5\n",
+ "\n",
+ "(b) Kinetic energy imparted to the recoil electron:\n",
+ "\t (i) 147.0 eV\n",
+ "\t (ii) 290 eV\n",
+ "\t (iii) 568.0 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "lembda_c=0.024 #Compton wavelength of electron (\u00c5)\n",
+ "Theta=(45*math.pi)/180 #Scattering angle (radian)\n",
+ "\n",
+ "#Calculation \n",
+ "lembda=lembda_c*(1-math.cos(Theta)) #Wavelength of incident photon (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) Wavelength of incident photon = \",round(lembda,4),\" \u00c5 (gamma ray)\"\n",
+ "print\"(b) Photon lies in the gamma ray spectrum\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Wavelength of incident photon = 0.007 \u00c5 (gamma ray)\n",
+ "(b) Photon lies in the gamma ray spectrum\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "E=1 #Energy of photon (MeV)\n",
+ "eta=0.25 #Relative change in photon's wavelength\n",
+ "\n",
+ "#Calculation\n",
+ "T=(E*eta)/(1+eta) #Kinetic energy of recoil electron (MeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe kinetic energy of recoil electron =\",T,\"MeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The kinetic energy of recoil electron = 0.2 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:11,Page no:69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Variable declaration\n",
+ "E=0.25 #Energy of photon (MeV)\n",
+ "Theta=(120*math.pi)/180 #Scattering angle of photon (radian)\n",
+ "a=0.51 #Value of m0*c**2 (Mev)\n",
+ "\n",
+ "#Calculation \n",
+ "E_das=E/(1+(E/a)*(1-math.cos(Theta))) #Energy of the scattered photon (MeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nEnergy of the scattered photon =\",round(E_das,3),\"Mev\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Energy of the scattered photon = 0.144 Mev\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "p=1.02 #momentum of the photon (MeV/c)\n",
+ "p_dash=0.255 #momentum of the photon after scattering (MeV/c)\n",
+ "a=0.51 #Value of m0*c**2 (Mev)\n",
+ "\n",
+ "#Calculation\n",
+ "Theta=2*math.degrees(math.asin(((0.5*a*(p-p_dash))/(p*p_dash))**(1.0/2.0))); \n",
+ "\n",
+ "#Result\n",
+ "print\"\\nAngle of the photon after scattering =\",Theta,\"degree\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Angle of the photon after scattering = 120.0 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "Theta=120 #Scattering angle of photon (degree)\n",
+ "T=0.45 #Kinetic energy of electron (MeV)\n",
+ "a=0.51 #Value of m0*c**2 (Mev)\n",
+ "import math\n",
+ "\n",
+ "#Calculation \n",
+ "\n",
+ "E=(T/2.0)*(1.0+math.sqrt(1.0+(2.0*a)/(T*((math.sin(math.radians(Theta/2.0)))**2)))) #Energy of the incident photon (MeV) \n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nEnergy of the incident photon =%.3g\"%E,\"Mev\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Energy of the incident photon =0.676 Mev\n"
+ ]
+ }
+ ],
+ "prompt_number": 75
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:14,Page no:74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda0=2536*10**-10 #wavelength of exciting line (meter)\n",
+ "lembda=2612*10**-10 #wavelength of Raman line (meter)\n",
+ "\n",
+ "#Calculation \n",
+ "v0=1.0/lembda0 #wave number of exciting line (1/meter)\n",
+ "v=1.0/lembda #wave number of Raman line (1/meter)\n",
+ "shift=v0-v #the Raman shift (1/meter)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe Raman shift =\",shift,\"m-1\"\n",
+ "print\"Note: v0 and v values in the book are VERY LESS PRECISE,Therefore an approximate answer\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The Raman shift = 114733.745248 m-1\n",
+ "Note: v0 and v values in the book are VERY LESS PRECISE,Therefore an approximate answer\n"
+ ]
+ }
+ ],
+ "prompt_number": 80
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:15,Page no:75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda0=5000*10**-10 #Wavelength of radiation (meter)\n",
+ "lembda=5050.5*10**-10 #Wavelength of Raman line (meter)\n",
+ "\n",
+ "#Calculation\n",
+ "#(a) Raman frequency\n",
+ "v0=1.0/lembda0 #Wave number of radiation (1/meter)\n",
+ "v=1.0/lembda #Wave number of Raman line (1/meter)\n",
+ "shift=v0-v #Raman shift (1/meter)\n",
+ "va=v0+shift #Frequency of antistoke's line (1/meter)\n",
+ "#(b) Position of the antistokes' line\n",
+ "lembdaa=(10.0**10.0)/va #Wavelength of antistoke's line (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a) Raman frequency =%.2e\"%va,\"m**-1\"\n",
+ "print\"(b) Wavelength of antistoke`s line =%.1f\"%lembdaa,\"\u00c5 (APPROX)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) Raman frequency =2.02e+06 m**-1\n",
+ "(b) Wavelength of antistoke`s line =4950.5 \u00c5 (APPROX)\n"
+ ]
+ }
+ ],
+ "prompt_number": 86
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_2.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_2.ipynb new file mode 100755 index 00000000..8ce6bc74 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_2.ipynb @@ -0,0 +1,665 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Wave Nature of Material Particles"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:89"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "h=6.6*10**-34 #planck's constant (joule-second)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "from sympy import *\n",
+ "V=Symbol('V')\n",
+ "a=(h*10**10)/(2.0*m*e*V)**(1/2.0) #wavelength of electron = h/(2*m*e*v)**(1/2) (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Wavelength of electron accelerated through a potential difference V =\",a,\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Wavelength of electron accelerated through a potential difference V = 12.2306137249082*V**(-0.5) \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:90"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m_e=9.1*10**-31 #mass of electron (kg)\n",
+ "m=100*10**-3 #mass of object (kg)\n",
+ "v=1000 #velocity of electron and object (meter/second)\n",
+ "h=6.63*10**-34 #planck's constant (joule-second)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) de Broglie wavelength of electron\n",
+ "lembda_e=h/(m_e*v) #de Broglie wavelength of electron\n",
+ "#(ii) de Broglie wavelength of object\n",
+ "lembda=h/(m*v) #de Broglie wavelength of object\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) de Broglie wavelength of electron =\",round(lembda_e*10**10),\"A\"\n",
+ "print\"(ii) de Broglie wavelength of object =%.2e\"%lembda,\"m\"\n",
+ "print\"Note: In the book the answer of part(ii) is wrong\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) de Broglie wavelength of electron = 7286.0 A\n",
+ "(ii) de Broglie wavelength of object =6.63e-36 m\n",
+ "Note: In the book the answer of part(ii) is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 105
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:90"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "T=100*e #kinetic energy (joule)\n",
+ "m_e=9.1*10**-31 #mass of electron (kg)\n",
+ "m_p=1.67*10**-27 #mass of proton (kg)\n",
+ "m_alpha=4*m_p #mass of alpha particle (kg)\n",
+ "h=6.63*10**-34 #planck's constant (joule-second)\n",
+ "\n",
+ "#Calculation\n",
+ "lembda_e=(h*10**10)/(2*m_e*T)**(1.0/2.0) #de Broglie wavelength of electron (\u00c5)\n",
+ "lembda_p=(h*10**10)/(2*m_p*T)**(1.0/2.0) #de Broglie wavelength of proton (\u00c5)\n",
+ "lembda_alpha=(h*10**10)/(2*m_alpha*T)**(1.0/2.0) #de Broglie wavelength of alpha particle (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"De Broglie wavelength of electron =\",round(lembda_e,2),\"\u00c5\"\n",
+ "print\"De Broglie wavelength of proton =\",round(lembda_p,3),\"\u00c5\"\n",
+ "print\"De Broglie wavelength of alpha particle =\",round(lembda_alpha,3),\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "De Broglie wavelength of electron = 1.23 \u00c5\n",
+ "De Broglie wavelength of proton = 0.029 \u00c5\n",
+ "De Broglie wavelength of alpha particle = 0.014 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 106
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:90"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.63*10**-34 #planck's constant (joule-second)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "lembda=5896*10**-10 #wavelength of yellow spectral line of sodium (meter)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "T_j=h**2/(2*m*lembda**2) #kinetic energy of the electron (joule)\n",
+ "T_eV=T_j/e #kinetic energy of the electron (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"Kinetic energy of electron =%.2e\"%T_j,\"J =%.1e\"%T_eV,\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Kinetic energy of electron =6.95e-25 J =4.3e-06 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 107
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.63*10**-34 #planck's constant (joule-second)\n",
+ "m_n=1.67*10**-27 #mass of neutron (kg)\n",
+ "T=300 #Temperature (kelvin)\n",
+ "k=1.38*10**-23 #Boltzmann constant (joule/kelvin)\n",
+ "\n",
+ "#Calculation\n",
+ "E=(3*k*T)/2.0 #Kinetic energy of thermal neutron (joule)\n",
+ "lembda=(h*10**10)/(2*m_n*E)**(1/2.0) #Wavelength of thermal neutron (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"The wavelength of thermal neutron =%.3g\"%lembda,\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The wavelength of thermal neutron =1.46 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 108
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.63*10**-34 #planck's constant (joule-second)\n",
+ "m_H2=2*1.67*10**-27 #mass of hydrogen molecule (kg)\n",
+ "T=27+273 #room temperature (kelvin)\n",
+ "k=1.38*10**-23 #Boltzmann constant (joule/kelvin)\n",
+ "\n",
+ "#Calculation\n",
+ "lembda=(h*10**10)/(2*m_H2*k*T)**(1/2.0) #de Broglie wavelength of hydrogen molecule (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"The de Broglie wavelength of hydrogen molecules at their most probable speed =%.2f\"%lembda,\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The de Broglie wavelength of hydrogen molecules at their most probable speed =1.26 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 109
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "a=0.51 #Value of m0*c**2 (Mev)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "T=a*(math.sqrt(2.0)-1) #Kinetic energy (MeV)\n",
+ "\n",
+ "print\"Kinetic energy of electron =\",round(T,2),\"MeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Kinetic energy of electron = 0.21 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 110
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "a=0.51 #Value of m0*c**2 (MeV)\n",
+ "b=0.0124 #Value of h*c (MeV \u00c5)\n",
+ "lembda_X=0.1 #Short wavelength limit of continuous X-ray spectrum (\u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "lembda=lembda_X/(1+(2*a*lembda_X)/b)**(1/2.0) #de Broglie wavelength of relativistic electrons\n",
+ "\n",
+ "print\"De Broglie wavelength of relativistic electrons =\",round(lembda,3),\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "De Broglie wavelength of relativistic electrons = 0.033 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 111
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "r=0.53 #Radius of the first Bohr orbit in hydrogen atom (\u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "lembda=2*math.pi*r #de Broglie wavelength of electron in first Bohr orbit in hydrogen atom\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nde Broglie wavelength of electron in first Bohr orbit in hydrogen atom =%.1f\"%lembda,\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "de Broglie wavelength of electron in first Bohr orbit in hydrogen atom =3.3 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 112
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v=10000 #speed of object (meter/second)\n",
+ "accu_v=0.0001 #accuracy of speed of object\n",
+ "m_b=0.05 #mass of the bullet (kg)\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "m_e=9.1*10**-31 #mass of electron (kg)\n",
+ "\n",
+ "#Calculation\n",
+ "#(a) fundamental accuracy of position for bullet\n",
+ "p_b=m_b*v #momentum of bullet (kg m/s)\n",
+ "p_uncer_b=p_b*accu_v #uncertainty in momentum of bullet (kg m/s)\n",
+ "x_uncer_b=h/p_uncer_b #minimum uncertainty in position of bullet (meter)\n",
+ "#(b) fundamental accuracy of position for electron\n",
+ "p_e=m_e*v #momentum of electron (kg m/s)\n",
+ "p_uncer_e=p_e*accu_v #uncertainty in momentum of electron (kg m/s)\n",
+ "x_uncer_e=h/p_uncer_e #uncertainty in position of electron (meter)\n",
+ "\n",
+ "print\"\\n(a) Minimum uncertainty in position of bullet =%.1e\"%x_uncer_b,\"meter\"\n",
+ "print\"(b) uncertainty in position of electron =%.3g\"%x_uncer_e,\"meter\"\n",
+ "\n",
+ "print\"Note:The answers given in the book are wrong. \\nAlso in the solution they have used speed=1000 while in the question it is given to be equal to 10000.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) Minimum uncertainty in position of bullet =2.1e-33 meter\n",
+ "(b) uncertainty in position of electron =0.000116 meter\n",
+ "Note:The answers given in the book are wrong. \n",
+ "Also in the solution they have used speed=1000 while in the question it is given to be equal to 10000.\n"
+ ]
+ }
+ ],
+ "prompt_number": 113
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "x_uncer=1*10**-10 #uncertainty in the position of elctrons (meter)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) uncertainty in the momentum of electron\n",
+ "p_uncer=h/x_uncer #The uncertainty in the momentum of electron (kg m/s)\n",
+ "#(ii) kinetic energy of electron\n",
+ "T=p_uncer**2/(2*m*e) #kinetic energy of electron (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) The uncertainty in the momentum of electron =\",p_uncer,\"kg m/s\"\n",
+ "print\"(ii) Kinetic energy of electron =%.1f\"%T,\"eV\" \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) The uncertainty in the momentum of electron = 1.054e-24 kg m/s\n",
+ "(ii) Kinetic energy of electron =3.8 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 114
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:14,Page no:94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "x=10**-14 #dimension of the nucleus (meter)\n",
+ "c=3*10**8 #speed of light (meter/second)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) Uncertainty in the momentum of electron\n",
+ "p_uncer=h/x #The uncertainty in the momentum of electron (kg m/s)\n",
+ "#(ii) kinetic energy of electron\n",
+ "T=(p_uncer*c)/(e*10**6) #kinetic energy of electron (MeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) The uncertainty in the momentum of electron =\",p_uncer,\"kg m/s\"\n",
+ "print\"(ii) Kinetic energy of electron =\",round(T),\" MeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) The uncertainty in the momentum of electron = 1.054e-20 kg m/s\n",
+ "(ii) Kinetic energy of electron = 20.0 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 115
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:15,Page no:94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "x=10**-14 #dimension of the nucleus (meter)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "m=1.67*10**-27 #mass of proton (kg)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) Uncertainty in the momentum of electron\n",
+ "p_uncer=h/x #The uncertainty in the momentum of electron (kg m/s)\n",
+ "#(ii) kinetic energy of proton\n",
+ "T=(p_uncer**2)/(2*m*e*10**6) #kinetic energy of proton (MeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) The uncertainty in the momentum of electron =\",p_uncer,\"kg m/s\"\n",
+ "print\"(ii) Kinetic energy of proton =\",round(T,2),\"MeV (approx)\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) The uncertainty in the momentum of electron = 1.054e-20 kg m/s\n",
+ "(ii) Kinetic energy of proton = 0.21 MeV (approx)\n"
+ ]
+ }
+ ],
+ "prompt_number": 116
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:17,Page no:95"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "delta_t=10**-12 #time for which nucleus remains in excited state (second)\n",
+ "\n",
+ "#Calculation\n",
+ "delta_E=h/delta_t #uncertainty in the energy of the gamma ray photon (joule)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe uncertainty in the energy of the gamma ray photon =\",delta_E,\"J\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The uncertainty in the energy of the gamma ray photon = 1.054e-22 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 117
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:18,Page no:95"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "delta_t=10**-8 #life-time of the average excited atom (second)\n",
+ "\n",
+ "#Calculation\n",
+ "delta_f=1/delta_t #minimum uncertainty in the frequency of photon (radian/second)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nminimum uncertainty in the frequency of photon =%.g\"%delta_f,\"rad/s\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "minimum uncertainty in the frequency of photon =1e+08 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 118
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:19,Page no:95"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=1.054*10**-34 #planck's constant (joule-second)\n",
+ "e=1.6*10**-19 #charge of electron (coulomb)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "E0=8.8542*10**-12 #permittivity of free space (C**2/N*m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) radius of ground state of hydrogen atom\n",
+ "r=(4*math.pi*E0*h**2)/(m*e**2) #radius of ground state of hydrogen atom (meter)\n",
+ "#(ii) Binding energy of electron in hydrogen atom in the ground state\n",
+ "E=(-0.5*m*e**4)/(4*math.pi*E0*h)**2 #binding energy of electron in hydrogen atom in the ground state (joule)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) Radius of ground state of hydrogen atom =%.1e\"%r,\"m (in scientific notation) OR 0.53*10**-10\"\n",
+ "print\"(ii) Binding energy of electron in ground state of hydrogen atom =%.2e\"%E,\"J\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) Radius of ground state of hydrogen atom =5.3e-11 m (in scientific notation) OR 0.53*10**-10\n",
+ "(ii) Binding energy of electron in ground state of hydrogen atom =-2.17e-18 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 119
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_6.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_6.ipynb new file mode 100755 index 00000000..b3905bdc --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_6.ipynb @@ -0,0 +1,110 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6:Particle in a box"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "L=1.0\n",
+ "x0=L/3.0 \n",
+ "x1=2*L/3.0 \n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "from scipy import integrate\n",
+ "def f(x):\n",
+ " w=math.sqrt(2/L)*math.sin(math.pi*x/L)\n",
+ " return(w**2)\n",
+ "P=integrate.quad(f,x0,x1)\n",
+ "\n",
+ "#Result\n",
+ "print\"The required probability =\",round(P[0],2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required probability = 0.61\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "L=1.0 \n",
+ "x0=0.0 \n",
+ "x1=L/3.0 \n",
+ "y0=0.0 \n",
+ "y1=L/3.0 \n",
+ "\n",
+ "#Calculation\n",
+ "from scipy.integrate import dblquad\n",
+ "import numpy as np\n",
+ "def f(x,y):\n",
+ "#w=(2.0/L)*(np.sin(np.pi*x/L))*(np.sin(np.pi*y/L))\n",
+ " return((1-np.cos(2*np.pi*x/L))*(1-np.cos(2*np.pi*y/L))) \n",
+ "\n",
+ "p=dblquad(f,x0,x1,lambda y:0,lambda y:L/3.0)\n",
+ "\n",
+ "#Result\n",
+ "print\"The required probability = \",round(p[0],3)\n",
+ "print\"NOTE:Wrong answer in book\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required probability = 0.038\n",
+ "NOTE:Wrong answer in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 66
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_9.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_9.ipynb new file mode 100755 index 00000000..8a33a661 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_2,Chapter_9.ipynb @@ -0,0 +1,64 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9:Particle in a Central Force Field"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Exampleno:3,Page no:244"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "a0=1\n",
+ "r0=0 \n",
+ "\n",
+ "#Calculation\n",
+ "from scipy.integrate import quad\n",
+ "import math\n",
+ "#calculation\n",
+ "def f(r):\n",
+ " w_100=math.sqrt(1.0/(math.pi*a0**3))*math.exp(-r/a0)\n",
+ " return((w_100**2)*4*math.pi*(r**2))\n",
+ "P=4*quad(f,r0,a0) \n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Probability =\",round(P[0] ,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Probability = 0.32\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_3,Chapter_1.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_3,Chapter_1.ipynb new file mode 100755 index 00000000..a80391a8 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_3,Chapter_1.ipynb @@ -0,0 +1,469 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:Preliminary Concepts "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "N=2 #no. of particles\n",
+ "n1=2 #occupation no. of particles\n",
+ "g1=3 #degeneracy of particles\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(i) particles are distinguishable\n",
+ "state1=(math.factorial(N)*g1**n1)/math.factorial(n1) #possible microstates of distinguishable particles\n",
+ "#(ii) particles are indistinguishable bosons \n",
+ "state2=math.factorial(n1+g1-1)/(math.factorial(n1)*math.factorial(g1-1)) #possible microstates of indistinguishable bosons\n",
+ "#(iii) particles are indistinguishable fermions\n",
+ "state3=math.factorial(g1)/(math.factorial(n1)*math.factorial(g1-n1)) #possible microstates of indistinguishable fermions\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) \u03a9(distinguishable) =\",state1,\"\\n(ii) \u03a9(indistinguishable bosons) = \",state2,\"\\n(iii) \u03a9(indistinguishable fermions) =\",state3 \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) \u03a9(distinguishable) = 9 \n",
+ "(ii) \u03a9(indistinguishable bosons) = 6 \n",
+ "(iii) \u03a9(indistinguishable fermions) = 3\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:259"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "N=4 #no. of particles\n",
+ "A1=[2,0,0,2] #possible macrostate\n",
+ "A2=[1,1,1,1] #possible macrostate\n",
+ "A3=[0,3,0,1] #possible macrostate\n",
+ "A4=[1,0,3,0] #possible macrostate\n",
+ "A5=[0,2,2,0] #possible macrostate\n",
+ "g1=1 #degeneracy of particles\n",
+ "g2=2 #degeneracy of particles\n",
+ "g3=2 #degeneracy of particles\n",
+ "g4=1 #degeneracy of particles\n",
+ "\n",
+ "import math\n",
+ "#(i) particles are distinguishable\n",
+ "print\"\\n(i)Possible macrostates are\\n \"\n",
+ "print A1,A2,A3,A4,A5\n",
+ "micro1=((math.factorial(N)*g1**A1[0]*g2**A1[1]*g3**A1[2]*g4**A1[3])/(math.factorial(A1[0])*math.factorial(A1[1])*math.factorial(A1[2])*math.factorial(A1[3]))) #The number of microstates\n",
+ "micro2=((math.factorial(N)*g1**A2[0]*g2**A2[1]*g3**A2[2]*g4**A2[3])/(math.factorial(A2[0])*math.factorial(A2[1])*math.factorial(A2[2])*math.factorial(A2[3]))) #The number of microstates\n",
+ "micro3=((math.factorial(N)*g1**A3[0]*g2**A3[1]*g3**A3[2]*g4**A3[3])/(math.factorial(A3[0])*math.factorial(A3[1])*math.factorial(A3[2])*math.factorial(A3[3]))) #The number of microstates\n",
+ "micro4=((math.factorial(N)*g1**A4[0]*g2**A4[1]*g3**A4[2]*g4**A4[3])/(math.factorial(A4[0])*math.factorial(A4[1])*math.factorial(A4[2])*math.factorial(A4[3]))) #The number of microstates\n",
+ "micro5=((math.factorial(N)*g1**A5[0]*g2**A5[1]*g3**A5[2]*g4**A5[3])/(math.factorial(A5[0])*math.factorial(A5[1])*math.factorial(A5[2])*math.factorial(A5[3]))) #The number of microstates\n",
+ "\n",
+ "print\"No. of macrostates is given by:\"\n",
+ "print A1,\"=\",micro1,\"\\n\",A2,\"=\",micro2,\"\\n\",A3,\"=\",micro3,\"\\n\",A4,\"=\",micro4,\"\\n\",A5,\"=\",micro5,\"\\n\",\n",
+ "\n",
+ "print\"\\nMost probable macrostates are\\n \" \n",
+ "if(micro1>=micro2 and micro1>=micro3 and micro1>=micro4 and micro1>=micro5) :\n",
+ " print A1 \n",
+ " \n",
+ "if(micro2>=micro1 and micro2>=micro3 and micro2>=micro4 and micro2>=micro5) :\n",
+ " print A2 \n",
+ " \n",
+ "if(micro3>=micro1 and micro3>=micro2 and micro3>=micro4 and micro3>=micro5) :\n",
+ " print A3 \n",
+ " \n",
+ "if(micro4>=micro1 and micro4>=micro2 and micro4>=micro3 and micro4>=micro5) :\n",
+ " print A4 \n",
+ " \n",
+ "if(micro5>=micro1 and micro5>=micro2 and micro5>=micro3 and micro5>=micro4) :\n",
+ " print A5 \n",
+ " \n",
+ "\n",
+ "#(ii) particles are indistinguishable bosons\n",
+ "print\"\\n(ii)Possible macrostates are\\n \" \n",
+ "print A1,A3,A3,A4,A5\n",
+ "micro1=(math.factorial(A1[0]+g1-1)*math.factorial(A1[1]+g2-1)*math.factorial(A1[2]+g3-1)*math.factorial(A1[3]+g4-1))/(math.factorial(A1[0])*math.factorial(A1[1])*math.factorial(A1[2])*math.factorial(A1[3])*math.factorial(g1-1)*math.factorial(g2-1)*math.factorial(g3-1)*math.factorial(g4-1)) \n",
+ "micro2=(math.factorial(A2[0]+g1-1)*math.factorial(A2[1]+g2-1)*math.factorial(A2[2]+g3-1)*math.factorial(A2[3]+g4-1))/(math.factorial(A2[0])*math.factorial(A2[1])*math.factorial(A2[2])*math.factorial(A2[3])*math.factorial(g1-1)*math.factorial(g2-1)*math.factorial(g3-1)*math.factorial(g4-1)) \n",
+ "micro3=(math.factorial(A3[0]+g1-1)*math.factorial(A3[1]+g2-1)*math.factorial(A3[2]+g3-1)*math.factorial(A3[3]+g4-1))/(math.factorial(A3[0])*math.factorial(A3[1])*math.factorial(A3[2])*math.factorial(A3[3])*math.factorial(g1-1)*math.factorial(g2-1)*math.factorial(g3-1)*math.factorial(g4-1)) \n",
+ "micro4=(math.factorial(A4[0]+g1-1)*math.factorial(A4[1]+g2-1)*math.factorial(A4[2]+g3-1)*math.factorial(A4[3]+g4-1))/(math.factorial(A4[0])*math.factorial(A4[1])*math.factorial(A4[2])*math.factorial(A4[3])*math.factorial(g1-1)*math.factorial(g2-1)*math.factorial(g3-1)*math.factorial(g4-1)) \n",
+ "micro5=(math.factorial(A5[0]+g1-1)*math.factorial(A5[1]+g2-1)*math.factorial(A5[2]+g3-1)*math.factorial(A5[3]+g4-1))/(math.factorial(A5[0])*math.factorial(A5[1])*math.factorial(A5[2])*math.factorial(A5[3])*math.factorial(g1-1)*math.factorial(g2-1)*math.factorial(g3-1)*math.factorial(g4-1)) \n",
+ "\n",
+ "print\"No. of macrostates is given by:\"\n",
+ "print A1,\"=\",micro1,\"\\n\",A2,\"=\",micro2,\"\\n\",A3,\"=\",micro3,\"\\n\",A4,\"=\",micro4,\"\\n\",A5,\"=\",micro5,\"\\n\"\n",
+ "\n",
+ "print\"\\nMost probable macrostate is\\n \"\n",
+ "if(micro1>=micro2 and micro1>=micro3 and micro1>=micro4 and micro1>=micro5) :\n",
+ " print A1\n",
+ " \n",
+ "if(micro2>=micro1 and micro2>=micro3 and micro2>=micro4 and micro2>=micro5) :\n",
+ " print A2 \n",
+ " \n",
+ "if(micro3>=micro1 and micro3>=micro2 and micro3>=micro4 and micro3>=micro5) :\n",
+ " print A3 \n",
+ " \n",
+ "if(micro4>=micro1 and micro4>=micro2 and micro4>=micro3 and micro4>=micro5) :\n",
+ " print A4 \n",
+ " \n",
+ "if(micro5>=micro1 and micro5>=micro2 and micro5>=micro3 and micro5>=micro4) :\n",
+ " print A5 \n",
+ " \n",
+ "\n",
+ "#(iii) Particles are indistinguishable fermions\n",
+ "print\"\\n(iii)Possible macrostates are\\n \"\n",
+ "print A2,A5\n",
+ "micro2=4/(math.factorial(A2[0])*math.factorial(A2[1])*math.factorial(A2[2])*math.factorial(A2[3])*math.factorial(g1-A2[0])*math.factorial(g2-A2[1])*math.factorial(g3-A2[2])*math.factorial(g4-A2[3])) \n",
+ "micro5=4/(math.factorial(A5[0])*math.factorial(A5[1])*math.factorial(A5[2])*math.factorial(A5[3])*math.factorial(g1-A5[0])*math.factorial(g2-A5[1])*math.factorial(g3-A5[2])*math.factorial(g4-A5[3])) \n",
+ "\n",
+ "print\"No. of macrostates is given by:\"\n",
+ "print A2,\"=\",micro2,\"\\n\",A5,\"=\",micro5,\"\\n\"\n",
+ "\n",
+ "print\"\\nMost probable macrostate is\\n \"\n",
+ "if(micro2>=micro5) :\n",
+ " print A2\n",
+ " \n",
+ "if(micro5>=micro2) :\n",
+ " print A5 \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i)Possible macrostates are\n",
+ " \n",
+ "[2, 0, 0, 2] [1, 1, 1, 1] [0, 3, 0, 1] [1, 0, 3, 0] [0, 2, 2, 0]\n",
+ "No. of macrostates is given by:\n",
+ "[2, 0, 0, 2] = 6 \n",
+ "[1, 1, 1, 1] = 96 \n",
+ "[0, 3, 0, 1] = 32 \n",
+ "[1, 0, 3, 0] = 32 \n",
+ "[0, 2, 2, 0] = 96 \n",
+ "\n",
+ "Most probable macrostates are\n",
+ " \n",
+ "[1, 1, 1, 1]\n",
+ "[0, 2, 2, 0]\n",
+ "\n",
+ "(ii)Possible macrostates are\n",
+ " \n",
+ "[2, 0, 0, 2] [0, 3, 0, 1] [0, 3, 0, 1] [1, 0, 3, 0] [0, 2, 2, 0]\n",
+ "No. of macrostates is given by:\n",
+ "[2, 0, 0, 2] = 1 \n",
+ "[1, 1, 1, 1] = 4 \n",
+ "[0, 3, 0, 1] = 4 \n",
+ "[1, 0, 3, 0] = 4 \n",
+ "[0, 2, 2, 0] = 9 \n",
+ "\n",
+ "\n",
+ "Most probable macrostate is\n",
+ " \n",
+ "[0, 2, 2, 0]\n",
+ "\n",
+ "(iii)Possible macrostates are\n",
+ " \n",
+ "[1, 1, 1, 1] [0, 2, 2, 0]\n",
+ "No. of macrostates is given by:\n",
+ "[1, 1, 1, 1] = 4 \n",
+ "[0, 2, 2, 0] = 1 \n",
+ "\n",
+ "\n",
+ "Most probable macrostate is\n",
+ " \n",
+ "[1, 1, 1, 1]\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#vairable initialization\n",
+ "N=4 #no. of particles\n",
+ "A1=(4,0) #possible macrostate\n",
+ "A2=(3,1) #possible macrostate\n",
+ "A3=(2,2) #possible macrostate\n",
+ "A4=(1,3) #possible macrostate\n",
+ "A5=(0,4) #possible macrostate\n",
+ "import math\n",
+ "#calculation\n",
+ "print\"\\nPossible macrostates are\\n \"\n",
+ "print A1,A2,A3,A4,A5\n",
+ "micro1=math.factorial(N)/(math.factorial(A1[0])*math.factorial(A1[1])) #no. of microstate corresponding to macrostate1\n",
+ "micro2=math.factorial(N)/(math.factorial(A2[0])*math.factorial(A2[1])) #no. of microstate corresponding to macrostate2\n",
+ "micro3=math.factorial(N)/(math.factorial(A3[0])*math.factorial(A3[1])) #no. of microstate corresponding to macrostate3\n",
+ "micro4=math.factorial(N)/(math.factorial(A4[0])*math.factorial(A4[1])) #no. of microstate corresponding to macrostate4\n",
+ "micro5=math.factorial(N)/(math.factorial(A5[0])*math.factorial(A5[1])) #no. of microstate corresponding to macrostate5\n",
+ "print\"No.of macrostates is:\"\n",
+ "print A1,\"=\",micro1,\"\\n\",A2,\"=\",micro2,\"\\n\",A3,\"=\",micro3,\"\\n\",A4,\"=\",micro4,\"\\n\",A5,\"=\",micro5,\"\\n\"\n",
+ "\n",
+ "\n",
+ "print\"\\nTotal no. of microstates are \",micro1+micro2+micro3+micro4+micro5\n",
+ "print\"\\nMost probable macrostate is\\n \" \n",
+ "if(micro1>=micro2 and micro1>=micro3 and micro1>=micro4 and micro1>=micro5) :\n",
+ " print A1\n",
+ "if(micro2>=micro1 and micro2>=micro3 and micro2>=micro4 and micro2>=micro5) :\n",
+ " print A2\n",
+ "if(micro3>=micro1 and micro3>=micro2 and micro3>=micro4 and micro3>=micro5):\n",
+ " print A3\n",
+ "if(micro4>=micro1 and micro4>=micro2 and micro4>=micro3 and micro4>=micro5):\n",
+ " print A4\n",
+ "if(micro5>=micro1 and micro5>=micro2 and micro5>=micro3 and micro5>=micro4):\n",
+ " print A5\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Possible macrostates are\n",
+ " \n",
+ "(4, 0) (3, 1) (2, 2) (1, 3) (0, 4)\n",
+ "No.of macrostates is:\n",
+ "(4, 0) = 1 \n",
+ "(3, 1) = 4 \n",
+ "(2, 2) = 6 \n",
+ "(1, 3) = 4 \n",
+ "(0, 4) = 1 \n",
+ "\n",
+ "\n",
+ "Total no. of microstates are 16\n",
+ "\n",
+ "Most probable macrostate is\n",
+ " \n",
+ "(2, 2)\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "N=4 #no. of particles\n",
+ "A1=(1,0,1,2) #possible macrostate\n",
+ "A2=(0,2,0,2) #possible macrostate\n",
+ "A3=(0,1,2,1) #possible macrostate\n",
+ "A4=(0,0,4,0) #possible macrostate\n",
+ "\n",
+ "#calculation\n",
+ "print\"\\nPossible macrostates are\\n \"\n",
+ "print A1,A2,A3,A4\n",
+ "micro1=math.factorial(N)/(math.factorial(A1[0])*math.factorial(A1[1])*math.factorial(A1[2])*math.factorial(A1[3])) #no. of microstate corresponding to macrostate1\n",
+ "micro2=math.factorial(N)/(math.factorial(A2[0])*math.factorial(A2[1])*math.factorial(A2[2])*math.factorial(A2[3])) #no. of microstate corresponding to macrostate2\n",
+ "micro3=math.factorial(N)/(math.factorial(A3[0])*math.factorial(A3[1])*math.factorial(A3[2])*math.factorial(A3[3])) #no. of microstate corresponding to macrostate3\n",
+ "micro4=math.factorial(N)/(math.factorial(A4[0])*math.factorial(A4[1])*math.factorial(A4[2])*math.factorial(A4[3])) #no. of microstate corresponding to macrostate4\n",
+ "print\"\\nThe number of microstates belonging to the above macrostates is:\"\n",
+ "print A1,\"=\",micro1,\"\\n\",A2,\"=\",micro2,\"\\n\",A3,\"=\",micro3,\"\\n\",A4,\"=\",micro4,\"\\n\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Possible macrostates are\n",
+ " \n",
+ "(1, 0, 1, 2) (0, 2, 0, 2) (0, 1, 2, 1) (0, 0, 4, 0)\n",
+ "\n",
+ "The number of microstates belonging to the above macrostates is:\n",
+ "(1, 0, 1, 2) = 12 \n",
+ "(0, 2, 0, 2) = 6 \n",
+ "(0, 1, 2, 1) = 12 \n",
+ "(0, 0, 4, 0) = 1 \n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:264"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def p(A): #function to calculate probability\n",
+ " probability=1 \n",
+ " i=0\n",
+ " for i in range(0,7):\n",
+ " probability=probability*(math.factorial(A[i]+2))/(2*math.factorial(A[i])) \n",
+ " return(probability)\n",
+ "#Variable declaration\n",
+ "A1=(5,0,0,0,0,0,1) #possible macrostate\n",
+ "A2=(4,1,0,0,0,1,0) #possible macrostate\n",
+ "A3=(4,0,1,0,1,0,0) #possible macrostate\n",
+ "A4=(3,2,0,0,1,0,0) #possible macrostate\n",
+ "A5=(4,0,0,2,0,0,0) #possible macrostate\n",
+ "A6=(3,1,1,1,0,0,0) #possible macrostate\n",
+ "A7=(2,3,0,1,0,0,0) #possible macrostate\n",
+ "A8=(3,0,3,0,0,0,0) #possible macrostate\n",
+ "A9=(2,2,2,0,0,0,0) #possible macrostate\n",
+ "A10=(1,4,1,0,0,0,0) #possible macrostate\n",
+ "A11=(0,6,0,0,0,0,0) #possible macrostate\n",
+ "\n",
+ "#calculation\n",
+ "p1=p(A1) #Thermodynamic probability of macrostate 1\n",
+ "p2=p(A2) #Thermodynamic probability of macrostate 2\n",
+ "p3=p(A3) #Thermodynamic probability of macrostate 3\n",
+ "p4=p(A4) #Thermodynamic probability of macrostate 4\n",
+ "p5=p(A5) #Thermodynamic probability of macrostate 5\n",
+ "p6=p(A6) #Thermodynamic probability of macrostate 6\n",
+ "p7=p(A7) #Thermodynamic probability of macrostate 7\n",
+ "p8=p(A8) #Thermodynamic probability of macrostate 8\n",
+ "p9=p(A9) #Thermodynamic probability of macrostate 9\n",
+ "p10=p(A10) #Thermodynamic probability of macrostate 10\n",
+ "p11=p(A11) #Thermodynamic probability of macrostate 11\n",
+ "\n",
+ "print\"\\nP1 =\",p1,\"P2 =\",p2,\"P3 =\",p3,\"P4 =\",p4,\"P5 =\",p5,\"P6 =\",p6,\"P7 =\",p7,\"P8 =\",p8,\"P9 =\",p9,\"P10 =\",p10,\"P11 =\",p11\n",
+ "print\"\\nThermodyanmic probability of the system = \",p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "P1 = 63 P2 = 135 P3 = 135 P4 = 180 P5 = 90 P6 = 270 P7 = 180 P8 = 100 P9 = 216 P10 = 135 P11 = 28\n",
+ "\n",
+ "Thermodyanmic probability of the system = 1532\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "def p(A): #function to calculate no. of microstates\n",
+ " micro=1 \n",
+ " i=1\n",
+ " for i in range(0,5):\n",
+ " micro=micro*(6/(math.factorial(A[i])*math.factorial(3-A[i]))) \n",
+ " return(micro)\n",
+ "#Variable declaration\n",
+ "A1=(3,2,0,0,1) #possible macrostate\n",
+ "A2=(3,1,1,1,0) #possible macrostate\n",
+ "A3=(2,3,0,1,0) #possible macrostate\n",
+ "A4=(3,0,3,0,0) #possible macrostate\n",
+ "A5=(2,2,2,0,0) #possible macrostate\n",
+ "\n",
+ "#calculation\n",
+ "p1=p(A1) #no. of microstates\n",
+ "p2=p(A2) #no. of microstates\n",
+ "p3=p(A3) #no. of microstates\n",
+ "p4=p(A4) #no. of microstates\n",
+ "p5=p(A5) #no. of microstates\n",
+ "\n",
+ "print\"No.of microstates associated with macrostates are :\"\n",
+ "print A1,\"=\",p1,\"\\n\",A2,\"=\",p2,\"\\n\",A3,\"=\",p3,\"\\n\",A4,\"=\",p4,\"\\n\",A5,\"=\",p5,\"\\n\"\n",
+ "print\"\\nThe thermodynamic probability of the system = \",(p1+p2+p3+p4+p5)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "No.of microstates associated with macrostates are :\n",
+ "(3, 2, 0, 0, 1) = 9 \n",
+ "(3, 1, 1, 1, 0) = 27 \n",
+ "(2, 3, 0, 1, 0) = 9 \n",
+ "(3, 0, 3, 0, 0) = 1 \n",
+ "(2, 2, 2, 0, 0) = 27 \n",
+ "\n",
+ "\n",
+ "The thermodynamic probability of the system = 73\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_1.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_1.ipynb new file mode 100755 index 00000000..516314f0 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_1.ipynb @@ -0,0 +1,361 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1:Atomic Spectra-I"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:405"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z=2 #atomic no. of He\n",
+ "a0=0.529 #radius of first Bohr orbit of H atom (\u00c5)\n",
+ "n=1 #no. of Bohr orbit\n",
+ "A=2.19*10**6 #velocity of e in first Bohr orbit of H atom (m/s)\n",
+ "B=4.14*10**15 #orbital frequency in the first Bohr orbit of H atom (rad/s)\n",
+ "E0=13.6 #energy of electron in ground state of H atom (eV)\n",
+ "n1=1 \n",
+ "n2=2 \n",
+ "R=1.097*10**7 #Rydberg constant (m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) radius of first Bohr orbit\n",
+ "r=a0/2.0 #radius of first Bohr orbit (\u00c5)\n",
+ "#(ii) velocity of electron in the first orbit\n",
+ "v=A*(z/n) #velocity of electron in the first orbit (m/s)\n",
+ "#(iii) orbital frequency in the first orbit\n",
+ "omega=B*(z**2/n**3) #orbital frequency in the first orbit (rad/s)\n",
+ "#(iv) kinetic and binding energy\n",
+ "KE=E0*(z**2/n**2) #kinetic energy of electron in the ground state (eV)\n",
+ "BE=KE #binding energy of electron in the ground state (eV)\n",
+ "#(v) ionization potential and first excitation potential\n",
+ "IP=KE #ionization potential (eV)\n",
+ "EE=E0*z**2*((1.0/n1**2)-(1.0/n2**2)) #first excitation potential (eV)\n",
+ "#(vi) wavelength of the resonance line emitted in the transition n=2 to n=1\n",
+ "lembda=(1.0/(R*z**2*((1.0/n1**2)-(1.0/n2**2))))*10**10 #wavelength of the resonance line emitted in the transition n=2 to n=1 (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) radius =\",round(r,3),\"\u00c5\"\n",
+ "print\"(ii) velocity =%.2e\"%v,\"m/s\"\n",
+ "print\"(iii) orbital frequency =\",omega,\"rad/s\"\n",
+ "print\"(iv) Kinetic energy =\",KE,\"eV Binding energy =\",BE,\"eV\"\n",
+ "print\"(v) Ionization potential =\",IP,\"eV EE =\",EE,\"eV\"\n",
+ "print\"(vi) wavelength =\",lembda,\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) radius = 0.265 \u00c5\n",
+ "(ii) velocity =4.38e+06 m/s\n",
+ "(iii) orbital frequency = 1.656e+16 rad/s\n",
+ "(iv) Kinetic energy = 54.4 eV Binding energy = 54.4 eV\n",
+ "(v) Ionization potential = 54.4 eV EE = 40.8 eV\n",
+ "(vi) wavelength = 303.85900942 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:406"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z=1 #atomic no. of H atom\n",
+ "m=1.68*10**-27 #mass of H atom (kg)\n",
+ "h=1.054*10**-34 #Planck's constant (joule second)\n",
+ "R=10967800 #Rydberg constant (m-1)\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(i) recoil velocity\n",
+ "v=(3*math.pi*h*R*z**2)/(2*m) #recoil velocity of H atom (m/s)\n",
+ "#(ii) recoil kinetic energy\n",
+ "Er=(9/8.0)*((math.pi*h*R*z**2)**2/(m*e)) #recoil kinetic energy of H atom (eV)\n",
+ "#(iii) energy of emitted photon\n",
+ "E=(1.5*math.pi*h*c*R*z**2)/e #energy of emitted photon (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"(i) recoil velocity =\",round(v,2),\"m/s\"\n",
+ "print\"(ii) recoil kinetic energy =%.1e\"%Er,\"eV\"\n",
+ "print\"(iii) energy of emitted photon =\",round(E,2),\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) recoil velocity = 3.24 m/s\n",
+ "(ii) recoil kinetic energy =5.5e-08 eV\n",
+ "(iii) energy of emitted photon = 10.21 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:407"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z=2 #atomic no. of He atom\n",
+ "h=1.054*10**-34 #Planck's constant (joule second)\n",
+ "R=10967800 #Rydberg constant (m-1)\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "\n",
+ "#calculation\n",
+ "E=1.5*math.pi*h*c*R*z**2 #The energy of the emitted photon (J)\n",
+ "IE=2*math.pi*h*c*R #Ionization energy of H atom (J)\n",
+ "KE=(E-IE)/e #Kinetic energy of the photoelectron (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nKinetic energy of photoelectron =\",round(KE,1),\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Kinetic energy of photoelectron = 27.2 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:407"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ratio=4 #ratio of wavelengths\n",
+ "z1=1 #atomic no. of hydrogen atom\n",
+ "\n",
+ "#calculation\n",
+ "z2=math.sqrt(ratio*z1**2) #atomic no. of unknown element\n",
+ "\n",
+ "#Result\n",
+ "print\"Atomic no. =\",z2,\"(helium)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Atomic no. = 2.0 (helium)\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:407"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda1=108.5*10**-9 #wavelength (m)\n",
+ "lembda2=30.4*10**-9 #wavelength (m)\n",
+ "R=1.097*10**7 #Rydberg constant (m-1)\n",
+ "z=2 #atomic no. of He\n",
+ "n0=1 #ground state\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "n=math.sqrt(1.0/((1.0/n0**2)-(((1.0/lembda1)+(1.0/lembda2))/(R*z**2)))) #quantum no. corresponding to the excited state of He+\n",
+ "\n",
+ "#Result\n",
+ "print\"n =\",round(n )\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "n = 5.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z=2 #atomic no. of He+ ion\n",
+ "lembda=133.7*10**-9 #difference b/w the first lines of the Balmer and Lyman series (m)\n",
+ "n1=1\n",
+ "n2=2\n",
+ "n3=3\n",
+ "\n",
+ "#calculation\n",
+ "R=(1.0/(lembda*z**2))*((1.0/((1.0/n2**2)-(1.0/n3**2)))-(1.0/((1.0/n1**2)-(1.0/n2**2)))) #Rudberg constant (m-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"R =%.3e\"%R,\"m**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R =1.097e+07 m**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=1.097*10**7 #Rydberg constant (m-1)\n",
+ "lembda=59.3*10**-9 #wavelength difference b/w first lines of Balmer and Lyman series (m)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "z=math.sqrt(88.0/(15.0*R*lembda)) #atomic no.\n",
+ "\n",
+ "#Result\n",
+ "print\"Z =\",round(z)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Z = 3.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=1.097*10**7 #Rydberg constant (m-1)\n",
+ "ratio=1836 #ratio of maas of tritium and hydrogen\n",
+ "\n",
+ "#calculation\n",
+ "lembda=(36*2*10**10)/(5*R*3*ratio) #separation of the first line of the Balmer series (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u0394\u03bb =\",round(lembda,1),\"\u00c5\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\u0394\u03bb = 2.4 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_2.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_2.ipynb new file mode 100755 index 00000000..bc22fbca --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_2.ipynb @@ -0,0 +1,363 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Atomic Spectra-II"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:460"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "rP = 4 \n",
+ "rD = 5 \n",
+ "LP = 1 \n",
+ "LP = 2 \n",
+ "jP = (5/2.0, 3/2.0, 1/2.0) \n",
+ "jD = (4, 3, 2, 1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "SP = (rP-1)/2.0 \n",
+ "SD = (rD-1)/2.0 \n",
+ "i=0 \n",
+ "JP=[0,0,0]\n",
+ "JD=[0,0,0,0,0]\n",
+ "for i in range(0,3):\n",
+ " JP[i] =round(math.sqrt(jP[i]*(jP[i])+1) ,2)\n",
+ "i=0 \n",
+ "for i in range(0,4):\n",
+ " JD[i] = round(math.sqrt(jD[i]*(jD[i]+1)) ,2)\n",
+ " \n",
+ "#Result\n",
+ "print\"\\nAngular moments allowed for 4P :\",JP\n",
+ "print\"\\nAngular moments allowed for 5D : \",JD\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Angular moments allowed for 4P : [2.69, 1.8, 1.12]\n",
+ "\n",
+ "Angular moments allowed for 5D : [4.47, 3.46, 2.45, 1.41, 0]\n"
+ ]
+ }
+ ],
+ "prompt_number": 80
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:462"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "l=1\n",
+ "s=1/2.0\n",
+ "j=3/2.0\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "angle=((j*(j+1))-(l*(l+1))-(s*(s+1)))/(2*math.sqrt(l*s*(l+1)*(s+1))) #value of cos \u03b8\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n cos \u03b8 = \",round(angle,3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " cos \u03b8 = 0.408\n"
+ ]
+ }
+ ],
+ "prompt_number": 81
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:462"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "e=1.6*10**-19 #charge of electron (C)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "B=0.1 #external magnetic field (Wb/m**2)\n",
+ "g=4/3.0\n",
+ "mu=9.27*10**-24 #(J/T)\n",
+ "\n",
+ "#calculation\n",
+ "from sympy import *\n",
+ "mu_b=Symbol(\"\u00b5b\")\n",
+ "import math\n",
+ "E=round(g*B,3)*mu_b #The spacing of adjacent sub-levels (J)\n",
+ "v=(e*B)/(4*math.pi*m) #Larmor frequency (Hz)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n The spacing of adjacent sub-levels =\",E,\"J\\n Larmor frequency =%.1e\"%v,\"Hz\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " The spacing of adjacent sub-levels = 0.133*\u00b5b J\n",
+ " Larmor frequency =1.4e+09 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 82
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:11,Page no:462"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=9.27*10**-24 #(J/T)\n",
+ "g=2 \n",
+ "ms=1/2.0 \n",
+ "dB=2*10**2 #gradient of magnetic field (T/m)\n",
+ "m=1.67*10**-27 #maas of hydrogen atom (kg)\n",
+ "l=0.2 #distance travelled by hydrogen atom (m)\n",
+ "v=2*10**5 #speed of hydrogen atom (m/s)\n",
+ "\n",
+ "#calculation\n",
+ "muz=g*mu*ms #Resolved part of magnetic moment in the direction of magnetic field (J/T)\n",
+ "Fz=muz*dB #Force on the atom (N)\n",
+ "z=0.5*(Fz/m)*(l/v)**2 #Displacement of beam (m)\n",
+ "sep=2*z #Total separation (m)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Total separation =%.2e\"%sep,\"m\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Total separation =1.11e-06 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 83
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:463"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "l=1.0\n",
+ "s=1.0/2.0\n",
+ "j1=1.0/2.0\n",
+ "j2=3.0/2.0\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "L=math.sqrt(l*(l+1.0)) #orbital angular momenta\n",
+ "S=math.sqrt(s*(s+1.0)) #spin angular momenta\n",
+ "J1=math.sqrt(j1*(j1+1.0)) #total angular momenta\n",
+ "J2=math.sqrt(j2*(j2+1.0)) #total angular momenta\n",
+ "theta1=(180.0/math.pi)*math.acos(((j2*(j2+1))-(l*(l+1))-(s*(s+1)))/(2.0*math.sqrt(l*(l+1.0))*math.sqrt(s*(s+1)))) #angle b/w l and s (degree)\n",
+ "theta2=(180.0/math.pi)*math.acos(((j1*(j1+1))-(l*(l+1))-(s*(s+1)))/(2.0*math.sqrt(l*(l+1.0))*math.sqrt(s*(s+1)))) #angle b/w l and s (degree)\n",
+ "#Result\n",
+ "print\"\\n |l| =\",round(L,2),\"*h=\u221a2h\\n |s| =\",round(S,2),\"*h=\u221a3/4 h\\n |j| =\",round(J1,2),\"*h=\u221a3/4 h,\",round(J2,2),\"*h=\u221a15/4 h\\n \u03b81 =%d\"%theta1,\"\u02da\\n \u03b82 =%d\"%round(theta2),\"\u02da\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " |l| = 1.41 *h=\u221a2h\n",
+ " |s| = 0.87 *h=\u221a3/4 h\n",
+ " |j| = 0.87 *h=\u221a3/4 h, 1.94 *h=\u221a15/4 h\n",
+ " \u03b81 =65 \u02da\n",
+ " \u03b82 =145 \u02da\n"
+ ]
+ }
+ ],
+ "prompt_number": 84
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:463"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "B=0.5 #magnetic field (T)\n",
+ "s=1/2.0 \n",
+ "g=2 \n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "from sympy import *\n",
+ "mu_B=Symbol(\"\u03bc\u03b2\")\n",
+ "S=math.sqrt(s*(s+1)) #Magnitude of spin vector\n",
+ "theta1=(180.0/math.pi)*math.acos(0.5/S) #Orientation of spin vector (degree)\n",
+ "theta2=(180.0/math.pi)*math.acos(-0.5/S) #Orientation of spin vector (degree)\n",
+ "E=2*g*mu_B*B #Separation of the energy levels (in terms of \u03bc\u03b2)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u03b8 =\",round(theta1,1),\"\u02da and \u03b8=\",round(theta2,1),\"\u02da\\n \u0394E =\",E\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " \u03b8 = 54.7 \u02da and \u03b8= 125.3 \u02da\n",
+ " \u0394E = 2.0*\u03bc\u03b2\n"
+ ]
+ }
+ ],
+ "prompt_number": 77
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:15,Page no:464"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "zH=1.0 #atomic no. of H\n",
+ "zHe=2.0 #atomic no. of He\n",
+ "deltaHe=5.84 #doublet splitting of the first excited state of He (cm-1)\n",
+ "\n",
+ "#calculation\n",
+ "deltaH=deltaHe*(zH/zHe)**4 #doublet splitting for hydrogen atom (cm-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Doublet splitting for H atom =\",deltaH,\"cm**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Doublet splitting for H atom = 0.365 cm**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 78
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:16,Page no:464"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z=1 #atomic no. of hydrogen atom\n",
+ "n=2\n",
+ "l=1\n",
+ "\n",
+ "#calculation\n",
+ "delta=(5.84*z**4)/(n**3*l*(l+1)) #spin-orbit interaction splitting (cm-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Spin-orbit interaction splitting =\",delta,\"cm**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Spin-orbit interaction splitting = 0.365 cm**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_3.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_3.ipynb new file mode 100755 index 00000000..4cb938e1 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_3.ipynb @@ -0,0 +1,426 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3:Atomic Spectra-III"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:485"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=109729.0 #(cm-1)\n",
+ "T1=43487.0 #(cm-1)\n",
+ "T2=28583.0 #(cm-1)\n",
+ "n=2.0\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "delta=n-math.sqrt(R/T2) #quantum defect\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nquantum defect =\",round(delta,4)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "quantum defect = 0.0407\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:485"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=109737 #(cm-1)\n",
+ "n=1.805 #effective quantum number for the ground state of rubidium\n",
+ "\n",
+ "#calculation\n",
+ "T=R/(8065*n**2) #ionization potential of rubidium (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"The ionization potential of rubidium =\",round(T,3),\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The ionization potential of rubidium = 4.176 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:485"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ratio=2.5 #ratio of ionization potential of hydrogen and sodium\n",
+ "n=3.0\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "z=math.sqrt(n**2/ratio) #effective atomic number of sodium\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nEffective atomic number of sodium =\",round(z,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Effective atomic number of sodium = 1.9\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:485"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "hc=12400.0 #value of product of plank's constant and speed of light (eV \u00c5)\n",
+ "E1=3.18 #separation of 4s and 3s level (eV)\n",
+ "lembda=5890.0 #wavelength of the first member of principal series of sodium (\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "E2=round(hc/lembda,1) #separation of 3s and 3p levels (eV)\n",
+ "deltaE=E1-E2 #separation of 4s and 3p level (eV)\n",
+ "lembda1=hc/deltaE #wavelength of the first member of sharp series (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u03bb =%d\"%lembda1,\"\u00c5\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\u03bb =11481 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:486"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda1=5890*10**-10 #wavelength of doublet (\u00c5)\n",
+ "lembda2=5896*10**-10 #wavelength of doublet (\u00c5)\n",
+ "h=6.63*10**-34 #Plank's constant (Js)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "\n",
+ "#calculation\n",
+ "deltaV=(lembda2-lembda1)/(lembda1*lembda2) #wave no. (m-1)\n",
+ "deltaE=(h*c*deltaV)/e #separation of energy levels (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u0394E =%.2e\"%deltaE,\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\u0394E =2.15e-03 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:486"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "deltaT=2.1*10**-3 #(eV)\n",
+ "lembda=5893*10**-8 #(\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "deltaV=deltaT*8065 #(cm-1)\n",
+ "deltalembda=deltaV*lembda**2 #(cm)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u0394\u03bb =%.2e\"%deltalembda,\"cm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\u0394\u03bb =5.88e-08 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:486"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "E1=16960.0 #mean position of the level (cm-1)\n",
+ "E2=24490 #convergence limit of sharp series (cm-1)\n",
+ "\n",
+ "#calculation\n",
+ "I=(E1+E2)/8065.0 #ionization energy of sodium atom (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"I =\",round(I,4),\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "I = 5.1395 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:11,Page no:486"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "E1=41450.0 #principal series for sodium atom (cm-1)\n",
+ "E2=24477.0 #sharp series for sodium atom (cm-1)\n",
+ "\n",
+ "#calculation\n",
+ "I=(E1)/8065.0 #ionization energy of sodium atom (eV)\n",
+ "\n",
+ "print\"\\nI =\",round(I,3),\"eV\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "I = 5.139 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 49
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:487"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "E1=14904 #mean position of the level (cm-1)\n",
+ "E2=28583 #convergence limit of sharp series (cm-1)\n",
+ "\n",
+ "#calculation\n",
+ "I=(E1+E2)/8065.0 #ionization energy of Li atom (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"I =\",round(I,2),\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "I = 5.39 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 50
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:487"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=109734 #(cm-1)\n",
+ "T=24477.0 #(cm-1)\n",
+ "Zeff=1\n",
+ "n=3\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "delta=n-(Zeff*math.sqrt(R/T)) #quantum defect for 3p configuration of sodium\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n\u0394 =\",round(delta ,3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\u0394 = 0.883\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:14,Page no:487"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z1=1.0 #atomic no.\n",
+ "z2=2.0 #atomic no.\n",
+ "deltaT2=5.84 #doublet splitting of the first excited state for z=2 (cm-1)\n",
+ "\n",
+ "#calculation\n",
+ "deltaT1=deltaT2*(z1/z2)**4 #separation in hydrogen atom (cm-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Separation in hydrogen atom =\",deltaT1,\"cm**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Separation in hydrogen atom = 0.365 cm**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_4.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_4.ipynb new file mode 100755 index 00000000..4e137e39 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_4.ipynb @@ -0,0 +1,349 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Magneto-optic and Electro-optic Phenomena"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:514"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "e=1.6*10**-19 #charge of electron (Coulomb)\n",
+ "B=0.5 #magnetic field (Tesla)\n",
+ "lembda=6438*10**-10 #wavelength of the line (m)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "dlembda=(e*B*lembda**2*10**10)/(4*math.pi*m*c) #normal Zeeman splitting (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"Zeeman shift =\",round(dlembda,3),\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Zeeman shift = 0.097 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:515"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "e=1.6*10**-19 #charge of electron (Coulomb)\n",
+ "B=1 #magnetic field (Tesla)\n",
+ "lembda=612*10**-9 #wavelength of the line (m)\n",
+ "m=9.1*10**-31 #mass of electron (kg)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "dlembda1=(e*B*lembda**2*10**10)/(4*math.pi*m*c) #normal Zeeman splitting (\u00c5)\n",
+ "dlembda2=2*dlembda1 #Separation of outer lines (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"Separation of outer lines =\",round(dlembda2,2),\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Separation of outer lines = 0.35 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:515"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=9.27*10**-24 #(J/T)\n",
+ "B=1*10**-1 #external magnetic field (T)\n",
+ "h=1.054*10**-34 #Plank's constant (Js)\n",
+ "J=3/2.0 \n",
+ "L=1.0 \n",
+ "S=1/2.0 \n",
+ "\n",
+ "#calculation\n",
+ "g=1+(((J*(J+1))+(S*(S+1))-(L*(L+1)))/(2*J*(J+1))) #Lande g-factor\n",
+ "omega=(g*mu*B)/h #angular velocity of precession (rad/s)\n",
+ "\n",
+ "#Result\n",
+ "print\"\u03c9 =%.1e\"%omega,\"rad/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\u03c9 =1.2e+10 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:515"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "J=5/2.0 \n",
+ "#Calculation\n",
+ "sub=2*J+1 \n",
+ "#Result\n",
+ "print\"\\n(i) Energy level does not split\"\n",
+ "print\"\\n(ii) number of sub-shells =\",sub\n",
+ "print\"\\n(iii) Energy level does not split\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) Energy level does not split\n",
+ "\n",
+ "(ii) number of sub-shells = 6.0\n",
+ "\n",
+ "(iii) Energy level does not split\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:515"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "S1=0.0\n",
+ "L1=2.0\n",
+ "J1=2.0\n",
+ "g1=1.0\n",
+ "S2=1.0\n",
+ "L2=3.0\n",
+ "J2=4.0\n",
+ "g2=5/4.0\n",
+ "B=0.25 #magnetic field (T)\n",
+ "mu=5.79*10**-5 #mass (eV/T)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i)\n",
+ "E1=4*g1*mu*B #total splitting (eV)\n",
+ "#(ii)\n",
+ "E2=8*g2*mu*B #total splitting (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) total splitting =\",E1,\"eV\\n(ii) total splitting =%.4e\"%E2,\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) total splitting = 5.79e-05 eV\n",
+ "(ii) total splitting =1.4475e-04 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:516"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=9.27*10**-24 #(J/T)\n",
+ "B=0.45 #magnetic field (\u03bcb/m**2)\n",
+ "h=1.054*10**-34 #Plank's constant (Js)\n",
+ "k=[5/3.0,1.0,1/3.0,-1/3.0,-1.0,-5/3.0] #value of g'Mj'-gMj\n",
+ "\n",
+ "#calculation\n",
+ "c=(mu*B)/h #constant (rad/s)\n",
+ "deltaomega1=c*k[0] #displacement of Zeeman component (rad/s)\n",
+ "deltaomega2=c*k[1] #displacement of Zeeman component (rad/s)\n",
+ "deltaomega3=c*k[2] #displacement of Zeeman component (rad/s)\n",
+ "\n",
+ "#Result\n",
+ "print\"Displcement of Zeeman component =\",\"+-%.3e\"%deltaomega1,\",+-%.2e\"%deltaomega2,\",+-%.2e\"%deltaomega3,\"rad/s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Displcement of Zeeman component = +-6.596e+10 ,+-3.96e+10 ,+-1.32e+10 rad/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:517"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m=9.1*10**-31 #mass of electron (Kg)\n",
+ "h=1.054*10**-34 #Plank's constant (Js)\n",
+ "B=1.2 #magnetic field (mu*b/m**2)\n",
+ "gs=2 #for a pure spin system\n",
+ "J=0.5 #for a pure spin system\n",
+ "\n",
+ "#calculation\n",
+ "mub=h/(2*m) #(eV/T)\n",
+ "deltaE=2*gs*mub*B*J #energy difference b/w electrons(eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n \u0394E =%.2e\"%deltaE,\"eV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " \u0394E =1.39e-04 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:517"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m=9.1*10**-31 #mass of electron (Kg)\n",
+ "h=1.054*10**-34 #Plank's constant (Js)\n",
+ "B=5 #magnetic field (T)\n",
+ "lembda=1210 #wavelength of spectral line (\u00c5)\n",
+ "M=[1,0,-1,1,0,-1] #value of Ml+2*Ms\n",
+ "ch=12400 #product of speed of light and Plank's constant (eV*\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "import numpy as np\n",
+ "M=np.array(M)\n",
+ "dE=(h/(2*m))*B*M #value of dE(upper)-dE(lower) (eV)\n",
+ "dlembda=(lembda**2/ch)*dE #wavelengths of the spectral lines in the pattern (\u00c5)\n",
+ "#Result\n",
+ "print\"Wavelengths of the line =\",round(lembda+dlembda[1],3),\",\",round(lembda+dlembda[0],3),\",\",round(lembda+dlembda[2],3),\"\u00c5\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Wavelengths of the line = 1210.0 , 1210.034 , 1209.966 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_5.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_5.ipynb new file mode 100755 index 00000000..715472a8 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_4,Chapter_5.ipynb @@ -0,0 +1,420 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 5:X-Rays and X-Ray Spectra "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:535"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12400.0 #product of speed of light and Plank's constant (eV*\u00c5)\n",
+ "lembda1=0.024 #Compton wavelength of X-ray (\u00c5)\n",
+ "lembda2=1.0 #wavelength of X-ray (\u00c5)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i)\n",
+ "x1=ch/lembda1 #minimum voltage across X-ray tube (V)\n",
+ "#(ii)\n",
+ "x2=ch/(lembda2*10**3) #minimum voltage across X-ray tube (kV)\n",
+ "#(iii)\n",
+ "x3=1.02 #minimum energy of X-ray photon (M*eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) voltage =%.2e\"%x1,\"V\\n(ii) voltage =\",x2,\"KV\\n(iii) energy =\",x3,\"MeV\"\n",
+ "print\"NOTE:Wrong answer of (i) in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) voltage =5.17e+05 V\n",
+ "(ii) voltage = 12.4 KV\n",
+ "(iii) energy = 1.02 MeV\n",
+ "NOTE:Wrong answer of (i) in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 58
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:535"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "n=3/2.0 \n",
+ "dlembda=26*10**-2 #shifting in short wave limit of X-ray spectrum (\u00c5)\n",
+ "ch=12400 #product of speed of light and Plank's constant (eV*\u00c5)\n",
+ "e=1.6*10**-19 #charge of electron (Coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "V=((n-1)/n)*(ch/(dlembda*10**3)) #initial voltage applied to the tube (KV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nInitial voltage =\",round(V,1),\"KV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Initial voltage = 15.9 KV\n"
+ ]
+ }
+ ],
+ "prompt_number": 59
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:535"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "R=10972900.0 #(m-1)\n",
+ "lembda=1.54*10**-10 #wavelength of K line (m)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "z=1+math.sqrt(4.0/(3.0*lembda*R)) #atomic number of the target element\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nZ =\",round(z)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Z = 29.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 60
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:536"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z1=29.0 #atomic no. of Copper\n",
+ "z2=26.0 #atomic no. of Iron\n",
+ "lembda1=193.0 #wavelength of K line in Iron (pm)\n",
+ "\n",
+ "#calculation\n",
+ "lembda=((z2-1)/(z1-1))**2*lembda1 #wavelength of K line in Copper (pm)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n\u03bb =\",round(lembda),\"pm\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\u03bb = 154.0 pm\n"
+ ]
+ }
+ ],
+ "prompt_number": 61
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:536"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "z1=13 #atomic no. of Al\n",
+ "z2=27 #atomic no. of Co\n",
+ "R=1.097*10**7 #(m-1)\n",
+ "\n",
+ "#calculation\n",
+ "lembda1=(4*10**12)/(3*R*(z1-1)**2) #wavelength of K line in Al (pm)\n",
+ "lembda2=(4*10**12)/(3*R*(z2-1)**2) #wavelength of k line in Co (pm)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n wavelength of Al =\",round(lembda1),\"pm\\n wavelength of Co =\",round(lembda2),\"pm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " wavelength of Al = 844.0 pm\n",
+ " wavelength of Co = 180.0 pm\n"
+ ]
+ }
+ ],
+ "prompt_number": 62
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:536"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "lembda1=250.0*10**-12 #wavelength of K-alpha line (m)\n",
+ "lembda2=179.0*10**-12 #wavelength of K-alpha line (m)\n",
+ "R=10972900.0 #(m-1)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "z1=int(1+math.sqrt(4/(3*lembda1*R))) #atomic number\n",
+ "z2=int(1+math.sqrt(4/(3*lembda2*R))) \n",
+ "\n",
+ "#Result\n",
+ "print\"\\nThe required elements are: Z =\"\n",
+ "for i in range(z1+1,z2):\n",
+ " print i \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The required elements are: Z =\n",
+ "24\n",
+ "25\n",
+ "26\n"
+ ]
+ }
+ ],
+ "prompt_number": 63
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:536"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12400.0 #product of speed of light and Plank's constant (eV*\u00c5)\n",
+ "Rch=13.6 #product of speed of light, Plank's constant and R (eV)\n",
+ "z=23.0 #atomic no. of vanadium\n",
+ "lembda=24.0 #wavelength of L absorption edge (\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "El=ch/(lembda*1000) #binding energy of L electron (KeV)\n",
+ "Ek=((3/(4.0*10**3))*Rch*(z-1)**2)+El #binding energy of K electron (KeV)\n",
+ "#Result\n",
+ "print\"\\nBinding energy of K-electron =\",round(Ek,2),\"KeV\"\n",
+ "\n",
+ "print\"NOTE:Approxmiate answer given in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Binding energy of K-electron = 5.45 KeV\n",
+ "NOTE:Approxmiate answer given in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 64
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:537"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12.4 #product of speed of light and Plank's constant (KeV*\u00c5)\n",
+ "lembda1=0.178 #wavelength of K-alpha line (\u00c5)\n",
+ "lembda2=0.210 #wavelength of K line (\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "Ek=ch/lembda1 #binding energy of K electron (KeV)\n",
+ "El=Ek-(ch/lembda2) #binding energy of K-alpha electron (KeV)\n",
+ "lembda=ch/El #wavelength of L absorption edge (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nWavelength of L absorption edge =\",round(lembda,2),\"\u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Wavelength of L absorption edge = 1.17 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 65
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:537"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12.4 #product of speed of light and Plank's constant (KeV*\u00c5)\n",
+ "lembdak=0.18 #wavelength of K absorption edge (\u00c5)\n",
+ "lembda=0.1 #wavelength of incident photon (\u00c5)\n",
+ "\n",
+ "#calculation\n",
+ "Ek=ch/lembdak #binding energy of K electron (KeV)\n",
+ "E=ch/lembda #energy of incident photon (KeV)\n",
+ "K=E-Ek #maximum kinetic energy of ejected electron (KeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"KE =\",round(K,2),\"KeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "KE = 55.11 KeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 66
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:538"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "ch=12.4 #product of speed of light and Plank's constant (KeV*\u00c5)\n",
+ "Rch=13.6/10**3 #product of speed of light, Plank's constant and R (KeV)\n",
+ "lembdak=1.74 #K band absorption edge wavelength of iron (\u00c5)\n",
+ "z=30 #atomic no. of zinc\n",
+ "\n",
+ "#calculation\n",
+ "Ek=ch/lembdak #binding energy of K electron in iron (KeV)\n",
+ "E=(3.0/4.0)*Rch*(z-1)**2 #energy of photon of K-alpha radiation (KeV)\n",
+ "K=E-Ek #kinetic energy of the photoelectrons liberated from iron (KeV)\n",
+ "\n",
+ "#Result\n",
+ "print\"KE =\",round(K,3),\"KeV\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "KE = 1.452 KeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 57
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Introduction_To_Modern_Physics_Volume_1/Unit_5,Chapter_5.ipynb b/Introduction_To_Modern_Physics_Volume_1/Unit_5,Chapter_5.ipynb new file mode 100755 index 00000000..acf91fe6 --- /dev/null +++ b/Introduction_To_Modern_Physics_Volume_1/Unit_5,Chapter_5.ipynb @@ -0,0 +1,992 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 5:Raman Spectra"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:1,Page no:592"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "#Variable declaration\n",
+ "r=1.21*10**-10 #internuclear distance (meter)\n",
+ "m=2.7*10**-26 #mass of oxygen atom (kg)\n",
+ "h=6.626*10**-34 #Plank's constant (joule second)\n",
+ "c=3.0*10**8 #speed of light (meter/second)\n",
+ "\n",
+ "#Calculation\n",
+ "def F(j):\n",
+ " wave=B*j*(j+1) \n",
+ " return(wave)\n",
+ "import math\n",
+ "#(a) moment of inertia\n",
+ "mu=m/2.0 #reduced mass (kg)\n",
+ "I=mu*r**2 #moment of inertia (kg m**2)\n",
+ "#(b) rotational constant\n",
+ "B=h/(8*math.pi**2*I*c) #rotational constant (m-1)\n",
+ "\n",
+ "#(c) wave number\n",
+ "waveno=F(1)-F(0) #wave no. of the line corresponding to the transition J=0 to J=1 (m-1)\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) I = %.3e\"%I,\"kg m**2\\n(b) B =\",round(B,1),\"m-1\\n(c) wave number =\",round(waveno),\"m**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) I = 1.977e-46 kg m**2\n",
+ "(b) B = 141.5 m-1\n",
+ "(c) wave number = 283.0 m**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 107
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:2,Page no:592"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m=1.6738*10**-27 #mass of hydrogen atom (kg)\n",
+ "r=0.74*10**-10 #intermolecular distance of hydrogen molecule (meter)\n",
+ "h=1.054*10**-34 #Planck's constant (joule second)\n",
+ "e=1.6*10**-19 #Charge of electron (coulombs)\n",
+ "\n",
+ "#Calculation\n",
+ "def F(j):\n",
+ " energy=a*j*(j+1) \n",
+ " return(energy)\n",
+ "mu=m/2.0 #reduced mass of hydrogen atom (kg)\n",
+ "I=mu*r**2 #moment of inertia of molecule (kg meter**2)\n",
+ "a=(h**2)/(2.0*I*e) #constant (eV)\n",
+ "E0=F(0) #energy of level 0 (eV)\n",
+ "E1=F(1) #energy of level 1 (eV)\n",
+ "E2=F(2) #energy of level 2 (eV)\n",
+ "E3=F(3) #energy of level 3 (eV)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nE0 =\",E0,\"\\nE1 =%.2e\"%E1,\"eV\\nE2 =%.2e\"%E2,\"eV\\nE3 =%.2e\"%E3,\"eV\"\n",
+ "print\"NOTE:Wrong answer for E3 in book\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "E0 = 0.0 \n",
+ "E1 =1.52e-02 eV\n",
+ "E2 =4.55e-02 eV\n",
+ "E3 =9.09e-02 eV\n",
+ "NOTE:Wrong answer for E3 in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 108
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:3,Page no:593"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "u=1.68*10**-27 #mass of hydrogen atom (kg)\n",
+ "m1=16.0 #mass of oxygen atom in terms u\n",
+ "m2=1.0 #mass of hydrogen atom in terms of u\n",
+ "I=1.48*10**-47 #moment of inertia of OH-radical (kg m**2)\n",
+ "h_bar=1.054*10**-34 #Planck's constant (joule second)\n",
+ "j=5.0 #energy level of OH-radical\n",
+ "c=3.0*10**8 #speed of light (meter/second)\n",
+ "h=6.626*10**-34 #Plank's constant (joule second)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(a) internuclear distance\n",
+ "mu=((m1*m2)/(m1+m2))*u #reduced mass of the molecule (kg)\n",
+ "r=(math.sqrt(I/mu))*10.0**10 #internuclear distance of molecule (\u00c5)\n",
+ "#(b) angular momentum\n",
+ "P=h_bar*math.sqrt(j*(j+1)) #angular momentum of molecule (joule second)\n",
+ "#(c) angular velocity\n",
+ "omega=P/I #angular velocity of molecule (radian/second)\n",
+ "#(d) wave number\n",
+ "B=h/(8*math.pi**2*I*c) #rotational constant (m-1)\n",
+ "no=2*B*(j+1) #wave no. of line corresponding to transition j=5 to j=6 (m-1)\n",
+ "#(e) energy absorbed\n",
+ "E=c*h*no #energy absorbed in the transition j=6 to j=5 (joule)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(a) r =\",round(r,2),\"\u00c5\\n(b) J =%.2e\"%P,\" joule second\\n\"\n",
+ "print\"(c) \u03c9 =%.2e\"%omega,\"rad/s\\n(d) wave number =%.2e\"%no,\"m**-1\\n(e) E =%.1e\"%E,\"J\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) r = 0.97 \u00c5\n",
+ "(b) J =5.77e-34 joule second\n",
+ "\n",
+ "(c) \u03c9 =3.90e+13 rad/s\n",
+ "(d) wave number =2.27e+04 m**-1\n",
+ "(e) E =4.5e-21 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 109
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:4,Page no:593"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.63*10**-34 #Plank's constant (joule second)\n",
+ "v=1.153*10**11 #Frequency of absorption line (Hz)\n",
+ "mu=11.38*10**-27 #Recuced mass of the molecule (kg)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "I=h/(4.0*math.pi**2*v) #moment of inertia of CO molecule (kg m**2)\n",
+ "r=math.sqrt(I/mu)*10**10 #Internuclear distance (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Internuclear distance =\",round(r,2),\" \u00c5\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Internuclear distance = 1.13 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 110
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:5,Page no:594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=1.62*10**-27 #Reduced mass of HCL (kg)\n",
+ "c=3*10**8 #Velocity of light (m/s)\n",
+ "h=6.62*10**-34 #Plank's constant (joule second)\n",
+ "v1_P=2906.3 #Wave no. of P branch (cm-1)\n",
+ "v2_P=2927.5 #Wave no. of P branch (cm-1)\n",
+ "v3_P=2948.7 #Wave no. of P branch (cm-1)\n",
+ "v4_P=2969.9 #Wave no. of P branch (cm-1)\n",
+ "v1_R=3012.2 #Wave no. of R branch (cm-1)\n",
+ "v2_R=3033.4 #Wave no. of R branch (cm-1)\n",
+ "v3_R=3054.6 #Wave no. of R branch (cm-1)\n",
+ "v4_R=3078.8 #Wave no. of R branch (cm-1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(i) Equilibrium internuclear distance\n",
+ "delta_v=v2_P-v1_P #Separation of successive line of P and R branch (cm-1)\n",
+ "B=delta_v/2.0 #rotational constant (cm-1)\n",
+ "I=h/(8.0*math.pi**2*B*10**2*c) #Moment of inertia (kg m**2)\n",
+ "r=math.sqrt(I/mu)*10**10 #Equilibrium internuclear distance (\u00c5)\n",
+ "#(ii) Force constant\n",
+ "v0=(v4_P+v1_R)/2.0 #Equlibrium frequency (cm-1)\n",
+ "k=4*math.pi**2*mu*c**2*v0**2*10**4 #Force constant of HCl (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n(i) Equilibrium internuclear distance =\",round(r,2),\"\u00c5\\n(ii) Force constant =\",round(k),\"N/m\"\n",
+ "\n",
+ "print\"Note: the answer of (ii) part is wrong in the book\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(i) Equilibrium internuclear distance = 1.28 \u00c5\n",
+ "(ii) Force constant = 515.0 N/m\n",
+ "Note: the answer of (ii) part is wrong in the book\n"
+ ]
+ }
+ ],
+ "prompt_number": 111
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:6,Page no:594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=8.37*10**-28 #Reducec mass of hydrogen molecule (kg)\n",
+ "h=6.58*10**-16 #Plank's constant (eV s)\n",
+ "E0=0.273 #Ground state vibrational energy of hydrogen molecule (eV)\n",
+ "\n",
+ "#Calculation\n",
+ "k=mu*((2*E0)/h)**2 #force constant of hydrogen molecule (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Force constant =\",round(k),\"N/m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Force constant = 576.0 N/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 112
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:7,Page no:595"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m1=1.0 #molar mass of H atom (amu)\n",
+ "m2=35.0 #molar mass of Cl atom (amu)\n",
+ "u=1.68*10**-27 #atomic mass unit (kg)\n",
+ "v=2885.9*100 #wave no. of line (m-1)\n",
+ "c=3.0*10**8 #Velocity of light (m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "mu=((m1*m2)/(m1+m2))*u #reduced mass of HCl molecule (kg)\n",
+ "mu=round(mu,29)\n",
+ "k=4*(math.pi*c*v)**2*mu #force constant of HCl molecule (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"Force constant =\",round(k),\"N/m\"\n",
+ "print\"NOTE:Approximate value of pi is used in book,that's why different answer\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force constant = 482.0 N/m\n",
+ "NOTE:Approximate value of pi is used in book,that's why different answer\n"
+ ]
+ }
+ ],
+ "prompt_number": 113
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:8,Page no:595"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "m1=12.0 #molar mass of C atom (amu)\n",
+ "m2=16.0 #molar mass of O atom (amu)\n",
+ "u=1.68*10**-27 #atomic mass unit (kg)\n",
+ "k=1870.0 #force constant of CO molecule (N/m)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "e=1.602*10**-19 #charge of electron (Coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "def F(V):\n",
+ " energy=((V+.5)*h*v)/e \n",
+ " return(energy)\n",
+ "\n",
+ "#def G(V):\n",
+ "# energy=((V+.5)*h*v*8065)/e \n",
+ "# return(energy)\n",
+ "import math\n",
+ "mu=((m1*m2)/(m1+m2))*u #reduced mass of CO molecule (kg)\n",
+ "v=(1.0/(2.0*math.pi))*math.sqrt(k/mu) #frequency of vibration of CO molecule (Hz)\n",
+ "e1=F(0) #energy of 1st level of CO molecule (eV)\n",
+ "#E1=G(0) #energy of 1st level of CO molecule (cm-1)\n",
+ "E1=round(e1,3)*8065\n",
+ "e2=F(1) #energy of 2nd level of CO molecule (eV)\n",
+ "E2=round(e2,3)*8065 #energy of 2nd level of CO molecule (cm-1)\n",
+ "e3=F(2) #energy of 3rd level of CO molecule (eV)\n",
+ "E3=round(e3,3)*8065 #energy of 3rd level of CO molecule (cm-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nE = \",round(e1,3),\"eV,\",round(e2,3),\"eV,\",round(e3,3),\"eV.........\\n =\",E1,\"cm**-1,\",E2,\"cm**-1,\",E3,\"cm**-1.........\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "E = 0.132 eV, 0.396 eV, 0.66 eV.........\n",
+ " = 1064.58 cm**-1, 3193.74 cm**-1, 5322.9 cm**-1.........\n"
+ ]
+ }
+ ],
+ "prompt_number": 114
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:9,Page no:595"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=1.61*10**-27 #reduced mass of HCl molecule (kg)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "lembda=3.465*10**-6 #wavelength of infrared radiation (m)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "v=c/lembda #frequency of radiation (s-1)\n",
+ "k=4*(math.pi*v)**2*mu #force constant of HCl molecule (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"Force constant =\",round(k),\"N/m\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force constant = 476.0 N/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 115
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:10,Page no:596"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "mu=1.62*10**-27 #reduced mass of HCl molecule (kg)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "v=2.886*10**5 #wave no. of absorption line in infrared spectrum (m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "k=4*(math.pi*c*v)**2*mu #force constant of HCl molecule (N/m)\n",
+ "amp=math.sqrt((h*c*v)/k)*10**10 #amplitude of vibration in the ground state (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"Amplitude of vibration =\",round(amp,2),\"\u00c5\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Amplitude of vibration = 0.11 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 116
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:11,Page no:596"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#Variable declaration\n",
+ "v1=214330.0 #fundamental band for CO molecule (m-1)\n",
+ "v2=425970.0 #first overtone for CO molecule (m-1)\n",
+ "\n",
+ "#calculation\n",
+ "import numpy as np\n",
+ "a=np.array([[1,-2],[2,-6]])\n",
+ "b=np.array([v1,v2])\n",
+ "x=np.linalg.solve(a,b)\n",
+ "we=x[0]\n",
+ "wexe=x[1]\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"We find we=\",we,\"m**-\",\"xe.we=\",wexe,\"m**-1\"\n",
+ "print\"NOTE:Wrong answer for xe.we in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "We find we= 217020.0 m**- xe.we= 1345.0 m**-1\n",
+ "NOTE:Wrong answer for xe.we in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 117
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:12,Page no:596"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v1=2886.0 #intense absorption (m-1)\n",
+ "v2=5668.0 #intense absorption (m-1)\n",
+ "v3=8347.0 #intense absorption (m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "from numpy.linalg import inv\n",
+ "A=np.array([[1,-2],[2,-6]]) #coefficient matrix\n",
+ "b=np.array([[v1],[v2]]) #right hand side matrix\n",
+ "mu=1.61*10**-27 #reduced mass (kg)\n",
+ "c=3*10**8 #speed of light (m/s)\n",
+ "x=np.dot(inv(A),b) #values of omega and x*omega (m-1)\n",
+ "k=4*(math.pi*c*x[0]*100)**2*mu #force constant (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"we =\",round(x[0]),\"cm**-1\\nxe*we =\",round(x[1]),\"cm**-1\\nforce constant =\",round(k),\"N/m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "we = 2990.0 cm**-1\n",
+ "xe*we = 52.0 cm**-1\n",
+ "force constant = 511.0 N/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 147
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:13,Page no:597"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v1=8.657*10**13 #frequency of rotation absorption spectrum (Hz)\n",
+ "v2=8.483*10**13 #frequency of rotation absorption spectrum (Hz)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "mu=1.544*10**-27 #Recuced mass of CH molecule (kg)\n",
+ "\n",
+ "#Calculation\n",
+ "#(i) equilibrium separation\n",
+ "import math\n",
+ "I=h/(2*math.pi**2*(v1-v2)) #Moment of inertia (kg m**2)\n",
+ "r=math.sqrt(I/mu) #equilibrium internuclear distance (m)\n",
+ "#(ii) force constant of molecule\n",
+ "v0=(v1+v2)/2.0 #Central frequency (Hz)\n",
+ "k=4*mu*(math.pi*v0)**2 #Force constant of CH molecule (N/m)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n (i) equilibrium separation =%.2e\"%r,\"m\\n (ii) force constant =\",round(k),\"N/m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " (i) equilibrium separation =1.12e-10 m\n",
+ " (ii) force constant = 448.0 N/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 118
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:14,Page no:597"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "k=448.0 #force constant of CH molecule (N/m)\n",
+ "mu=4.002*10**-27 #reduced mass of CH molecule (kg)\n",
+ "r=0.112*10**-9 #internuclear distance (m)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "v0=(1/(2*math.pi))*math.sqrt(k/mu) #central frequency (s-1)\n",
+ "I=mu*r**2 #moment of inertia of molecule (kg m**2)\n",
+ "x=h/(4.0*math.pi**2*I) #additional frequency (s-1)\n",
+ "v1=v0+x #peak frequency (Hz)\n",
+ "v2=v0-x #peak frequency (Hz)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n Peak frequencies =%.3e\"%v1,\"Hz,%.3e\"%v2,\"Hz\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Peak frequencies =5.358e+13 Hz,5.292e+13 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 119
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:15,Page no:598"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v1=2174.07 #peak wave number (cm-1)\n",
+ "v2=2166.35 #peak wave number (cm-1)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "c=3*10**8 #Speed of light (m/s)\n",
+ "mu=1.145*10**-26 #Reduced mass of CO molecule (kg)\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "#(a) central frequency\n",
+ "B=(v1-v2)/4 #Rotational constant (cm-1)\n",
+ "v0=(v1+v2)/2 #Central frequency (cm-1)\n",
+ "#(b) internuclear distance\n",
+ "I=h/(8*math.pi**2*B*100*c) #moment of inertia of molecule (kg m**2)\n",
+ "r=math.sqrt(I/mu)*10**10 #equilibrium internuclear distance (\u00c5)\n",
+ "#(c) force constant\n",
+ "k=4*mu*(math.pi*c*v0*100)**2 #force constant (N/m)\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"\\n(a) central frequency =\",v0,\"cm**-1\\n(b) internuclear distance =\",round(r,2),\"\u00c5\\n(c) force constant =%d\"%k,\"N/m\"\n",
+ "print\"NOTE:Wrong answer for 'k' in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "(a) central frequency = 2170.21 cm**-1\n",
+ "(b) internuclear distance = 1.12 \u00c5\n",
+ "(c) force constant =1916 N/m\n",
+ "NOTE:Wrong answer for 'k' in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 120
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:16,Page no:598"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=3.142*10**-27 #reduced mass of the molecule (kg)\n",
+ "r=1.288*10**-10 #internuclear distance (m)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "c=3*10**8 #Speed of light (m/s)\n",
+ "v0=201100.0 #central frequency (m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "I=mu*r**2 #moment of inertia of molecule (kg m**2)\n",
+ "B=h/(8.0*math.pi**2*I*c) #Rotational constant (m-1)\n",
+ "vR0=v0+(2*B) #wave no. of 1st line of R-branch (m-1)\n",
+ "vR1=v0+(4*B) #wave no. of 2nd line of R-branch (m-1)\n",
+ "vP1=v0-(2*B) #wave no. of 1st line of P-branch (m-1)\n",
+ "vP2=v0-(4*B) #wave no. of 2nd line of P-branch (m-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n V_R(0) =\",round(vR0),\"m**-1\\n V_R(1) =\",round(vR1),\"m**-1\\n V_P(1) =\",round(vP1),\"m**-1\\n V_P(2) =\",round(vP2),\"m**-1\"\n",
+ "\n",
+ "print\"NOTE:Very approximate value of 'B' is calculated in book,that's why difference in answers\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " V_R(0) = 202169.0 m**-1\n",
+ " V_R(1) = 203238.0 m**-1\n",
+ " V_P(1) = 200031.0 m**-1\n",
+ " V_P(2) = 198962.0 m**-1\n",
+ "NOTE:Very approximate value of 'B' is calculated in book,that's why difference in answers\n"
+ ]
+ }
+ ],
+ "prompt_number": 121
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:17,Page no:599"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "mu=1.62*10**-27 #reduced mass of HCl molecule (kg)\n",
+ "r=1.293*10**-10 #internuclear distance (m)\n",
+ "h=6.6*10**-34 #Plank's constant (joule second)\n",
+ "c=3*10**8 #Speed of light (m/s)\n",
+ "\n",
+ "#Calculation\n",
+ "I=mu*r**2 #moment of inertia of molecule (kg m**2)\n",
+ "I=round(I,48)\n",
+ "\n",
+ "B=h/(8*math.pi**2*I*c) #Rotational constant (m-1)\n",
+ "B=round(B)\n",
+ "sep=4*B #separation b/w lines R(0) and P(1) (m-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n\u0394\u03bd =\",sep,\"m**-1\"\n",
+ "print\"NOTE:Note:Again I is wrongly approximated due to which 'B' and thus fina answer does not match\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "\u0394\u03bd = 4128.0 m**-1\n",
+ "NOTE:Note:Again I is wrongly approximated due to which 'B' and thus fina answer does not match\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:18,Page no:599"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "import math\n",
+ "a=214.6*100 #(m-1)\n",
+ "b=0.6*100 #(m-1)\n",
+ "h=6.62*10**-34 #Plank's constant (joule second)\n",
+ "c=3.0*10**8 #Speed of light (m/s)\n",
+ "no=1.0/(math.e) #number of molecules in state with respect to ground state\n",
+ "k=1.38*10**-23 #Boltzmann constant (J K-1)\n",
+ "\n",
+ "#Calculation\n",
+ "deltaE=h*c*(a-2*b) #difference in the energies of state 0 and state 1 (J)\n",
+ "deltaE=round(deltaE,24)\n",
+ "T1=deltaE/k #temperature at which number of molecules in state 1 is 1/e times of state 0 (K)\n",
+ "T2=deltaE/(k*math.log(10.0)) #temperature at which number of molecules in state 1 is 10% of state 0 (K)\n",
+ "\n",
+ "#Result\n",
+ "print\"n(i) T =\",round(T1),\"K\\n(ii) T =\",round(T2),\"K\" \n",
+ "print\"NOTE:Calculation mistake in book\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "n(i) T = 307.0 K\n",
+ "(ii) T = 133.0 K\n",
+ "NOTE:Calculation mistake in book\n"
+ ]
+ }
+ ],
+ "prompt_number": 123
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:19,Page no:599"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "vexc=4358.0*10**-10 #wavelength of exciting line (m)\n",
+ "vsto=4458.0*10**-10 #wavelength of Stokes line (m)\n",
+ "\n",
+ "#Calculation\n",
+ "vbar_exc=1/vexc #wave number of exciting line (m-1)\n",
+ "vbar_sto=1/vsto #wave number of Stokes line (m-1)\n",
+ "delta_vbar=vbar_exc-vbar_sto #Raman shift (m-1)\n",
+ "vbar_antistoke=vbar_exc+delta_vbar #Wave number of Anti-Stokes line (m-1)\n",
+ "lembda_antistoke=(1/vbar_antistoke)*10**10 #Wavelength of Anti-Stokes line (\u00c5)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nwavelength of Anti-stokes line =\",round(lembda_antistoke,1),\"\u00c5\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "wavelength of Anti-stokes line = 4262.4 \u00c5\n"
+ ]
+ }
+ ],
+ "prompt_number": 124
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:20,Page no:600"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "h=6.62*10**-34 #Plank's constant (joule second)\n",
+ "c=3.0*10**8 #Speed of light (m/s)\n",
+ "x=62.4*100 #(m-1)\n",
+ "y=41.6*100 #(m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "B=y/4.0 #Rotational constant of HCl (m-1)\n",
+ "I=h/(8*math.pi**2*B*c) #Moment of inertia (kg m**2)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\n I =%.1e\"%I,\"kg m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " I =2.7e-47 kg m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 125
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example no:21,Page no:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def F(v):\n",
+ " energy=(((v+.5)*a)-(((v+.5)**2)*b))*h*c \n",
+ " return(energy)\n",
+ "#Variable declaration\n",
+ "h=6.62*10**-34 #Plank's constant (joule second)\n",
+ "c=3.0*10**8 #Speed of light (m/s)\n",
+ "a=1580.36*100 #value of \u03c9e (m-1)\n",
+ "b=12.07*100 #value of \u03c9exe (m-1)\n",
+ "\n",
+ "#Calculation\n",
+ "E0=F(0) #Zero point energy of the molecule (J)\n",
+ "shift=(F(1)-F(0))/(h*c) #Expected vibrational Raman shift (m-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"\\nZero point energy =%.3e\"%E0,\"J\\nExpected vibrational Raman shift =\",shift/100,\"cm**-1\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Zero point energy =1.563e-20 J\n",
+ "Expected vibrational Raman shift = 1556.22 cm**-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 126
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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