3: Inadequacy of Classical Physics

Example number 1, Page number 128

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration  
me=9.1*10**-31;           #mass of electron(kg)
h=6.6*10**-34;            #planks constant(Js)
c=3*10**8;                #velocity(m/sec)
lamda=1700*10**-10;       #wavelength(m)
lamda0=2300*10**-10;      #wavelength(m)

#Calculations
KE=h*c*((1/lamda)-(1/lamda0));       #maximum energy of photoelectron(J)
vmax=math.sqrt(2*KE/me);             #maximum velocity of electron(ms-1)

#Result
print "maximum energy of photoelectron is",round(KE*10**19,3),"*10**-19 J"
print "maximum velocity of electron is",round(vmax/10**5,2),"*10**5 ms-1"

maximum energy of photoelectron is 3.038 *10**-19 J
maximum velocity of electron is 8.17 *10**5 ms-1

Example number 2, Page number 128

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration  
e=1.6*10**-19;            #charge(coulomb)
W=2.3*e;                  #work function(J)
h=6.6*10**-34;            #planks constant(Js)
c=3*10**8;                #velocity(m/sec)
lamda=6850;               #wavelength of orange light(angstrom)

#Calculations
lamda0=h*c/W;             #threshold wavelength(m)

#Result
print "threshold wavelength is",int(lamda0*10**10),"angstrom"
print "since wavelength of orange light is more, photoelectric effect doesn't take place"

threshold wavelength is 5380 angstrom
since wavelength of orange light is more, photoelectric effect doesn't take place

Example number 3, Page number 129

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration  
e=1.6*10**-19;            #charge(coulomb)
W=1.3*e;                  #work function(J)
h=6.6*10**-34;            #planks constant(Js)
new=6*10**14;             #frequency(Hertz)

#Calculations
V0=((h*new)-W)/e;         #retarding potential(volts)

#Result
print "retarding potential is",V0,"volts"

retarding potential is 1.175 volts

Example number 4, Page number 129

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration  
h=6.6*10**-34;            #planks constant(Js)
e=1.6*10**-19;            #charge(coulomb)
c=3*10**8;                #velocity(m/sec)
lamda=3*10**-7;           #wavelength(m)
me=9.1*10**-31;           #mass of electron(kg)
v=1*10**6;                #velocity(m/sec)

#Calculations
W=(h*c/lamda)-(me*v**2/2);      #work function(J)
W=W/e;                          #work function(eV)

#Result
print "work function is",round(W,2),"eV"

work function is 1.28 eV

Example number 5, Page number 129

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration  
h=6.6*10**-34;            #planks constant(Js)
e=1.6*10**-19;            #charge(coulomb)
c=3*10**8;                #velocity(m/sec)
lamda=4600*10**-10;       #wavelength(m)
qe=0.5;                   #efficiency(%)

#Calculations
E=h*c/lamda;              #energy(J)
n=10**-3/E;               #number of photons/second
i=n*qe*e*10**6/100;       #photoelectric current(micro ampere)

#Result
print "photoelectric current is",round(i,2),"micro ampere"

photoelectric current is 1.86 micro ampere

Example number 6, Page number 130

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration  
T1=3*10**-19;             #temperature(J)
T2=1*10**-19;             #temperature(J)
c=3*10**8;                #velocity(m/sec)
lamda1=3350;              #wavelength(m)
lamda2=5060;              #wavelength(m)

#Calculations
x=10**10*((1/lamda1)-(1/lamda2));
h=(T1-T2)/(c*x);          #planck's constant(joule second)

#Result
print "planck's constant is",round(h*10**34,2),"*10**-34 joule second"

planck's constant is 6.61 *10**-34 joule second

Example number 7, Page number 131

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;               #velocity of light(m/sec)
m0=9.1*10**-31;          #mass(kg)
h=6.62*10**-34;          #planks constant(Js)
theta=60*math.pi/180;    #angle(radian)
lamda=3*10**-10;         #wavelength(angstrom)
lamda_dash=3.058;        #wavelength(angstrom)

#Calculations
lamda_sr=h/(m0*c);   
lamda_dash=lamda+(lamda_sr*(1-math.cos(theta)));   #wavelength of scattered radiation(m)    
lamda_dash=round(lamda_dash*10**10,4)*10**-10;     #wavelength of scattered radiation(m)
E=h*c*((1/lamda)-(1/lamda_dash));                  #energy of recoil electron(joule)

#Result
print "wavelength of scattered radiation is",lamda_dash*10**10,"angstrom"
print "energy of recoil electron is",round(E*10**18,2),"*10**-18 joule"
print "answers given in the book are wrong"

wavelength of scattered radiation is 3.0121 angstrom
energy of recoil electron is 2.66 *10**-18 joule
answers given in the book are wrong

Example number 8, Page number 132

In [42]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;               #velocity of light(m/sec)
m0=9.1*10**-31;          #mass(kg)
h=6.62*10**-34;          #planks constant(Js)
theta=30*math.pi/180;    #angle(radian)
lamda=2*10**-10;         #wavelength(angstrom)

#Calculations
lamda_sr=h/(m0*c);   
lamda_dash=lamda+(lamda_sr*(1-math.cos(theta)));   #wavelength of scattered radiation(m)    
E=h*c*((1/lamda)-(1/lamda_dash));                  #energy of recoil electron(joule)
x=1+(E/(m0*c**2));
v=c*math.sqrt(1-((1/x)**2));                       #velocity of recoil electron(m/sec)

#Result
print "wavelength of scattered radiation is",round(lamda_dash*10**10,3),"angstrom"
print "velocity of recoil electron is",round(v/10**8,4),"*10**8 ms-1"
print "answer for velocity given in the book is wrong"

wavelength of scattered radiation is 2.003 angstrom
velocity of recoil electron is 0.0188 *10**8 ms-1
answer for velocity given in the book is wrong

Example number 9, Page number 133

In [49]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;               #velocity of light(m/sec)
e=1.6*10**-19;           #charge(coulomb)
m0=9.1*10**-31;          #mass(kg)
h=6.62*10**-34;          #planks constant(Js)
theta=90*math.pi/180;    #angle(radian)
lamda=3*10**-10;         #wavelength(m)   

#Calculations
lamda_dash=lamda+(h*(1-math.cos(theta))/(m0*c));   #wavelength of scattered photon(m)    
E=h*c*((1/lamda)-(1/lamda_dash));                  #energy of recoil electron(joule)
x=h/(lamda*m0*c);
tanphi=lamda*math.sin(theta)/(lamda_dash-(lamda*math.cos(theta)));
phi=math.atan(tanphi);                             #direction of recoil electron(radian)
phi=phi*180/math.pi;                               #direction of recoil electron(degrees)
phim=60*(phi-int(phi));                            #angle(minutes)

#Result
print "wavelength of scattered photon is",round(lamda_dash*10**10,3),"angstrom"
print "energy of recoil electron is",round(E*10**17,1),"*10**-17 joules"
print "direction of recoil electron is",int(phi),"degrees",int(phim),"minutes"
print "answer for angle given in the book is wrong"

wavelength of scattered photon is 3.024 angstrom
energy of recoil electron is 0.5 *10**-17 joules
direction of recoil electron is 44 degrees 46 minutes
answer for angle given in the book is wrong

Example number 10, Page number 134

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;               #velocity of light(m/sec)
e=1.6*10**-19;           #charge(coulomb)
m0=9.1*10**-31;          #mass(kg)
h=6.62*10**-34;          #planks constant(Js)
theta=180*math.pi/180;   #angle(radian)
E=1.96*10**6*e;          #energy of scattered photon(J)

#Calculations
lamda=h*c/E;             #wavelength(m)
delta_lamda=2*h/(m0*c);   
lamda_dash=lamda+delta_lamda;   #wavelength of scattered photon(m)    
Edash=h*c/(e*lamda_dash);       #energy of scattered photon(eV)

#Result
print "energy of scattered photon is",round(Edash/10**6,3),"MeV"

energy of scattered photon is 0.226 MeV

Example number 11, Page number 135

In [65]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;               #velocity of light(m/sec)
e=1.6*10**-19;           #charge(coulomb)
m0=9.1*10**-31;          #mass(kg)
h=6.6*10**-34;           #planks constant(Js)
theta=90*math.pi/180;    #angle(radian)
E=500*10**3*e;           #energy of scattered photon(J)

#Calculations
lamda=h*c/E;             #wavelength(m)
delta_lamda=h*(1-math.cos(theta))/(m0*c);   
lamda_dash=lamda+delta_lamda;           #wavelength of scattered radiation(m) 
lamda_dash=round(lamda_dash*10**12,1)*10**-12;   #wavelength of scattered radiation(m) 
E=h*c*((1/lamda)-(1/lamda_dash));       #energy of recoil electron(J)
tanphi=lamda*math.sin(theta)/(lamda_dash-(lamda*math.cos(theta)));
phi=math.atan(tanphi);                             #direction of recoil electron(radian)
phi=phi*180/math.pi;                               #direction of recoil electron(degrees)
phim=60*(phi-int(phi));                            #angle(minutes)

#Result
print "wavelength of scattered radiation is",lamda_dash,"m"
print "energy of recoil electron is",round(E*10**14,4),"*10**-14 Joules"
print "direction of recoil electron is",int(round(phi)),"degrees",int(phim),"minutes"
print "answer for energy and direction of recoil electron and given in the book is wrong"

wavelength of scattered radiation is 4.9e-12 m
energy of recoil electron is 3.9592 *10**-14 Joules
direction of recoil electron is 27 degrees 47 minutes
answer for energy and direction of recoil electron and given in the book is wrong