Chapter 15: Optical Properties of Materials

Exa 15.1

In [1]:
from __future__ import division
import math
 # Python Code Ex15.1 Determining Photon number by 
 #using Planck quantum law: Page-486 (2010)
 
 
  
#Variable declaration


h = 6.626e-034; # Planck's constant, Js
f = 1760e+03; # Frequency of the radio transmitter, Hz
P = 10e+03; # Power of radio transmitter, W




#Calculation

E = h*f; # Energy carried by one photon from Planck's law, J
N = P/E; # Number of photons emitted per second, number per second


#Result

print"\nThe number of photons emitted per second ="
print round( (N*10**-30),2)*10**30
 

The number of photons emitted per second =
8.58e+30

Exa 15.2

In [2]:
from __future__ import division
import math
 # Python Code Ex15.2 Finding suitable energy for
# Photoelectric Effect from Na metal: Page-486 (2010)


 
#Variable declaration


e = 1.602e-019;                         # Charge on an electron, C
h = 6.626e-034;                         # Planck's constant, Js
c = 3.0e+08;                            # Speed of light in vacuum, m/s
lamb = 2800e-010;                     # Wavelength of incident light, m



#Calculation

W = 2.3*e;                              # Work function of Na metal, J
f = c/lamb;                      # Frequency of the incident light, Hz
E = h*f;                # Energy carried by one photon from Planck's law, J



#Result

print"\nThe energy carried by each photon of radiation =",round(E/e,2)," eV"
if (E > W):
  print"\nThe photoelectric effect is possible.."
else:
  print"\nThe photoelectric effect is impossible.."

 

The energy carried by each photon of radiation = 4.43  eV

The photoelectric effect is possible..

Exa 15.3

In [3]:
from __future__ import division
import math
 # Python Code Ex15.3 Finding number of photons for
# green wavelength of Hg: Page-487 (2010)



 
#Variable declaration


h = 6.626e-034; # Planck's constant, Js
c = 3.0e+08; # Speed of light in vacuum, m/s
lamb = 496.1e-09; # Wavelength of green light of mercury, m
E_total = 1; # Work done by photons from green light, J



#Calculation

f = c/lamb; # Frequency of the green light, Hz
E = h*f; # Energy carried by one photon from Planck's law, J
N = E_total/E; # Number of photons of green light of Hg


#Result

print"\nThe number of photons of green light of Hg ="
print round( (N*10**-18),2)*10**18
 

The number of photons of green light of Hg =
2.5e+18

Exa 15.4

In [4]:
from __future__ import division
import math
 # Python Code Ex15.4 Photoelectric effect in a photocell: Page-487 (2010)
 
 
 
  
#Variable declaration


e = 1.602e-019; # Charge on an electron, C
h = 6.626e-034; # Planck's constant, Js
c = 3.0e+08; # Speed of light in vacuum, m/s
lamb = 1849e-010; # Wavelength of incident light, m
V_0 = 2.72; # Stopping potential for emitted electrons, V


#Calculation

f = c/lamb; # Frequency of incident radiation , Hz
E = h*f; # Energy carried by one photon from Planck's law, J
T_max = e*V_0; # Maximum kinetic energy of electrons, J
 # We have, T_max = E - h*f_0 = h*f - W
f_0 = (-T_max + E )/h # Threshold frequency for Cu metal, Hz
W = h*f_0/e; # Work function of Cu metal, eV



#Result

print"\nThrehold frequency for Cu metal =",round((f_0*10**-14),2)*10**14," Hz"
print"\nThe work function of Cu metal = ",round(W)," eV"
print"\nThe maximum kinetic energy of photoelectrons =",round(T_max/e,2)," eV"
 

Threhold frequency for Cu metal = 9.65e+14  Hz

The work function of Cu metal =  4.0  eV

The maximum kinetic energy of photoelectrons = 2.72  eV

Exa 15.5

In [5]:
from __future__ import division
import math
 # Python Code Ex15.5 Energy required to stimulate the emission of
#  Na d-lines: Page-497 (2010)


 
#Variable declaration


e = 1.6e-019; # Charge on an electron, C
h = 6.626e-034; # Planck's constant, Js
c = 3.0e+08; # Speed of light in vacuum, m/s
lambda_mean = 5893e-010; # Wavelength of incident light, m


#Calculation

# The energy of the electron which must be transferred to the atoms of Na 
delta_E = h*c/(lambda_mean*e); 



#Result

print"\nThe energy which must be transferred to stimulate"
print" the emission of Na d-lines = ",round(delta_E,2)," eV"
 

The energy which must be transferred to stimulate
 the emission of Na d-lines =  2.11  eV