# Chapter 4:Magneto-optic and Electro-optic Phenomena¶

## Example no:1,Page no:514¶

In :
#Variable declaration
e=1.6*10**-19                                                                    #charge of electron (Coulomb)
B=0.5                                                                           #magnetic field (Tesla)
lembda=6438*10**-10                                                              #wavelength of the line (m)
m=9.1*10**-31                                                                    #mass of electron (kg)
c=3*10**8                                                                        #speed of light (m/s)

#calculation
import math
dlembda=(e*B*lembda**2*10**10)/(4*math.pi*m*c)                                        #normal Zeeman splitting (Å)

#Result
print"Zeeman shift =",round(dlembda,3),"Å"

Zeeman shift = 0.097 Å


## Example no:2,Page no:515¶

In :
#Variable declaration
e=1.6*10**-19                                                                    #charge of electron (Coulomb)
B=1                                                                             #magnetic field (Tesla)
lembda=612*10**-9                                                                #wavelength of the line (m)
m=9.1*10**-31                                                                    #mass of electron (kg)
c=3*10**8                                                                        #speed of light (m/s)

#calculation
import math
dlembda1=(e*B*lembda**2*10**10)/(4*math.pi*m*c)                                       #normal Zeeman splitting (Å)
dlembda2=2*dlembda1                                                             #Separation of outer lines (Å)

#Result
print"Separation of outer lines =",round(dlembda2,2),"Å"

Separation of outer lines = 0.35 Å


## Example no:3,Page no:515¶

In :
#Variable declaration
mu=9.27*10**-24                                                                  #(J/T)
B=1*10**-1                                                                       #external magnetic field (T)
h=1.054*10**-34                                                                  #Plank's constant (Js)
J=3/2.0
L=1.0
S=1/2.0

#calculation
g=1+(((J*(J+1))+(S*(S+1))-(L*(L+1)))/(2*J*(J+1)))                               #Lande g-factor
omega=(g*mu*B)/h                                                                #angular velocity of precession (rad/s)

#Result

ω =1.2e+10 rad/s


## Example no:4,Page no:515¶

In :
#Variable declaration
J=5/2.0
#Calculation
sub=2*J+1
#Result
print"\n(i) Energy level does not split"
print"\n(ii) number of sub-shells =",sub
print"\n(iii) Energy level does not split"

(i) Energy level does not split

(ii) number of sub-shells = 6.0

(iii) Energy level does not split


## Example no:5,Page no:515¶

In :
#Variable declaration
S1=0.0
L1=2.0
J1=2.0
g1=1.0
S2=1.0
L2=3.0
J2=4.0
g2=5/4.0
B=0.25                                                                          #magnetic field (T)
mu=5.79*10**-5                                                                   #mass (eV/T)

#Calculation
#(i)
E1=4*g1*mu*B                                                                    #total splitting (eV)
#(ii)
E2=8*g2*mu*B                                                                    #total splitting (eV)

#Result
print"\n(i) total splitting =",E1,"eV\n(ii) total splitting =%.4e"%E2,"eV"

(i) total splitting = 5.79e-05 eV
(ii) total splitting =1.4475e-04 eV


## Example no:7,Page no:516¶

In :
#Variable declaration
mu=9.27*10**-24                                                                  #(J/T)
B=0.45                                                                          #magnetic field (μb/m**2)
h=1.054*10**-34                                                                  #Plank's constant (Js)
k=[5/3.0,1.0,1/3.0,-1/3.0,-1.0,-5/3.0]                                                      #value of g'Mj'-gMj

#calculation
deltaomega1=c*k                                                              #displacement of Zeeman component (rad/s)
deltaomega2=c*k                                                              #displacement of Zeeman component (rad/s)
deltaomega3=c*k                                                              #displacement of Zeeman component (rad/s)

#Result

Displcement of Zeeman component = +-6.596e+10 ,+-3.96e+10 ,+-1.32e+10 rad/s


## Example no:8,Page no:517¶

In :
#Variable declaration
m=9.1*10**-31                                                                    #mass of electron (Kg)
h=1.054*10**-34                                                                  #Plank's constant (Js)
B=1.2                                                                           #magnetic field (mu*b/m**2)
gs=2                                                                            #for a pure spin system
J=0.5                                                                           #for a pure spin system

#calculation
mub=h/(2*m)                                                                     #(eV/T)
deltaE=2*gs*mub*B*J                                                             #energy difference b/w electrons(eV)

#Result
print"\n ΔE =%.2e"%deltaE,"eV"

 ΔE =1.39e-04 eV


## Example no:9,Page no:517¶

In :
#Variable declaration
m=9.1*10**-31                                                                    #mass of electron (Kg)
h=1.054*10**-34                                                                  #Plank's constant (Js)
B=5                                                                             #magnetic field (T)
lembda=1210                                                                     #wavelength of spectral line (Å)
M=[1,0,-1,1,0,-1]                                                               #value of Ml+2*Ms
ch=12400                                                                        #product of speed of light and Plank's constant (eV*Å)

#calculation
import numpy as np
M=np.array(M)
dE=(h/(2*m))*B*M                                                                #value of dE(upper)-dE(lower) (eV)
dlembda=(lembda**2/ch)*dE                                                        #wavelengths of the spectral lines in the pattern (Å)
#Result
print"Wavelengths of the line =",round(lembda+dlembda,3),",",round(lembda+dlembda,3),",",round(lembda+dlembda,3),"Å"

Wavelengths of the line = 1210.0 , 1210.034 , 1209.966 Å