Chapter 2:Atomic Spectra-II

Example no:4,Page no:460

In [80]:
#Variable declaration
rP = 4 
rD = 5 
LP = 1 
LP = 2 
jP = (5/2.0, 3/2.0, 1/2.0) 
jD = (4, 3, 2, 1)

#Calculation
import math
SP = (rP-1)/2.0 
SD = (rD-1)/2.0 
i=0 
JP=[0,0,0]
JD=[0,0,0,0,0]
for i in range(0,3):
    JP[i] =round(math.sqrt(jP[i]*(jP[i])+1) ,2)
i=0 
for i in range(0,4):
    JD[i] = round(math.sqrt(jD[i]*(jD[i]+1)) ,2)
    
#Result
print"\nAngular moments allowed for 4P :",JP
print"\nAngular moments allowed for 5D : ",JD

Angular moments allowed for 4P : [2.69, 1.8, 1.12]

Angular moments allowed for 5D :  [4.47, 3.46, 2.45, 1.41, 0]

Example no:9,Page no:462

In [81]:
#Variable declaration
l=1
s=1/2.0
j=3/2.0

#calculation
import math
angle=((j*(j+1))-(l*(l+1))-(s*(s+1)))/(2*math.sqrt(l*s*(l+1)*(s+1)))                 #value of cos θ

#Result
print"\n cos θ = ",round(angle,3)

 cos θ =  0.408

Example no:10,Page no:462

In [82]:
#Variable declaration
e=1.6*10**-19                                                                    #charge of electron (C)
m=9.1*10**-31                                                                    #mass of electron (kg)
B=0.1                                                                           #external magnetic field (Wb/m**2)
g=4/3.0
mu=9.27*10**-24                                                                  #(J/T)

#calculation
from sympy import *
mu_b=Symbol("µb")
import math
E=round(g*B,3)*mu_b                                                                        #The spacing of adjacent sub-levels (J)
v=(e*B)/(4*math.pi*m)                                                               #Larmor frequency (Hz)

#Result
print"\n The spacing of adjacent sub-levels =",E,"J\n Larmor frequency =%.1e"%v,"Hz"

 The spacing of adjacent sub-levels = 0.133*µb J
 Larmor frequency =1.4e+09 Hz

Example no:11,Page no:462

In [83]:
#Variable declaration
mu=9.27*10**-24                                                                  #(J/T)
g=2 
ms=1/2.0 
dB=2*10**2                                                                       #gradient of magnetic field (T/m)
m=1.67*10**-27                                                                   #maas of hydrogen atom (kg)
l=0.2                                                                           #distance travelled by hydrogen atom (m)
v=2*10**5                                                                        #speed of hydrogen atom (m/s)

#calculation
muz=g*mu*ms                                                                     #Resolved part of magnetic moment in the direction of magnetic field (J/T)
Fz=muz*dB                                                                       #Force on the atom (N)
z=0.5*(Fz/m)*(l/v)**2                                                            #Displacement of beam (m)
sep=2*z                                                                         #Total separation (m)

#Result
print"\n Total separation =%.2e"%sep,"m" 

 Total separation =1.11e-06 m

Example no:12,Page no:463

In [84]:
#Variable declaration
l=1.0
s=1.0/2.0
j1=1.0/2.0
j2=3.0/2.0

#calculation
import math
L=math.sqrt(l*(l+1.0))                                                                 #orbital angular momenta
S=math.sqrt(s*(s+1.0))                                                                 #spin angular momenta
J1=math.sqrt(j1*(j1+1.0))                                                              #total angular momenta
J2=math.sqrt(j2*(j2+1.0))                                                              #total angular momenta
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)
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)
#Result
print"\n |l| =",round(L,2),"*h=√2h\n |s| =",round(S,2),"*h=√3/4 h\n |j| =",round(J1,2),"*h=√3/4 h,",round(J2,2),"*h=√15/4 h\n θ1 =%d"%theta1,"˚\n θ2 =%d"%round(theta2),"˚"

 |l| = 1.41 *h=√2h
 |s| = 0.87 *h=√3/4 h
 |j| = 0.87 *h=√3/4 h, 1.94 *h=√15/4 h
 θ1 =65 ˚
 θ2 =145 ˚

Example no:13,Page no:463

In [77]:
#Variable declaration
B=0.5                                                                           #magnetic field (T)
s=1/2.0 
g=2 

#calculation
import math
from sympy import *
mu_B=Symbol("μβ")
S=math.sqrt(s*(s+1))                                                                 #Magnitude of spin vector
theta1=(180.0/math.pi)*math.acos(0.5/S)                                                    #Orientation of spin vector (degree)
theta2=(180.0/math.pi)*math.acos(-0.5/S)                                                   #Orientation of spin vector (degree)
E=2*g*mu_B*B                                                                         #Separation of the energy levels (in terms of μβ)

#Result
print"θ =",round(theta1,1),"˚ and θ=",round(theta2,1),"˚\n ΔE =",E

 θ = 54.7 ˚ and θ= 125.3 ˚
 ΔE = 2.0*μβ

Example no:15,Page no:464

In [78]:
#Variable declaration
zH=1.0                                                                            #atomic no. of H
zHe=2.0                                                                           #atomic no. of He
deltaHe=5.84                                                                    #doublet splitting of the first excited state of He (cm-1)

#calculation
deltaH=deltaHe*(zH/zHe)**4                                                       #doublet splitting for hydrogen atom (cm-1)

#Result
print"Doublet splitting for H atom =",deltaH,"cm**-1"

Doublet splitting for H atom = 0.365 cm**-1

Example no:16,Page no:464

In [20]:
#Variable declaration
z=1                                                                             #atomic no. of hydrogen atom
n=2
l=1

#calculation
delta=(5.84*z**4)/(n**3*l*(l+1))                                                  #spin-orbit interaction splitting (cm-1)

#Result
print"Spin-orbit interaction splitting =",delta,"cm**-1"

Spin-orbit interaction splitting = 0.365 cm**-1