MPH-16 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
ATOMIC AND MOLECULAR PHYSICS
Course Code: MPH-016
Assignment Code: MPH-016/TMA/2025
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) Consider a wavefunction given by:
   
 
   
 
 
  
 
     x x
Et x p i
dp t p e t x
x
, 2 , 2
1
 
If the wavefunction ) , ( t r   is normalised, show that ) , ( t r   is also normalised. (10)
b) For a non-degenerate time indepedent perturbation, show that the first-order
energy shift is equal to the expectation value of the perturbing Hamiltonian in the
unperturbed energy eigenstate. (10)
c) Determine the shift in energy caused by the ‘relativistic correction to kinetic energy’
1 E  , the spin-orbit term 2 E  , and Darwin term 3 E  for 2  n level of . He (15)
d) Prove that the spin function   ) 1 ( ) 2 ( ) 2 ( ) 1 (
2
1 ) 2 , 1 (        is symmetric with
respect to the exchange of the two electrons. (5)
e) A  2 Li ion is placed in an electric field of magnitude 1 8Vm 10 1   along the Z
direction. Determine the energy shift for levels with 1  n and 2  n in presence of
this field. (5)
f) A Hydrogen atom is in a region of strong magnetic field. How many energy levels
will be there corresponding to the unperturbed p 2 level of this atom? (5)
PART B
2. a) Determine the term symbols associated with a two electron configuration , p n ns 
where . 3 , 2    n n Write the term symbols in order of increasing energy using
Hund’s rules. (10)
b) Determine the equilibrium dissociation energy of CO and 2 F , if the ground
vibrational state dissociation energy is eV 09 . 11 and eV 60 . 1 for COand 2 F
molecule, respectively. The fundamental vibrational frequency is 1 cm 2170  for
CO and 1 cm 917  for 2 F . (10)
c) Establish the molecular Hamiltonian for 2 C molecules. (5)
d) Explain the Linear Combination of Atomic Orbitals (LCAO) method for constructing
the molecular orbital of the 
2
H
ion. Derive the expression for the ground state
molecular orbital and discuss how the overlap integral affects the bonding.
e) Write the electronic configuration of HF,HCl, and LiF molecules, hence obtain the
bond orders. Draw the schematics of the molecular orbitals and atomic orbitals for
each molecule.