IGNOU MPH 16 SOLVED ASSIGNMENT

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MPH 016 (January 2025 - July 2025) - ENGLISH

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:

If the wavefunctions normalised, show that is also normalised.

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.

c) Determine the shift in energy caused by the ‘relativistic correction to kinetic energy’

 , the spin-orbit term  , and Darwin term  for n = 2 level of He .

d) Prove that the spin function symmetric with respect to the exchange of the two electrons. 

e)  Li ion is placed in an electric field of magnitude   direction. Determine the energy shift for levels with n =₁ and n = ₂ in presence of this field.

f) A Hydrogen atom is in a region of strong magnetic field. How many energy levels will be there corresponding to the unperturbed 2p level of this atom?

PART B

2. a) Determine the term symbols associated with a two electron configuration 

where . Write the term symbols in order of increasing energy using Hund’s rules.

b) Determine the equilibrium dissociation energy of CO and F₂ , if the groundvibrational state dissociation energy is 11.09eV and 1.60eV for CO and F₂ molecule, respectively. The fundamental vibrational frequency is 1 2170cm^_-1 for CO and 1 917cm^-1 for F₂ .

c) Establish the molecular Hamiltonian for C₂ molecules.

d) Explain the Linear Combination of Atomic Orbitals (LCAO) method for constructing the molecular orbital of the   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.

 

MPH 016 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment
ATOMIC AND MOLECULAR PHYSICS

Course Code: MPH-016
Assignment Code: MPH-016/TMA/2026
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

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PART A

1. a) Determine the shift in energy caused by relativistic correction to kinetic energy for and levels of hydrogen atom. Using appropriate selection rules, show which transitions are allowed. 

b) The anti-symmetric spin function for a two electron system is given as:
$
Prove that is an eigenfunction of .

c) Using Thomas-Fermi method, derive an expression for the total kinetic energy of N electrons in a cubic box of side L, and hence obtain the expression for pressure. 

d) Using molecular orbital method, construct all pssible trial wavefunctions (including spin) for a diatomic molecule. Of these functions, which trial function is expected to have the minimum energy? Give justification for your answer. 

e) Write the Hamiltonian of a multi-electron atom. Obtain an expression for the effective potential experienced by an electron of this atom under the central field approximation. 

PART B

2. a) The HCl molecule shows its first and second overtone transitions at and , respectively. Assuming anharmonic oscillator model, determine the anharmonicity constant, the equilibrium vibrational frequency, zero point energy, and the force constant of this molecule. 

b) The rotational constant for the excited electronic state of a particular molecule is 20% smaller as compared to the rotational constant of its ground electronic state. Determine the values for the first 15 lines of the R-branch. Discuss the variation of the separation between successive transition lines of this branch. 

c) i) The fundamental vibrational frequency of a molecule occurs at .
Determine the position of Raman line if the molecule is excited with a laser of wavelength .

ii) The spacing between of molecule in Raman spectrum is .
Calculate the bond length of the molecule.

d) Determine the collisional width for laser operating at a gas pressure of and gas temperature of . Obtain the ratio of spontaneous and stimulated emission if the wavelength is .

e) Write the laser rate equation for a two level system and hence prove that the steady state population inversion cannot be achieved in a two level system.

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