Obtain the frequency $ u_r$ of the spectral line of rotation spectra of a diatomic molecule and discuss the characteristics of its spectrum.

Outline elementary theory of Nuclear Magnetic Resonance (NMR) and discuss its applications.

Outline the Stern-Gerlach experiment and discuss its importance in the context of quantum nature of atom.

Distinguish between fluorescence and phosphorescence in electronically excited molecules.

Use Hund's rules to find the ground-state quantum numbers, L and S of (i) Carbon and (ii) Oxygen atoms.

State the postulates of Bohr regarding his atom model. Obtain the expressions for the radius and electron-energy of the n^\text{th} orbit. Explain how Bohr's atom model successfully accounts for the hydrogen spectrum.

What is 'multiplicity' ? Give the term symbol for the following cases :

(i) S = \frac{1}{2} \qquad L = 2

(ii) S = 1 \qquad L = 1

Explain Russel Saunders coupling. Discuss the summation rules for orbital angular momentum, spin angular momentum and total angular momentum quantum numbers.

Derive the rotational-vibrational energy levels of a diatomic molecule. Give the analysis of spectral lines.

Explain spin-spin and spin-lattice relaxation times in NMR spectroscopy. How do they influence the line width of the NMR line ?

How is proton magnetic resonance applied to determine the chemical shifts in molecules containing hydrogen atom ? Illustrate your answer with a suitable example.

What are the characteristics of a Raman spectrum ? How do you study Raman spectra in the laboratory ? Give two applications of Raman effect.

What is Lamb shift ? How is it measured ?

Discuss the different coupling schemes in atomic spectroscopy with suitable diagrams.

An atom in an excited state of 4\cdot 7\text{ eV} emits a photon and ends up in the ground state. The lifetime of the excited state is 10^{-13}\text{ s}. Calculate the energy uncertainty and obtain the spectral line width in wavelength of photon.

Given that the rotational inertia of \text{HCl} molecule has the value I = 2\cdot 66 \times 10^{-47}\text{ kg-m}^2, estimate the energy difference between the lowest and first excited state of \text{HCl}.

Explain why the separation between vibrational levels is smaller in an excited electronic state than in the ground electronic state.

Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation of Hooke's law type of interaction.

A substance shows a Raman line at 4567\text{ \AA} when exciting line 4358\text{ \AA} is used. Estimate the positions of Stokes and anti-Stokes lines for the same substance when exciting line 4047\text{ \AA} is used.

Explain the concept of shared pair of electrons with antiparallel spins forming a covalent bond in \text{H}_2-like molecule with reference to total energy.