UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Consider a hydrogen atom in Bohr atomic model. Outline its importance in the context of spatial quantization and the spin of the electron.

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

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

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

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

Distinguish between fluorescence and phosphorescence in electronically excited molecules.

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

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

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.

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

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.

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

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

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

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

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.