UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

The energy levels of a hydrogen atom are given by E_n = \left(\frac{-1}{n^2}\right)R_{\mathrm{yd}} where 1R_{\mathrm{yd}} = hcR. Show that R = 1.097 \times 10^7\ \mathrm{m^{-1}}.

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

Distinguish between fluorescence and phosphorescence in electronically excited molecules.

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

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.

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

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

A sample of a certain element is placed in a magnetic field of flux density 0.3 tesla. How far apart is the Zeeman component of a spectral line of wavelength 4500\mathring{\mathrm{A}}? Given : e/m = 1.76 \times 10^{11}\ \mathrm{c/kg}, c = 3.0 \times 10^8\ \mathrm{m\,s^{-1}}.

Obtain an expression for the normal Zeeman shift. Illustrate the Zeeman splitting of spectral lines of H atom and the allowed transitions for the l = 1 and l = 2 states.

Given that the spacing between vibrational levels of CO molecules is 8.45 \times 10^{-2}\ \mathrm{eV} of energy. Find the force constant of the molecule.

Discuss the vibrational spectra of a diatomic molecule treating it as an anharmonic oscillator.

Obtain an expression for the resonance condition in NMR.

Explain the relaxation processes in NMR spectroscopy.

What is Lamb shift ? How is it measured ?

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

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

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}.

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.