UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.

(i) Homonuclear diatomic molecules do not give any pure rotational or vibrational spectra, whereas they do give a rotational Raman spectra. Comment. (ii) The separation between the adjacent rotational Raman lines is 4B in hydrogen molecule, whereas in oxygen molecule it is 8B. Why?

Evaluate the Landé g-factor for the {}^3\mathrm{P}_1 level in the 2p 3s configuration of the {}^6\mathrm{C} atom, and then calculate the splitting of the level in eV, when the atom is in an external magnetic field of 0.2 tesla.

Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.

The quantum numbers of the two optical electrons in a two-valence electron atom are n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} Assuming j-j coupling, find the possible values of J.

The fine-structure lines of CN band at 3883\cdot 4\text{ \AA} can be represented by the following equation : \nu = 25798 + 3\cdot 85m + 0\cdot 068m^2\text{ cm}^{-1} Calculate the separation between the null-line and the band-head, and state the direction of degradation of the band.

Discuss the main features of the vibrational and the rotational Raman spectra of diatomic molecules. How is it used to explain the structure of a molecule?

Explain the mechanism of phosphorescence emission of radiation. Distinguish between fluorescence and phosphorescence.

Distinguish between normal and anomalous Zeeman effects. Explain the Zeeman pattern of the resonance (D_1, D_2) lines of sodium.

Determine the possible terms of a one-electron atom corresponding to n = 3 and compute the angle between \vec{L} and \vec{S} vectors for the term {}^{2}\text{D}_{5/2}.

Explain ‘Lamb Shift’ and describe the experimental arrangement to observe it. What is its importance ?

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

The zero point energy of the ground state of \text{N}_2 is 1176\text{ cm}^{-1} and that of its lowest excited state is 727\text{ cm}^{-1}. The energy difference between the minima of the two potential energy curves is 50,206\text{ cm}^{-1}. What is the energy of the v' = 0 \rightarrow v'' = 0 transition and its corresponding wavelength in cm ?

State the Franck – Condon principle and give its wave-mechanical interpretation. How does it help in understanding the intensity distribution in the vibrational structure of the electronic transitions of a diatomic molecule ?

Describe and explain different types of coupling in atoms. Deduce the various interaction energy terms for L – S coupling.

A beam of electrons enters a uniform magnetic field of flux density 1\cdot 2\text{ tesla}. Calculate the energy difference between electrons whose spins are parallel and antiparallel to the field.

A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600\text{ \AA} when excited by light of wavelength 4358\text{ \AA}. Calculate the wavelength of the corresponding infrared band.

The calcium line of wavelength \lambda = 4226\cdot 73\text{ \AA} (\text{P} \rightarrow \text{S}) exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4\text{ Weber/metre}^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.

Obtain an expression for the rotational energy levels of a diatomic molecule, taking it as a rigid rotator. Discuss its spectrum and the selection rule.

Explain the mechanism of Fluorescent emission of radiation. Distinguish between Fluorescence spectra and Raman spectra of a diatomic molecule.