UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Define Franck-Condon principle. How does it help in explaining the intensity distribution of vibrational-electronic spectra of diatomic molecules.

(i) In a diatomic molecule when one constituent atom is replaced by one of its heavier isotopes, what change takes place in the rotational spectrum?

(ii) Calculate the change in rotational constant B when hydrogen is replaced by deuterium in the hydrogen molecule.

(iii) Draw the spectra of rigid and non-rigid rotors by using the schematic representation of the rotational energy levels and comment on it.

(i) Briefly explain the effect of anharmonicity on the vibrational spectra of diatomic molecules.

(ii) Calculate the average period of rotation of HCl molecule if it is in the J=3 state. The internuclear distance and the moment of inertia of HCl are 0.1274\,\mathrm{nm} and 0.0264\times10^{-45}\,\mathrm{kg\,m^2} respectively.

(i) Why does Stern-Gerlach experiment enjoy so much importance in atomic physics?

(ii) Draw the schematic diagram of this experiment and comment on the shapes of the magnet pole pieces.

(iii) Why was the atomic beam of silver used in this experiment?

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

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

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

Show that the Landé g-factor for pure orbital angular momentum and pure spin angular momentum are 1 and 2 respectively. Further, evaluate the g-factor for the state {}^3P_1.

Calculate the magnetic field strength required to observe the NMR spectrum of protons in benzene at 120\,\mathrm{MHz}. [Given the value of nuclear g-factor g_N for protons is 5.585]

An atomic state is denoted by {}^4D_{5/2}. Find the values of L, S and J. For this state, what should be the minimum number of electrons involved? Suggest a possible electronic configuration.

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 ?

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 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.

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

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 ?

The first line in the pure rotational spectrum of HCl appears at 21\mathbin{\cdot}18\,\mathrm{cm}^{-1}. Calculate bond length of the molecule. Given atomic masses of H and Cl are 1.008 and 35.45\,\mathrm{amu}, respectively.

The quantum numbers of two electrons in a two-valence electron atom are; n_1=8\quad l_1=4\quad s_1=\frac{1}{2} n_2=7\quad l_2=2\quad s_2=\frac{1}{2}

(i) Assuming L-S coupling, find the possible value of L and hence of J.

(ii) Assuming j-j coupling, find the possible values of J.

In observing the Raman spectrum of a sample using 3637\,\mathring{\mathrm{A}} as the exciting line, one gets stoke line at 3980\,\mathring{\mathrm{A}}. Deduce the Raman shift in \mathrm{m}^{-1} units. Compute the wavelength in \mathring{\mathrm{A}} for corresponding stokes and anti-stokes lines if the exciting line is 6465\,\mathring{\mathrm{A}}.

Explain spin-orbit coupling. Discuss the splitting of spectral lines of H-atom due to spin-orbit coupling.