PYQ Bank

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

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?

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.

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.

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.

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

(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?

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.

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}}.

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 ?

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.

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 ?

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

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

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.

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