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.

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 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.

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

Write the principle of nuclear magnetic resonance (NMR). Explain the design and working of NMR, and write its important applications.

The potential energy of a diatomic molecule in terms of the interatomic spacing R is given by U(R)=-\frac{A}{R^2}+\frac{B}{R^{10}} where A=1.44\times10^{-3}\,\mathrm{J\,m^2} and B=2.19\times10^{-115}\,\mathrm{J\,m^{10}}. Calculate the equilibrium spacing, R_e and the dissociation energy.

Calculate the frequency of the first Bohr orbit of hydrogen atom.

Explain how the magnetic moments of atoms, the space quantization of angular momentum and the spin of electron are measured using Stern--Gerlach experiment.

Determine the normal Zeeman splitting of the cadmium red line of 6438\,\mathring{\mathrm{A}}, when the atoms are places in a magnetic field of 0.009\,\mathrm{T}.

Why are Raman active vibrations and IR vibrations in \mathrm{CO}_2 molecule complementary to each other?

What is Franck-Condon principle? Discuss the intensity distribution in the vibrational electronic spectra of a diatomic molecule on the basis of this principle.

What is Lamb shift? Discuss its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom.

What is nuclear precession? How is it used in the principle of working of an NMR?

Discuss the fine structure of hydrogen spectrum. How is it of importance in the astronomical observations?

Describe the importance of L-S and J-J coupling in atomic spectroscopy. What are experimental evidences of their existence?

Discuss the theory of rotational and vibrational spectra of diatomic molecules. What is the difference between fluorescence and phosphorescence?

State Franck-Condon principle. Define Franck-Condon factors. Using schematic diagram, explain the decay of excited states leading to the phenomena of fluorescence and phosphorescence.

Given the force constant of HCl molecule = 516\ \mathrm{N\,m}^{-1}, determine the wave number of the fundamental mode of vibration of the molecule. How many transition lines one can expect in the vibration spectra of HCl molecule at room temperature?

Explain Stokes and anti-Stokes Raman scattering with the help of energy level diagram. For a diatomic molecule, obtain expressions for transition energies of its Raman spectra with rotational fine structure and hence the wave numbers of the Stokes lines.