Discuss the pure rotational Raman spectra of symmetric top molecules. What are R and S branches ?

Calculate the two longest wavelengths of the Balmer series of triply ionized beryllium (z = 4).

(i) Explain 'term symbol' for a particular atomic state. (ii) Show that the spectral lines of alkali metals are doublets.

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

The wavelengths (\lambda) in the visible spectrum of H atom can be expressed by the empirical formula \lambda = \left( \frac{n_1^2}{n_1^2 - 4} \right) \cdot G where n_1 is an integer and n_1 = 3, 4 etc. and G is an empirical constant. Prove from the above, the wave number \bar{\nu} = R_H \left( \frac{1}{2^2} - \frac{1}{n_1^2} \right), \text{ where } R_H = \frac{4}{G}.

What is the mechanism of emission of light in fluorescent lamps and in painted signboards ? Explain.

Give the elementary theory of NMR. Explain the two different relaxation processes.

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

Obtain the term symbols for two singlet states and two triplet states for two electron atoms.

Consider a diatomic molecule as a rigid rotator. Obtain its rotational energy levels and hence the rotational spectra.

Describe Stern--Gerlach experiment. In performing this experiment, beams of neutral atoms are used. Why are electrons or ion beams not used ? Explain how it demonstrates the discrete nature of the magnetic moment of an atom.

State and explain the Heisenberg's uncertainty principle. Show that the natural line width of a spectral line follows from this principle. The lifetime of an excited state of an atom is 10^{-8}\text{ s}. Calculate the energy width of such a state.

Derive the combined vibration--rotation spectrum of a diatomic molecule. What are P and R branches ?

What is Raman effect ? Discuss its application to molecular structure.