PYQ Bank

Discuss the fine structure of hydrogen atom spectrum. Draw the compound doublet spectrum arising as a result of transitions between {}^2P and {}^2D levels.

What is Lamb shift?

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

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}.

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

Treating a diatomic molecule as a simple harmonic oscillator, obtain its vibrational energy levels.

The observed vibrational frequency of the \mathrm{CO} molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of this molecule? (Mass of carbon atom = 12u and mass of oxygen atom = 16u, where u is atomic mass unit)

Discuss pure rotational spectra of linear molecules.

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

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

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.

In \mathrm{CO} molecule J = 0 \to J = 1 line occurs at a frequency 1.153 \times 10^{11}\ \mathrm{Hz}. Calculate the moment of inertia of \mathrm{CO} molecule.

Is it possible to obtain pure rotational spectra of \mathrm{H}_2, \mathrm{HF}, \mathrm{O}_2 and \mathrm{NO} molecules?

Discuss occurrence of rotational energy levels of a diatomic molecule and show that the pure rotation spectrum of such a molecule consists of a series of equally spaced lines separated by a constant wave number difference 2B. Write down the selection rules.

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

What is Zeeman effect? How it can be understood on quantum mechanical basis? Obtain an expression for Zeeman splitting of atomic energy levels in a magnetic field B. Explain the magnetic splitting of sodium D-lines.

What is spin-orbit interaction? Calculate the energy shift due to spin-orbit interaction term in H-like system. Discuss the significance of this shift in relation to the fine structure of hydrogen spectral lines.

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.

What is Raman Effect? How does it differ from Rayleigh scattering? Explain Raman Effect on the basis of quantum mechanical theory. How is Raman Effect experimentally studied? What are the advantages of using laser sources in the study of Raman Effect?

State and explain Franck-Condon principle. Discuss its applications in molecular spectroscopy.