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

Obtain an expression for the resonance condition in NMR.

Obtain an expression for the normal Zeeman shift. Illustrate the Zeeman splitting of spectral lines of H atom and the allowed transitions for the l = 1 and l = 2 states.

Explain the relaxation processes in NMR spectroscopy.

What do you understand by H-one (HI) interstellar clouds and their importance to understand the universe.

Why are Raman active vibrations and infrared vibrations in \mathrm{CO_2} molecule complementary to each other?

With proper selection rules, construct the energy level diagram and allowed transitions for ESR spectrum of hydrogen atom.

Discuss the fine structure of sodium D line. Draw D_1 and D_2 lines due to the transitions between {}^2P and {}^2S levels.

The term symbol for atomic states are quoted as {}^3P_2 and {}^2D_{5/2}. What are the values of L, S and J?

How are electrons distributed in the various sub-shells for n=3? Give the quantum numbers for the electrons in the second shell.

In a Raman spectrum of a linear triatomic molecule, the first three lines are 4.86, 8.14 and 11.36\ \mathrm{cm^{-1}}. Calculate the rotational constant, B and the moment of inertia of the molecule. (Given h = 6.626 \times 10^{-27}\ \mathrm{J\,s}, C = 3.0 \times 10^{10}\ \mathrm{cm/sec.})

Why should rotational Raman spectrum show a separation of the first Raman line from the exciting line equal to 6B\ \mathrm{cm}^{-1}, while the separation between successive lines equals to 4B\ \mathrm{cm}^{-1}, where B is the rotational constant?

Describe the vibration-rotation spectra of a polyatomic linear molecule. What are P, Q and R branches? Draw rotational energy levels of the vibrational states v=0 and v=1 and perpendicular vibrational-rotational transitions of a linear polyatomic molecule.

What will happen to the energy level of an unpaired electron when subjected to an external magnetic field? Find the condition for electron spin resonance.

Sodium doublets are produced by transitions 3{}^2p_{1/2}\rightarrow 3{}^2s_{1/2}(D_1) and 3{}^2p_{3/2}\rightarrow 3{}^2s_{1/2}(D_2). Calculate the Landé g-factors for these levels.

What do you mean by ‘term symbols’? Obtain term symbols for the following sets of values of S and L:

(i) S=\frac{1}{2},\ L=2

(ii) S=1,\ L=1

(iii) S=\frac{3}{2},\ L=1

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?

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)