PYQ Bank

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

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

(i) Establish that hc = 1240 \text{ eV. nm} = 1240 \text{ MeV. fm} (ii) The energy levels of a hydrogen atom are given by E_n = (-1/n^2) \text{ Ryd,} where 1 \text{ Ryd} = hcR. Show that R = 1 \cdot 097 \times 10^7 \text{ m}^{-1}. What exactly is R ?

2^2S_{y_2} level in H atom is 1058 \text{ MHz} above the 2^2P_{y_2} level. (i) What is this known as ? (ii) Express the above frequency in \text{cm}^{-1}. (iii) Calculate the energy difference between the above two levels in eV.

(i) Find the ground state total orbital (L) and total spin (S) quantum numbers for nitrogen. (ii) Find the L and S values of the two "first excited states" of helium atom.

What was the aim of Stern – Gerlach experiment ? Why were silver atoms chosen instead of electrons in the experiment ? What was the outcome of the experiment ?

Explain Born – Oppenheimer approximation. Discuss the intensity distribution in the vibrational electronic spectra of a diatomic molecule on the basis of Franck – Condon principle.

Explain fluorescence and phosphorescence in electronically excited molecules.

Discuss the vibrational spectra of a diatomic molecule treating it as a harmonic oscillator as well as an anharmonic oscillator and compare them.

For transition to the ground state what is the longest wavelength that can be emitted by hydrogen ?

Draw the potential energy of a diatomic molecule as a function of interatomic distance. Mark the vibrational and rotational energy levels. Explain the selection rule for transition between vibrational states.

Assume a diatomic molecule consisting of two at- oms of masses m_1 and m_2, separated by a distance \vec{r}. Write down the Hamiltonian operator for the molecule. Determine the rotational energy levels of the molecule.

Write full form of acronyms EPR and NMR. Give underlying principle of EPR.

What do you understand by Raman effect ? Explain with help of a diagram, how it can be observed experimentally.

On the basis of electronic spectra of molecules explain, how fluorescence and phosphorescence occur. Distinguish between the two.

(i) What is Lamb shift ? Has it been observed in any atom other than hydrogen? (10) (ii) How does the 21 cm hydrogen line originate? Comment on its astronomical applications. (10)

Describe Stern-Gerlach experiment. Explain how it demonstrates the discrete nature of the magnetic moment of an atom.

Write an expression for the energy of a diatomic molecule executing both rotation and vibration in a given electronic state. Explain the observed spectra giving a schematic diagram. What are O, P, Q, R and S branches ?

(i) State and explain Franck-Condon principle. (5) (ii) In three separate pairs of electronic states (one ground and another upper state) of diatomic molecules, the average internuclear distances are -

1. equal;
2. slightly greater;
3. appreciably greater. In accordance with Franck-Condon principle, obtain most favorable transitions from the ground state vibrational levels in each of the above situations. Illustrate the transitions by drawing suitable energy-level diagrams. (15)

Examine whether the molecule ^{11}\text{B}^{16}\text{O} can show -- (i) a pure rotation spectrum ; (ii) a vibration-rotation spectrum. Give reasons.