PYQ Bank

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

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

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

Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation of Hooke's law type of interaction.

Explain why the separation between vibrational levels is smaller in an excited electronic state than in the ground electronic state.

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

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

Explain the concept of shared pair of electrons with antiparallel spins forming a covalent bond in \text{H}_2-like molecule with reference to total energy.

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

A substance shows a Raman line at 4567\text{ \AA} when exciting line 4358\text{ \AA} is used. Estimate the positions of Stokes and anti-Stokes lines for the same substance when exciting line 4047\text{ \AA} is used.

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

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.

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

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.

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?

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

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.

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

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