UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

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.

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

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.

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 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?

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

Explain fluorescence and phosphorescence in electronically excited molecules.

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 ?

(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.

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) 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 ?

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

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.

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

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

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

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.