UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate the change in rotational constant (B_v) when deuterium is substituted for hydrogen in a hydrogen molecule.

Derive an expression for the spin-orbit interaction energy in one electron system. Calculate the energy separation between the levels {}^2P_{1/2} and {}^2P_{3/2}.

(i) What is Lamb shift? Explain it by illustrating through a suitable energy level diagram. Has Lamb shift been observed in any atom other than hydrogen? (ii) How does the 21 cm hydrogen line originate? Comment on its astronomical applications.

(i) Discuss qualitatively the occurrence of rotational energy levels at a diatomic molecule. Write down the selection rule. (ii) Is it possible to obtain rotational spectra of \text{H}_2, \text{HF}, \text{O}_2, and \text{NO} molecules? Can one obtain pure rotational spectra in emission? Comment (on both of the above-mentioned queries). (iii) In \text{CO} molecule J = 0 \rightarrow J = 1 line occurs at frequency 1.153 \times 10^{11}\text{ Hz}. Calculate the moment of inertia of \text{CO} molecule.

(i) What is Raman effect ? How does it differ from Rayleigh scattering? Write down its important applications. (ii) Explain Raman effect with the aid of quantum mechanical theory. (iii) Why is Raman effect considered complimentary to infrared absorption spectra? (iv) A Raman Stokes' line is observed at 552\text{ nm} when a sample is excited by Hg green line of wavelength 546\text{ nm}. Calculate the wavelength of anti-Stokes' line.

(i) State and explain Franck-Condon principle. (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, and (3) appreciably greater. In accordance with Franck-Condon principle, obtain most favourable transitions from the ground state vibrational levels to the upper state vibrational levels in each of the three situations. Illustrate the transitions in all the aforesaid situations by drawing suitable energy level diagrams.

(i) On the basis of vector atom model, discuss briefly the L-S and J-J coupling schemes. (ii) Write down expressions for spin angular momentum, orbital angular momentum and total angular momentum under L-S coupling scheme. (iii) Obtain the energy states for {}^{2}\text{He} atom for n = 1, 2, 3 levels (n is principal quantum number). Draw the energy level diagram. Does L-S coupling scheme hold good in {}^{80}\text{Hg} atom which like He has 2 optical electrons (6S^2) ? Comment.

Determine all the Term symbols of p^2 equivalent electrons and arrange these states in increasing order of energy. Justify your answer.

A \mu (of mass 207\text{ m}) is in the ground state of a muonic atom whose nucleus is Pb (Z = 82, A = 204, and radius = 7\text{ fm}). Calculate the first Bohr radius in units of the nuclear radius and the Rydberg constant in units of the Rydberg constant in units of the Rydberg constant of the hydrogen atom. Comment on your results.

Describe the Stern-Gerlach experiment and discuss its significance.

Explain why in optical absorption discrete lines are observed but X-ray absorption shows continue with edges. Why the emission and absorption spectra of X-rays are not identical ?

The atomic number of Na is 11. (i) Write down the electronic configuration for the ground state of the Na atoms (ii) Give the standard spectroscopic notation for the ground state. (iii) The lowest frequency in the absorption spectrum of Na is a doublet. What are the spectroscopic designations of the pair of energy levels to which the atom is excited as a result of this absorption process? (iv) What is the mechanism responsible for the splitting between the pairs of energy levels? (v) Does the level corresponding to the higher value of j lie lower or higher?

Describe the broad features of characteristic X-rays spectra and discuss how these have been accounted for

Draw the energy level diagram showing the Zeeman splitting of {}^2P_{1/2, 3/2} and {}^2S_{1/2} levels in a weak magnetic field. Give the selection rules and the resulting transitions, between the sub-levels. Does the magnetic interaction lift the degeneracy of the level only partially or wholly?

Calculate the force constant for the coupling between H and Cl, given that the fundamental frequency of H^1 Cl^{35} molecule is 8.7 \times 10^{13}\text{ Hz}. Assuming the force constant of H^2 Cl^{35} to be the same as that of H^1 Cl^{35}, calculate the vibration frequency of H^2 Cl^{35}

Draw the energy level diagram and show the allowed transitions for Zeeman pattern for n = 3_1 \rightarrow 2_0 transition line of a hydrogen atom placed in a uniform magnetic field of 1\text{ kg}. Calculate the doublet splittings.

Draw the expression for Lande's g-factor for LS coupled state.

Explain the origin of continuous X-rays. Compare the phenomenon with photoelectric effect.

Write in brief the differences between the IR active and Raman active bands.

Explain the fine structure of H_\alpha line of H-atom arising due to LS coupling.