(i) What are the typical energies (eV) of the radiations, required to excite (i) electronic transitions. (ii) vibrational transitions and (iii) rotational transitions in a molecule ? (ii) The rotational spectrum of HI consists of equidistant lines with a separation of 12.8\text{ cm}^{-1}. Calculate the (a) M.I. and (b) bond length of HI molecule.

Explain the nature, origin and significance of 21 cm hydrogen line.

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}.

Write the electronic configuration of mercury (Z = 80). Obtain the spectral term for the normal and the first excited configuration of the atom.

A diatomic gas is found to have a number of absorption bands in the ultraviolet region. Each band is also observed to have a fine structure. How can the observed spectrum be explained and analyzed?

(i) A sample is irradiated by a 5000 \AA\ radiation to give a Raman line at 5050.5 \AA. Calculate the Raman frequency. (ii) Explain, both red and violet degraded bands have been observed in electronic band systems, but rotation-vibration spectra show bands degraded to red only.

(i) Treating CH molecule as an united atom, derive its resultant molecular electronic states. (ii) Calculate the moment of inertia of HCl molecule from the expression u_{\text{HCl}} = 20.68 (J+1), where J = 0, 1, 2, \dots

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

(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) 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) 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) 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.

(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.

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.

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

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 ?

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?

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?