UPSC Physics Optional PYQs (CSE & IFoS)PYQs

State Franck-Condon principle. Define Franck-Condon factors. Using schematic diagram, explain the decay of excited states leading to the phenomena of fluorescence and phosphorescence.

Given the force constant of HCl molecule = 516\ \mathrm{N\,m}^{-1}, determine the wave number of the fundamental mode of vibration of the molecule. How many transition lines one can expect in the vibration spectra of HCl molecule at room temperature?

Explain Stokes and anti-Stokes Raman scattering with the help of energy level diagram. For a diatomic molecule, obtain expressions for transition energies of its Raman spectra with rotational fine structure and hence the wave numbers of the Stokes lines.

Explain why lines in some Raman spectra are found to be plane polarized to different extents even though the exciting radiation is completely unpolarized?

What is Raman effect? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6\ \mathrm{cm}^{-1}. Find the internuclear distance between the atoms forming the molecule.

Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli’s exclusion principle.

Explain in detail L-S coupling and j-j coupling schemes.

What is Lamb shift? What is its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom?

In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 K, l \approx 25\ \mathrm{cm} and \frac{\partial B_z}{\partial z} \simeq 10^{+3}\,\text{Tesla/m}. Calculate the separation of the two components.

Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum \vec{S} and its z-component of an electron moving along the external magnetic field \vec{B}.

The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646\,\mathring{\mathrm{A}}. Find the wavelength of the first line of this series.

If K, L and M energy levels of platinum are approximately 78, 12 and 3\ \mathrm{keV}, respectively, below the vacuum level, calculate the wavelengths of K_\alpha and K_\beta lines.

Find the magnetic moment of an atom in {}^3P_2 state, assuming that LS coupling holds for this case.

Obtain Zeeman splitting for sodium D-lines.

Two successive lines in the rotational emission spectrum of HCl molecule appear at wave numbers 83.5\ \mathrm{cm^{-1}} and 104.1\ \mathrm{cm^{-1}}. Calculate the position of the next line appearing at the higher wave number.

The observed vibrational frequency of CO molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of the molecule?

Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode.

The energy levels of a hydrogen atom are given by E_n = \left(\frac{-1}{n^2}\right)R_{\mathrm{yd}} where 1R_{\mathrm{yd}} = hcR. Show that R = 1.097 \times 10^7\ \mathrm{m^{-1}}.

Obtain an expression for the resonance condition in NMR.

Discuss the vibrational spectra of a diatomic molecule treating it as an anharmonic oscillator.