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.

Show that the lines in the absorption spectra corresponding to the rotational transitions from two adjacent energy levels of a medium sized molecule at room temperature have comparable intensities.

The first rotational line in the rotational spectrum of CO is observed at 3\cdot84235\text{ cm}^{-1}. Calculate the rotational constant B and the bond length.

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

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

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

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.

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}.

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.

Consider a hydrogen atom in Bohr atomic model. Outline its importance in the context of spatial quantization and the spin of the electron.

Outline the Stern-Gerlach experiment and discuss its importance in the context of quantum nature of atom.

Obtain the frequency u_r of the spectral line of rotation spectra of a diatomic molecule and discuss the characteristics of its spectrum.

Outline elementary theory of Nuclear Magnetic Resonance (NMR) and discuss its applications.

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.

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.

Distinguish between fluorescence and phosphorescence in electronically excited molecules.

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.

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

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.