UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What are hot bands in vibrational spectroscopy? Why are they called so?

Explain how Pauli's exclusion principle helps in determining the electronic configuration in a many-electron system.

Find the positions of the first four rotational Raman lines in the spectrum of \text{H}_2, if its bond length is 0\cdot 742\text{ \AA}. What will be the effect of nuclear spin on the spectrum?

{[Given : Mass of {}^1\text{H} = 1\cdot 673 \times 10^{-27}\text{ kg}]}

The OH-radical has a moment of inertia of 1\cdot 48 \times 10^{-46}\text{ kg}\cdot\text{m}^2. For J = 6, calculate its angular velocity and angular momentum. Find the energy absorbed in the J = 6 \rightarrow J = 7 transition.

The fundamental and 2^{\text{nd}} harmonic transitions of {}^{14}\text{N}^{16}\text{O} are recorded at 1876\cdot 06\text{ cm}^{-1} and 3724\cdot 2\text{ cm}^{-1}, respectively. Calculate the equilibrium vibrational frequency, the anharmonicity constant and the zero-point energy of the molecule.

{[Given : Mass of {}^{14}\text{N} = 23\cdot 25 \times 10^{-27}\text{ kg}, Mass of {}^{16}\text{O} = 26\cdot 56 \times 10^{-27}\text{ kg}]}

Explain why the rotational transition J = 0 \rightarrow J = 1 is often not the most intense.

Why are {}^{12}\text{C} and {}^{16}\text{O} nuclei not suitable for the study of NMR?

Why is the relaxation process so important in nuclear magnetic resonance (NMR)?

In a Stern–Gerlach experiment, the magnetic field varies with distance in the z-direction according to \dfrac{dB_z}{dz} = 1\cdot 5\text{ T/mm}. The speed of silver atoms coming from the oven is 725\text{ m/s}. Silver atoms travel a distance of 3\text{ cm} through the magnet. Calculate the separation of the two beams of atoms when they leave the magnet.

{[Given : The mass of a silver atom = 1\cdot 8 \times 10^{-25}\text{ kg} and its magnetic moment is 1\text{ Bohr magneton}.]}

Why does the electron paramagnetic resonance (EPR) spectroscopy utilize the microwave region of the electromagnetic spectrum, while nuclear magnetic resonance (NMR) uses radio waves?

Calculate the number of permitted electrons in a sub-shell and a shell in an atom.

Why can the experimental observation of the Lamb shift not be explained by the Dirac theory?

Distinguish between fluorescence and phosphorescence. Explain the mechanisms responsible for these phenomena. Discuss the applications of fluorescence and phosphorescence in the fields such as biochemistry, material science, etc.

Find out the difference in frequencies of Lyman-alpha line in hydrogen and deuterium atoms.

n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} The quantum numbers of two electrons in a two-valence electron atom are n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} Assuming L\text{-}S coupling, find the possible values of L and J.

From the pure rotational absorption spectra of a diatomic molecule (HF), the wave number difference between the consecutive rotational lines is found to be \Delta \bar{\nu} = 4050 \text{ m}^{-1}. Calculate the following : (1) Rotational constant (2) Moment of inertia (3) Distance between two atoms (bond length) [ Given, M_{\text{H}} = 1 \text{ u}, M_{\text{F}} = 19 \text{ u} ]

The Stern-Gerlach experiment is a landmark experiment in quantum mechanics. Discuss about the most important findings of this experiment.

Draw the normal Zeeman pattern for {}^1\text{F}_3 - {}^1\text{D}_2 transition.

The force constant of \text{HCl} molecule is 4\cdot 8 \times 10^5 \text{ dyne/cm}. Calculate the wave numbers of Stokes and anti-Stokes lines, when excited with a radiation of wavelength 4358 \text{ \AA}. [ Given, \mu_{\text{HCl}} = 1\cdot 61 \times 10^{-24} \text{ g} ]

In case of pure rotational states, if the temperature will be doubled, then calculate the rotational quantum number corresponding to maximum population density. [ Assume that temperature is high ]