UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What do you understand by \text{SU}(3) symmetry for the quark model? On the basis of it, explain that the baryons can have +2 charge but mesons cannot have the same.

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.

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 ]

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} ]

(i) With suitable diagrams, explain the intensity distribution of spectral lines in vibrational-electronic spectra by using the Franck-Condon principle. (ii) Calculate the positions of the first two rotational Raman lines in the spectrum of \text{H}_2, if its bond length is 0\cdot 074\text{ nm}. [Given : {}^{1}\text{H} = 1\cdot 673 \times 10^{-27}\text{ kg}]

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.

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

Obtain the resonance condition of nuclear magnetic resonance spectroscopy. Write down at least three important applications.

(i) Discuss the importance of studying the isotope effect in rotational spectroscopy. (ii) If hydrogen is substituted by deuterium in hydrogen molecule, calculate the change in rotational constant B.

Explain the salient features of fluorescence and phosphorescence with the help of energy level diagram. Name a few applications of these phenomena in our daily life.

Why were silver atoms used in Stern-Gerlach experiment? Also, write the importance of this experiment.

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.

Write the electronic configurations for carbon (C), nitrogen (N) and oxygen (O) atoms, and then derive their ground states.

If {}^{11}\text{Na} atoms in their ground state are placed in a region having electromagnetic radiation of frequency \nu = 1\cdot 0 \times 10^{10}\text{ Hz}, calculate the required magnetic field B at which the electromagnetic radiation will be in resonance with the Zeeman splitting.

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} ]

Experimental observation for the line spectrum of an atom shows that the separations between adjacent energy levels of increasing energy in a multiplet are in the ratio 3:5. By using the Landé interval rule, assign the quantum numbers L, S and J to these levels.

Explain the phenomenon of penetration of a particle through a barrier whose height exceeds the total energy of the particle with necessary diagram.

Obtain the expressions for reflection coefficient (R) and transmission coefficient (T) for reflected waves and transmitted waves from an infinite thin barrier.

g(E) = \frac{V}{\pi^2 \hbar^3 c^3} E^2 What is the density of states? For a relativistic particle of rest mass \mu, prove that the density of states in the extreme relativistic limit (E \gg \mu c^2) g(E) = \frac{V}{\pi^2 \hbar^3 c^3} E^2 where g(E) = density of states, V = volume of the system containing the particle, E = total energy, c = velocity of light and \hbar = Planck's constant.