UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation of Hooke's law type of interaction.

Explain the concept of shared pair of electrons with antiparallel spins forming a covalent bond in \text{H}_2-like molecule with reference to total energy.

Explain why the separation between vibrational levels is smaller in an excited electronic state than in the ground electronic state.

A substance shows a Raman line at 4567\text{ \AA} when exciting line 4358\text{ \AA} is used. Estimate the positions of Stokes and anti-Stokes lines for the same substance when exciting line 4047\text{ \AA} is used.

The particle in a box has a ground state wave function given as \psi(x) = \frac{1}{\sqrt{l}} \cos \frac{\pi x}{2l} The box width is 2l and the particle is confined within (-l, +l). Calculate the expectation value of x^2.

(i) Enumerate the possible values of quantum numbers j and m_j for state in which l = 2 and s = 1/2.

(ii) Draw the corresponding vector model diagram.

Write down Schrödinger equations for a particle of energy E < V_0, incident on a step potential height V_0. Solve them to find out the transmission and reflection coefficients in terms of k and k', where k = \sqrt{\frac{2mE}{\hbar^2}} and k' = \sqrt{\frac{2m(V_0 - E)}{\hbar^2}}. Show that in this case, there is a finite probability of finding the particle in a classically forbidden region.

A particle is bound in a potential well given by V(x) = \begin{cases} \infty & \text{for } x \le 0 \\ cx & \text{for } x > 0 \end{cases} Estimate the ground state energy of the system from uncertainty principle.

Show that the spherical harmonics Y_{lm}(\theta, \phi) are simultaneous eigenfunctions of L^2, L_z and L_z^2. What are their corresponding eigenvalues?

Develop and write down the expressions of L^2, L_z and L_z^2 in angular momentum operator algebra.

State Dulong-Petit's law and discuss its limitations in explaining heat capacities of solids. How were these efficiencies overcome by Debye ?

What is transport phenomenon ? Obtain the expression for the coefficient of viscosity. Discuss its temperature dependence.

Discuss the significance of Saha's ionisation formula in classification of stars.

Calculate the net change in entropy when 10\text{ g} water at 60^\circ\text{C} is mixed with 30\text{ g} water at 20^\circ\text{C}.

Establish Van der Waals equation of state for a real gas. Deduce expressions for critical constants and show that critical coefficient is independent of the nature of gas.

For a completely degenerate BE gas, discuss the condition for onset of BE condensation.

What do you understand by the term polarization in dielectrics ? Obtain Clausius-Mossotti formula for linear dielectrics.

Using Poisson equation and spherical co-ordinates, calculate the density of continuous charge distribution that will provide the Yukawa potential \phi = \frac{\exp(-\alpha r)}{r}, where \alpha is a constant.

Sea water has resistivity 0\cdot 3\ \Omega\text{m} and its dielectric constant is 81. Calculate the ratio of the amplitudes of the conduction and polarisation current intensities when the applied field is oscillating at 100\text{ MHz}.

Define a black body. How can we realise a black body in practice ? Derive expression for Planck's radiation law.