UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe briefly the different types of physical processes with which gamma rays are absorbed by matter as they are emitted.

Name the various classifications of the gamma rays based on electric, magnetic and order. How does parity affect these radiations ?

Illustrate the Geiger-Nuttall law in a plot between the decay constant and energy of various nuclides for any radioactive series.

What is the role of neutrino in the weak interaction of radioactive nuclides ? Explain the experimental detection of neutrino.

In the following reactions indicate with an explanation, whether they proceed by strong, electromagnetic or weak interaction or they are forbidden : \pi^+ \rightarrow \mu^+ + u_\mu p \rightarrow n + e^+ + u_e p + \pi^- \rightarrow K^+ + \Sigma^-

(i) Discuss in detail the classification of elementary particles. 10 (ii) On the basis of band theory, explain the classification of solids by considering their electrical properties. 10

Determine the order of magnitude of the energy involved in the spin-orbit interaction of 2p state of an atom with an electron. Given the magnetic field due to the state is 0.28 T.

State and discuss the Franck-Condon principle giving special reference to its applications.

Explain and discuss the basic principle of nuclear magnetic resonance (NMR).

Examine whether the molecule {}^{11}\text{B}^{16}\text{O} can show – (i) a pure rotation spectrum ; (ii) a vibration-rotation spectrum. Give reasons.

What are the gyromagnetic factors of the three cases, viz., a spinning electron, an orbiting electron and a free proton ?

Prove that \frac{d}{dt}(x) = \frac{1}{m}(p_x) Define all the terms of this relation and give its physical interpretation.

Distinguish between potential well and potential barrier. Given their illustrations. Considering one-dimensional potential step, prove that sum of the reflection and transmission coefficients is unity.

Explain how the problem of the hydrogen atom could be solved using Schrodinger equation. Also derive an expression for its energy eigenvalue and discuss the associated bound states of this case.

(i) Using Pauli matrices \sigma_x, \sigma_y and \sigma_z, show that \left(\vec{\sigma} \cdot \vec{r}\right) \left(\vec{\sigma} \cdot \vec{p}\right) = \vec{r} \cdot \vec{p} + i \vec{\sigma} \cdot \vec{L} \quad 10 (ii) For the radiation of wavelength 6000~\text{\AA}, determine the wavelength separation between its two component lines which are observed in the normal Zeeman effect. The magnetic field used is \frac{\pi}{4}~\text{weber}/\text{m}^2 and the specific charge of the electron = 1.76 \times 10^{11}~\text{C}~\text{kg}^{-1}. 10

(i) Calculate the de Broglie wavelength of a thermal neutron at 27~^\circ\text{C} temperature. 10 (ii) Considering one-dimensional case for free particle, show that the plane wave function is the eigenfunction of a linear momentum operator and kinetic energy operator. 10

Using thermodynamic principles show that the Joule-Thomson coefficient \mu can be expressed as \mu = \frac{1}{C_p} \left[ T \left( \frac{\partial V}{\partial T} \right)_p - V \right] . Calculate the value of \mu for an ideal gas and interpret your result physically.

Derive the expression for the Fermi-Dirac distribution function. Represent it graphically for T = 0 and T \neq 0.

State Dulong and Petit's law. How does it agree with experiment ? Discuss the limitations of the classical theory and success of the quantum theory in explaining the specific heat of solids.

1 kg of ice at 0^\circ\text{ C} floats on 10 kg of water at 30^\circ\text{ C}, the whole system being thermally isolated. What will be the change in entropy of the sytem when thermal equilibrium is reached ? [Specific heat of water = 4.2\text{ kJ kg}^{-1}\text{ K}^{-1} and latent heat of fusion of ice = 336\text{ kJ kg}^{-1}]