UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe the phenomenon of Meissner effect and its importance in the study of superconductors.

Give an elementary outline of high-temperature superconductors and their experimental status.

Distinguish between diamagnetic, paramagnetic and ferromagnetic substances.

What is parity transformation? Discuss the experiment that confirms the violation of parity in beta decay.

Give an outline of meson theory of nuclear forces. Describe the physical basis of short-range nuclear repulsion between like nucleons : proton-proton (p\text{-}p) or neutron-neutron (n\text{-}n). Consider the following two three-nucleon systems : (p\text{-}p\text{-}p) and (n\text{-}n\text{-}n). Which one is more likely to form a bound state?

Obtain the Q-values for the following four nuclear reactions :

(i) {}^{14}_{7}\text{N} + ^{4}_{2}\text{He} \rightarrow ^{17}_{8}\text{O} + ^{1}_{1}\text{H}

(ii) {}^{7}_{3}\text{Li} + ^{4}_{2}\text{He} \rightarrow ^{10}_{5}\text{B} + ^{1}_{0}\text{n}

(iii) {}^{6}_{3}\text{Li} + ^{1}_{1}\text{H} \rightarrow ^{3}_{2}\text{He} + ^{4}_{2}\text{He}

(iv) {}^{23}_{11}\text{Na} + ^{1}_{1}\text{H} \rightarrow ^{20}_{10}\text{Ne} + ^{4}_{2}\text{He}

In a nuclear fusion process, four hydrogen nuclei combine to form a helium nucleus. Obtain the energy released in such a process. If the same process is responsible for energy of a star of mass 2 \times 10^{30}\text{ kg}, each kilogram having 6 \times 10^{26} protons, what could be the magnitude of energy released in it?

What are leptons? How are they different from other baryons? Define their quantum numbers and identify the forbidden ones in the following scattering or decay processes, justifying your conclusions :

(i) \pi^0 \rightarrow \gamma + \gamma

(ii) \pi^0 \rightarrow \gamma + \gamma \rightarrow (e^+ + e^-) + (\mu^- + \mu^+)

(iii) n \rightarrow p + e^- + \bar{\nu}_\mu

(iv) \pi^+ + p \rightarrow p + p + u_\tau + \bar{\nu}_e

(v) u_e + p \rightarrow u_\mu + p + \pi^0

Describe the properties of field quanta of electro-weak and strong interactions of particles.

What are the quantum numbers of u, d and s quarks and of the corresponding antiquarks (\bar{u}, \bar{d}, \bar{s})? Obtain the quark contents of proton (p), neutron (n), positively charged pion (\pi^+) and negatively charged omega minus (\Omega^-) particle.

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.

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

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

In a nuclear experiment, beams of electrons and protons are moving with velocities c / 10 and c / 20 respectively. Calculate the de Broglie wavelengths of both the particles in metre (c is the speed of light = 3 \times 10^8\text{ m / s}).

Explain the phenomenon of Zeeman effect of atomic physics.

What does the uncertainty principle signify? Consider an electron in a box of size 10^{-10}\text{ m}. What will be its maximum uncertainty in momentum?

Consider a two-electron system in ground state with orbital quantum number zero (l = 0). Use Pauli's exclusion principle to obtain orientations of the two electrons.

Recall the Pauli matrix representation of two-state system of electron, \sigma_x, \sigma_y, \sigma_z, and show that they do not commute.

Consider a one-dimensional harmonic oscillator potential V(x) = \frac{1}{2} m \omega_0^2 x^2 where m represents the mass of a particle, \omega_0 is the classical frequency of the oscillator and x is the displacement from equilibrium position. Obtain the solution of the corresponding Schrödinger equation. Using the normalization condition on the solution, show that the ground-state wave function has the form \psi_0(x) = \left( \frac{\alpha}{\pi} \right)^{1/2} e^{-\frac{1}{2} \alpha^2 x^2} \alpha = \left( \frac{m \omega_0}{\hbar} \right)^{1/2}