UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Obtain Laue's equations for X-ray diffraction by crystals. Show that these are consistent with the Bragg's law.

With the help of a schematic diagram, show how entropy and specific heat vary with temperature for a superconductor.

What is the difference between direct and indirect band gap semiconductors? Which one is suitable for use in solar cells?

What are elementary particles and how are they classified? Describe in brief the different types of interactions that can occur between the elementary particles.

Explain why the deuteron has no excited state.

Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, state whether the following reactions are possible or not:

(i) \pi^- \to \mu^- \bar{\nu}_\tau

(ii) n \to p + e^- \bar{\nu}_e

Explain unification of electromagnetic and weak interactions. What is Z^0-boson? What is its relevance in electroweak unification?

Write down the quark structure of the following hadrons: \Delta^{++}, \Omega^-, \Sigma^- and \Lambda^0 Write down the following decays in terms of quarks:

(i) n \to p + e^- \bar{\nu}_e

(ii) \Delta^+ \to \pi^+ + n

(iii) \Sigma^+ \to p + \pi^0

Predict the spin and parity of ground states of the following nuclei on the basis of shell model:

(i) {}_{8}\mathrm{O}^{15}

(ii) {}_{8}\mathrm{O}^{16}

(iii) {}_{17}\mathrm{Cl}^{38}

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega = 41\,A^{-1/3}\,\mathrm{MeV}.

State the basic assumption of single particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of a three-dimensional spherical harmonic oscillator?

In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 K, l \approx 25\ \mathrm{cm} and \frac{\partial B_z}{\partial z} \simeq 10^{+3}\,\text{Tesla/m}. Calculate the separation of the two components.

Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum \vec{S} and its z-component of an electron moving along the external magnetic field \vec{B}.

The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646\,\mathring{\mathrm{A}}. Find the wavelength of the first line of this series.

Explain in detail L-S coupling and j-j coupling schemes.

What is Lamb shift? What is its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom?

Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli’s exclusion principle.

What is Raman effect? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6\ \mathrm{cm}^{-1}. Find the internuclear distance between the atoms forming the molecule.

Calculate the density of states for an electron moving freely inside a metal with the help of quantum mechanical Schrodinger's equation for free particle in a box.

Write down the matrix representation of the three Pauli matrices \sigma_x, \sigma_y and \sigma_z. Prove that these matrices satisfy the following identities:

(i) [\sigma_x,\sigma_y]=2i\sigma_z

(ii) [\sigma^2\cdot\sigma_x]=0

(iii) (\vec{\sigma}\cdot\vec{A})(\vec{\sigma}\cdot\vec{B})=\vec{A}\cdot\vec{B}+i\vec{\sigma}\cdot(\vec{A}\times\vec{B}) if \vec{A} and \vec{B} commute with Pauli matrices.