UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What are the differences in electrical characteristics of FET (JFET) and MOSFET?

Consider a uranium nucleus ({}_{92}\text{U}^{236}) breaking up spontaneously into two equal parts. Estimate the reduction of electrostatic energy of the nucleus considering uniform charge distribution. [ Assume that nuclear radius is 1\cdot 2 \times 10^{-13} A^{1/3} \text{ cm} ]

What is the minimum energy required to break a {}_2^4\text{He} nucleus into free protons and neutrons? [ Given, m_{\text{H}} = 1\cdot 007825 \text{ amu}, m_n = 1\cdot 008665 \text{ amu}, m_e = 0\cdot 00055 \text{ amu} and m_{\text{He}} = 4\cdot 002603 \text{ amu} ]

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

\rho^0 and \text{K}^0 mesons both decay mostly to \pi^+ and \pi^-. Why the mean lifetime of \rho^0 is 10^{-23} \text{ s}, whereas that of \text{K}^0 is 0\cdot 89 \times 10^{-10} \text{ s}?

The total binding energies of {}_8^{15}\text{O}, {}_8^{16}\text{O} and {}_8^{17}\text{O} are 111\cdot 96 \text{ MeV}, 127\cdot 62 \text{ MeV} and 131\cdot 76 \text{ MeV} respectively. Determine the energy gap between 1p_{1/2} and 1d_{5/2} neutron shells for the nuclide whose mass number is close to 16.

(i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, tell whether the following reactions are possible or not : (i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e

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

Draw the normal Zeeman pattern for {}^1\text{F}_3 - {}^1\text{D}_2 transition.

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} ]

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 ]

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.

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.

The Stern-Gerlach experiment is a landmark experiment in quantum mechanics. Discuss about the most important findings of this experiment.

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} ]

Explain how the uncertainty in position is different from the uncertainty or inaccuracy of the measuring instruments.

Determine the ground state energy of an electron in an infinite potential well of width of 2\text{ \AA}.

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.

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

V(x) = \begin{cases} 0, & x < -a \\\\ V, & -a < x < a \\\\ 0, & x > a \end{cases} For a potential with the boundary conditions V(x) = \begin{cases} 0, & x < -a \\\\ V, & -a < x < a \\\\ 0, & x > a \end{cases} solve the Schrödinger's equation in one dimension and find out the conditions for tunnelling.