UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Evaluate the most probable distance of the electron from nucleus of a hydrogen atom in its 2p state. What is the probability of finding the electron at this distance?

Estimate the de Broglie wavelength of the electron orbiting in the first excited state of the hydrogen atom.

Explain why the square of the angular momentum (L^2) and only one of the components (L_x,L_y,L_z) of L are regarded as constants of motion.

Calculate the lowest energy of an electron confined to move in a 1-dimensional potential well of width 10\,\mathrm{nm}.

Draw a schematic diagram of the single particle energy levels in a shell model including the effect of spin-orbit coupling. Show how it explains magic numbers in nuclei. Give two examples to show how this scheme predicts the spins and parities of odd A nuclei.

Using Schrodinger equation, obtain the eigenfunctions and eigenvalues of energy for a 1- dimensional harmonic oscillator. Sketch the profiles of eigenfunctions for first three energy states.

Calculate the probability of transmission of an electron of 1.0\,\mathrm{eV} energy through a potential barrier of 4.0\,\mathrm{eV} and 0.1\,\mathrm{nm} width.

Write and explain the Maxwell-Boltzmann distribution. Using this distribution, find the expressions for the most probable speed, mean speed and root-mean-square speed.

Explain Bose-Einstein distribution and obtain the same from the grand canonical ensemble.

Calculate the critical temperature for helium, given the values for critical constants, a = 6.15 \times 10^{-5}, b = 9.95 \times 10^{-4}, where the unit of pressure is atm and the sample is kept at NTP.

Derive Clausius-Clapeyron equation. How does it explain the effect of pressure on melting point of solids and boiling point of liquids?

A reversible engine converts 1/6 of the heat input into work. When the temperature of the sink is reduced by 62\ {}^{\circ}\mathrm{C}, its efficiency is doubled. Find the temperatures of source and sink.

1 litre of hydrogen at 127^{\circ}\mathrm{C} and 10^{6} dynes \mathrm{/cm}^{2} pressure expands isothermally until its volume is doubled and then expands adiabatically until its volume is redoubled. Calculate the resulting pressure. \gamma = 1.42

Write down the electromagnetic wave equations in non-conducting dielectric medium. Hence show that the velocity of wave propagation is given by v=\sqrt{\frac{1}{\varepsilon\mu}}, where the symbols have their usual meanings.

Write down the physical significance of Maxwell's equations and explain the concept of displacement current by using a proper example.

Write down Stefan-Boltzmann law of radiation and derive it from Planck's law of radiation. An aluminium foil of relative emittance 0.1 is placed between two concentric spheres (assumed perfectly black) at temperatures 300\,\mathrm{K} and 200\,\mathrm{K} respectively. Find the temperature of the foil once the steady state is reached.

When a person carrying something metallic walks through the doorway of a metal detector, it emits a sound. Explain the reason behind it. A 200\Omega resistor and a 15\mu\mathrm{F} capacitor are connected in series to 220 V, 50 Hz a.c. supply. Calculate the current in the circuit and the r.m.s. voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the supply voltage? If yes, resolve the paradox.

How large an inductance needs to be connected in series with a 120 V, 60 W lightbulb if it is to operate normally when the combination is connected across a 240 V, 60 Hz supply?

Why does a soap bubble expand upon electrification? A sphere of radius R contains a charge +Q and a charge -Q distributed uniformly in the upper and lower hemispheres respectively. Show that the dipole moment of charge distribution is \dfrac{3}{4}QR\hat{k}, where \hat{k} is directed along the polar axis of the spherical coordinate system.

A charge q=2\,\mu\mathrm{C} is placed at a=10\,\mathrm{cm} from an infinite grounded conducting plane sheet. Find the (i) total charge induced on the sheet, (ii) force on the charge q and (iii) total work required to remove the charge slowly to an infinite distance from the plane.