UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe the Stern-Gerlach experiment and discuss its significance.

The momentum of an electron is 600\text{ keV/c}. Determine its de Brogue wavelength and the phase and group velocities of its de Brogue waves.

X-ray photons of wavelength 2.0\text{ pm} are incident on free electrons. They are scattered at an angle of 60^\circ from the incident direction. Determine the following: (i) Momentum of the incident photon in keV/c (ii) Compton shift (iii) Kinetic energy and recoil angle of the electron

A 500\ \mu\text{A} beam of electrons of kinetic energy 1.5\text{ eV} enter a region with a sharply defined boundary in which their energy is reduced to 10\text{eV} by a difference of potential. Determine the reflected and transmitted currents. Derive the formulae used.

Determine the eigenvalues and eigenfunctions of the operators D + 137, D^2 - 2xD + 4. where D = d/dx. Assume the eigenfunction of the second operator to be a quadratic.

A tank whose capacity is 0.1\text{ m}^3 contains helium at a pressure of 10\text{ atmospheres} and a temperature of 20^\circ\text{C}. A rubber weather balloon is inflated with this helium.

(i) When the pressure of helium in the balloon is 1\text{ atmosphere}, its temperature is -40^\circ\text{ C}. Find the volume of the balloon.

(ii) Eventually the helium in the balloon absorbs heat from the air around ii and returns to 20^\circ\text{ C}. Find the volume of the balloon at this time.

Write a short note on Debye's theory of specific heat.

Write a short note on Adiabatic demagnetisation.

What is the most probable distribution of speeds in a large number of molecules of a gas and indicate the steps for its derivation.

Explain the evaporation of a liquid at a temperature below its boiling point on the basis of kinetic theory of matter.

Write a short note on Clausius-Clapeyron equation.

What is an adiabatic process? Give three engineering examples of adiabatic processes which are in common use.

Define the efficiency of a Carnot Engine. An engine is designed to have an efficiency of 25\% and to absorb heat at a temperature of 267^\circ\text{ C}. Find the maximum temperature at which it can exhaust heat.

How one can obtain the various types of information about the physical conditions on the stellar surface using thermal ionization equation to interpret the stellar spectra.

Using Maxwell's equations, derive the electromagnetic wave equations for a conducting medium and solve it.

The introduction of the displacement current is one of the major contributions of Maxwell. Discuss.

Show that the steady -state energy is stored in the magnetic field.

Current is flowing in a single-turn circular coil of radius 0.1\text{ m} such that at a point 5\text{ mm} from the centre of the coil on the axis perpendicular to the plane of the coil the magnetic field is 0.1\text{ mT}. Find the current in the coil. Hence calculate the magnetic moment of the current carrying coil.

A series R-L circuit has a constant d.c. voltage V applied at the time t = 0 by closing a switch. Derive an expression for the current in the circuit.

For an R-L- C series resonant circuit, show that f_0 = \sqrt{f_1 f_2}, where f_0 is the resonance frequency and f_1, and f_2 are the half-power frequencies. Is this relation true for a parallel resonance circuit in which R, L and C are connected in parallel to each other? Explain.