UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write an essay on elementary particles with the following points: (i) Types of particles (ii) Quantum numbers (iii) Conservation laws (iv) Types of interactions

A sample shows a Raman line at 4200\text{ \AA}, with incident radiation having \lambda = 4400\text{ \AA}. Where Will the other corresponding Ramas line fall with the same exciting radiation? Will that line be stronger or weaker than the line at 4200\text{ \AA}, and why?

Give the salient features of electronic band spectra of diatomic molecules in emission. Why would absorption, spectra of the same molecules be simpler? The absorption spectrum of iodine (\text{I}_2) vapour has longest wavelength band at \lambda_0, initial band separation \Delta\lambda_0, and bands converge at wavelength \lambda_0'. Relate these data broadly to the concerned parameters of \text{I}_2 molecule.

Using de Broglie's relation, deduce an expression for energy values of a particle enclosed in a one-dimensional box. 'Free electrons' in a long-chain molecule may be treated as particles in a one-dimensional box. From a long-chain molecule of length 60\text{ \AA} deduce the lowest three energy state values in eV units.

What values of J quantum number may be observed in normal atoms of alkalis and alkaline earths ? Which of the spectral lines in alkaline earth would show normal Zeeman effect and why?

With incident X-rays of wavelength 1.618\text{ \AA} Compton scattering is observed at 90^\circ from the incident beam. Calculate. (i) the wavelength of Compton radiation, and (ii) the angle at which the recoil electron may be observed. In what state should the electrons be in Compton scattering?

Define entropy. Write a general expression for the elemental entropy change dS for 1 mole of an ideal gas. How would this become for cases where the change is (i) isothermal, (ii) isochoric, (iii) isobaric? Deduce expression for S_2 - S_1 for each of these cases, where (i) and (ii) refer to the initial and final stage entropies respectively. Constants C_p, C_v, R may be used, as needed, to express the results.

Define thermodynamic temperature of a magnetic system. Making use of Gibb's equation, derive an expression for cooling produced due to adiabatic demagnetization process. Why is the method use only after pre-cooling to a low temperature?

Under standard temperature and pressure a gas has density P = 1.29\text{mg/cc}, and the velocity (v) of sound propagation in it is 330\text{ m/s}. Calculate the number of degrees of freedom, the gas molecules may possess.

Write a short note on Thermal ionization.

Write a short note on Equipartition of energy.

Derive an expression for the specific heat of solids in Einstein model. Explain Einstein temperature T_E. Find the value of specific heat when. (i) T \gg T_E (ii) T \ll T_E (iii) T = T_E/2

Derive an expression for the pressure exerted by an ideal gas on the walls of the walls of the chamber in terms of concentration of molecules (n), gas temperature (T) and a universal constant. Specifically discuss how T comes into the picture.

Assuming Clausius inequality, show that working between two given temperatures, all the engines of irreversible cycle are less efficient than a Carnot cycle and that all reversible cycles have the same efficiency as Carnot cycle.

What Poynting vector ? Explain how the transport of electromagnetic energy is expressed quantitatively by Poynting vector.

A harmonic emf is applied to a series circuit containing resistance, inductance and capacitance. Derive the expression for the current and condition for resonance.

Give the four basic experimental laws of electro magnetics in words and in mathematical form. Explain how they are modified to obtain the Maxwell's equations. Show how these equations lead to prediction about the speed at which e.m. waves are propagated in vacuum.

An excess charge placed on an insulated conductor, resides entirely on its outer surface. Priestly checked his observation and showed that the inverse square law of force followed from it. Explain.

A series circuit consisting of 410\text{ ohms} of resistance, 81.0\ \mu\text{H} of inductance and 225\ \mu\mu\text{F} of capacitance is excited by a constant voltage amplitude generator of variable frequency. At what frequency is the maximum power delivered?

What is Fraunhofer diffraction? Under what conditions may it be observed ? Find an expression for the intensity distribution in double slit Fraunhofer diffraction, taking the result for diffraction at a single slit as given.