UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe the broad features of characteristic X-rays spectra and discuss how these have been accounted for

Calculate the force constant for the coupling between H and Cl, given that the fundamental frequency of H^1 Cl^{35} molecule is 8.7 \times 10^{13}\text{ Hz}. Assuming the force constant of H^2 Cl^{35} to be the same as that of H^1 Cl^{35}, calculate the vibration frequency of H^2 Cl^{35}

Draw the energy level diagram showing the Zeeman splitting of {}^2P_{1/2, 3/2} and {}^2S_{1/2} levels in a weak magnetic field. Give the selection rules and the resulting transitions, between the sub-levels. Does the magnetic interaction lift the degeneracy of the level only partially or wholly?

Explain why in optical absorption discrete lines are observed but X-ray absorption shows continue with edges. Why the emission and absorption spectra of X-rays are not identical ?

The atomic number of Na is 11. (i) Write down the electronic configuration for the ground state of the Na atoms (ii) Give the standard spectroscopic notation for the ground state. (iii) The lowest frequency in the absorption spectrum of Na is a doublet. What are the spectroscopic designations of the pair of energy levels to which the atom is excited as a result of this absorption process? (iv) What is the mechanism responsible for the splitting between the pairs of energy levels? (v) Does the level corresponding to the higher value of j lie lower or higher?

Derive an expression for the Compton shift (\Delta\lambda) and show that it is independent of the wavelength of incident radiation. Establish parallelism between Compton and Raman scattering

An infinite well potential is V(x) = \begin{cases} 0, & -a/2 < x < a/2 \\ \infty, & x < -a/2, \quad x > a/2 \end{cases} Solve the time independent Schrodinger equation and find the closed form expressions for the eigenvalues and eigenfunction of potential. Give a schematic representation of the first three energy levels and corresponding wave functions and probability distribution functions. Show that the zero-point energy is in accord with the uncertainty principle.

Prove the latent heat equation \left(\frac{\delta L}{\delta T}\right)_{sv} - \frac{L}{T} = C_s - C_p where C_s and C_p are specific heats of saturated vapour aid the liquid in contact with it respectively. Given the following values referring to 1\text{ gm} of water at 100^\circ\text{C} L = 539\text{ Cal/gm} \left(\frac{\delta L}{\delta T}\right)_{sv} = -0.64\text{ Cal K}^{-1}\text{ gm}^{-1} C_p = 1.01\text{ Cal K}^{-1}\text{ g}^{-1} Calculate C_s. Explain why the specific heat takes a negative value.

Write a short note on Clausius Calpeyron equation.

Write a short note on Brownian motion.

The molecules of a gas are made up of four non coplanar atoms. Enumerate the translational, vibrational and rotational degrees of freedom of each molecule. Hence obtain the specific heat at constant volume C_V of the gas. Does the value so obtained agree with the observed value in general? If not why?

Prove that \int_A^B \delta Q / T evaluated along a reversible path joining the states A and B does not depend on the path chosen. Hence define the entropy function S. Calculate the entropy change in an ideal gas undergoing a state change from (V, P) to (2V, P/2) for three suitably chosen different paths and show that the result turns out to be the same all the cases.

State the basic assumptions of Debye theory of specific heat of solids and write the expression for C_V derived from this theory. Show that this expression yields the famous T^3 law of specific heat at low temperature. Discuss the extent to which the theory agrees (or disagrees) with observation on specific heat through the variation of the Debye characteristic temperature \Theta_D with temperature, in general.

The two atoms is a molecule of a gas interact according to the potential \phi(r) = \frac{A}{r^6} + \frac{B}{r^{12}} r being the separation distance between the two atoms. Determine A and B if the potential energy \phi(r) = \phi(r_0) at the equilibrium separation r = r_0.

Determine the energy of attraction between an electric dipole and a plane conducting surface at zero potential.

A series LCR circuit has L = 20\text{ mH}, C = 0.5\ \mu\text{F} and R = 10\,\Omega. The circuit is driven by an alternating emf with amplitude 200\text{ V}. Calculate (i) resonance frequency (ii) the current at resonance frequency (iii) Q value and (iv) half width of the resonance current.

Derive the wave equations for \vec{E} and \vec{B} and solve one of these for plane wave propagation in an unbounded, homogenous dielectric medium. Further show that in a plane wave (\vec{E}, \vec{B}, \vec{K}) form a mutually orthogonal right-handed system.

A travelling electromagnetic wave is described by the equation. E_x(z, t) = 0.5 \cos (20t - 2z) Determine: (i) Speed of the wave, v (ii) Wavelength. \lambda (iii) Time period, T (iv) Direction of propagation

Two coils are connected in series and their total self inductance is 4.40 mH. When one coil is reversed, the total self-inductance is 1.60 mH. All the flux due to the first coil links the second coil, but only 40% of the flux due to the second coil links the first coil. Find the self-inductance of each of the coils and their mutual inductance.

A potential difference with a frequency of 50 cycles per second is applied to a coil of resistance 1 k ohms and inductance 2H. Calculate the power factor of the circuits.