UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What are type I and type II superconductors? Give examples. Discuss and compare Meissner effect and perfect diamagnetic behaviour for type I and type II superconductors.

What are operational amplifiers? How can it be used as an inductor? Prove it mathematically.

What are intrinsic and extrinsic semiconductors? Show that in the intrinsic semiconductors, Fermi level lies exactly in the middle of bottom of conduction band and top of valence band.

Derive an expression for lattice specific heat in Debye model. Find its low temperature limit (Debye T^3 law).

Calculate Atomic Packing Fraction (APF) for FCC and HCP structures, and show that these are the most closely packed structures.

Describe the working of a microprocessor system in block diagram. How is its performance affected in a pipelined processor?

Derive Bragg diffraction law for X-ray diffraction. Compare Laue and Debye-Scherrer methods for crystal structure determination.

Obtain an expression for the magnetic moment of a nucleus having one nucleon outside the closed core. Use this to calculate the magnetic moment of \,{}_{8}^{17}\mathrm{O} nucleus.

Assuming that the neutron-proton interaction has a square well form V(r)=-V_0\quad\text{for }r\leq b =0\quad\text{for }r>b, the ground state wave function of deuteron nucleus is given as \psi(r)=A\sin kr\quad\text{for }r\leq b =Ce^{-\gamma r}\quad\text{for }r>b where k=\sqrt{\frac{M}{\hbar^2}(V_0+W)} and \gamma=\sqrt{\frac{MW}{\hbar^2}}. Here M is the nucleon mass, W is the binding energy of deuteron and A and C are constants.

(i) Show that for a just bound state of deuteron V_0b^2=\frac{\pi^2\hbar^2}{4M}.

(ii) Explain why deuteron is a loosely bound extended structure.

A \pi^--meson at rest decays into a \mu^--meson: \pi^-\to\mu^-+\bar{\nu}_{\mu} Calculate the kinetic energy of the \mu^--meson emitted in the reaction.

Write the semi-empirical mass formula for nuclei and on its basis draw mass parabolas for odd and even isobars. What would be the most stable isobar in each case?

Which of the following elementary particle reactions/decays are allowed under various conservation laws? If allowed, write down the type of interaction and the characteristic time by which it would proceed:

(i) p + n \to \Lambda^0 + \Sigma^+

(ii) \pi^+ + n \to \Lambda^0 + K^+

(iii) p+n\to K^{+}+\Sigma^{+}

(iv) \pi^{0}\to\gamma+

(v) \bar{n}\to\bar{p}+e^{+}+\nu_e

Nuclear forces are mediated by exchange of \pi-mesons of rest mass 140\,\mathrm{MeV}. Estimate the range of nuclear forces.

The maximum energy of a positron (e^+) released in the decay of \,{}_{6}^{13}\mathrm{C} atom into a \,{}_{7}^{13}\mathrm{N} atom is 1.202\,\mathrm{MeV}. If the mass of the \,{}_{6}^{13}\mathrm{C} atom is 13.003354\,\mathrm{u}, calculate the mass of the \,{}_{7}^{13}\mathrm{N} atom.

Describe the importance of L-S and J-J coupling in atomic spectroscopy. What are experimental evidences of their existence?

Discuss the fine structure of hydrogen spectrum. How is it of importance in the astronomical observations?

What is nuclear precession? How is it used in the principle of working of an NMR?

Discuss the theory of rotational and vibrational spectra of diatomic molecules. What is the difference between fluorescence and phosphorescence?

The ground state wave function for hydrogen atom is \psi(r)=\frac{1}{\sqrt{\pi a_0^3}}e^{-r/a_0} where a_0 is the Bohr radius. Sketch the wave function and the probability density as a function of the separation distance r. Calculate the probability that the electron in the ground state is found beyond the Bohr radius.

Calculate the zero-point energy of a system consisting of a mass of 10^{-3}\,\mathrm{kg} connected to a fixed point by a spring which is stretched by 10^{-2}\,\mathrm{m} by a force of 10^{-1}\,\mathrm{N}. The system is constrained to move only in one direction.