UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What do you understand by length contraction? Calculate the percentage length contraction of a rod moving with a velocity 0.8c in a direction at 60^\circ with respect to its own length.

A rocket starts vertically upwards with speed v_0. Then define its speed v at a height h in terms of v_0, h, R (radius of Earth) and g (acceleration due to gravity on Earth's surface). Also calculate the maximum height attained by a rocket fired with a speed of 90% of the escape velocity.

The angles between the tetrahedral bonds of diamond are the same as the angles between the body diagonals of a stack of neighbouring cubes having common edges and not faces. Use vector analysis to find the value of the angle.

Consider a face-centred cubic lattice of side a. Deduce –

(i) The primitive translation vectors;

(ii) The volume of the primitive cell;

(iii) The reciprocal primitive translation vectors;

(iv) The volume of the reciprocal lattice

A silicon semiconductor sample at T=300\,\mathrm{K} having cross-sectional area of 0.5\,\mu\mathrm{m}^2 has a pentavalent donor doping profile given by C(x)=5\times10^{16}e^{-x/L_n}\,\mathrm{cm^{-3}}. Given, the mobility of the electrons in the sample is 1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the diffusion length of the electrons, L_n, is 4\,\mu\mathrm{m}. Calculate the diffusion current in the sample at distance x=2\,\mu\mathrm{m}.

Sketch the cross-sectional structure of an enhancement mode MOSFET and explain its principles of operation with the help of its output characteristics.

A 5\,\mathrm{cm^2} Ge solar cell with a dark reverse saturation current of 2\,\mathrm{nA} has solar radiation incident upon it, producing 4\times10^{17} electron-hole pairs per second. The electron and hole diffusion lengths are given to be 5\,\mu\mathrm{m} and 2\,\mu\mathrm{m}, respectively. Calculate for the cell of the following:

(i) The short-circuit current

(ii) The open-circuit voltage

A silicon semiconductor sample is doped with 6\times10^{16}\,\mathrm{cm^{-3}} of aluminium and 7\times10^{15}\,\mathrm{cm^{-3}} of phosphorus atoms. Given at T=300\,\mathrm{K}, the intrinsic carrier concentration, n_i=1.5\times10^{10}\,\mathrm{cm^{-3}}; the band gap, E_g=1.1\,\mathrm{eV}; the electron mobility, \mu_n=1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the hole mobility, \mu_p=480\,\mathrm{cm^2\,V^{-1}\,s^{-1}}. Determine in the sample of the following:

(i) The type of the semiconductor, n or p

(ii) The hole carrier concentration

(iii) The electron carrier concentration

(iv) The position of the Fermi level in the sample with respect to the bottom of the conduction band

(v) The conductivity of the sample

Deduce the Miller indices of the close-packed planes of atoms in the f.c.c. lattice.

Explain the origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.

Given that the single particle energy separation between 1d_{5/2} and 1d_{3/2} in {}^{17}\mathrm{O} is 5\,\mathrm{MeV}. Calculate the strength of spin-orbit interaction. It is observed that 1d_{5/2} level is lower than 1d_{3/2} level.

Stable light nuclei have equal number of protons and neutrons, whereas heavy nuclei have excess of neutrons. Explain why.

Why is it not possible to detect the parity violation in weak interaction by observing only the beta decay rate? Justify your answer.

Explain the various methods of finding the size of the nucleus. How will you determine the nuclear radius from the observation of beta rays resulting from nuclear transition when the initial and final nuclei are mirror nuclei?

Assuming equal masses for up (u) and down (d) quarks, find the ratio (\mu_n/\mu_p) of the magnetic moments of neutron and proton.

For a system consisting of one proton and one neutron (not necessarily a deuteron), write down the various possible states specifying clearly its isospin, spin and orbital quantum numbers.

What is Franck-Condon principle? Discuss the intensity distribution in the vibrational electronic spectra of a diatomic molecule on the basis of this principle.

What is Lamb shift? Discuss its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom.

Why are Raman active vibrations and IR vibrations in \mathrm{CO}_2 molecule complementary to each other?

Estimate the size of hydrogen atom and the ground state energy from the uncertainty principle.