UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe an operational amplifier based integrator. Using operational amplifier integrators, design a circuit to solve the following differential equation: \frac{d^2v}{dt^2}+2\frac{dv}{dt}+3v=0

Find an expression for lattice specific heat of a solid, and its low and high temperature limits. What is Debye temperature?

Distinguish between a superconductor and perfect conductor. Explain what is a Cooper pair.

Draw the device structure of a p-n junction solar cell and explain how light energy is converted into electrical energy. Draw and explain its I-V characteristics.

Describe the motion of an electron in one dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the conductors, semiconductors and insulators discriminated on the basis of band structure?

Differentiate between n-p-n and p-n-p transistors. Give their device structure and biasing circuits when used as an amplifier.

Design a transistor based Colpitt oscillator which can oscillate at 9\,\mathrm{MHz}. Explain how the oscillations are created and sustained.

Show that any arbitrary rotation axis is not permitted in a crystal lattice.

Write down the following decays in terms of quarks:

(i) \Omega^- \to \Lambda^0 + K^-

(ii) \Lambda^0 \to p + \pi^-

(iii) K^- \to \mu^- \bar{\nu}_\mu

Describe grand unification theories (GUT).

The energy levels of a hydrogen atom are given by E_n = \left(\frac{-1}{n^2}\right)R_{\mathrm{yd}} where 1R_{\mathrm{yd}} = hcR. Show that R = 1.097 \times 10^7\ \mathrm{m^{-1}}.

If K, L and M energy levels of platinum are approximately 78, 12 and 3\ \mathrm{keV}, respectively, below the vacuum level, calculate the wavelengths of K_\alpha and K_\beta lines.

Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode.

The observed vibrational frequency of CO molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of the molecule?

Two successive lines in the rotational emission spectrum of HCl molecule appear at wave numbers 83.5\ \mathrm{cm^{-1}} and 104.1\ \mathrm{cm^{-1}}. Calculate the position of the next line appearing at the higher wave number.

Find the magnetic moment of an atom in {}^3P_2 state, assuming that LS coupling holds for this case.

Obtain Zeeman splitting for sodium D-lines.

Solve the Schrödinger equation for a particle in a three-dimensional rectangular potential barrier. Explain the terms degenerate and non-degenerate states in this context.

A particle trapped in an infinitely deep square well of width a has a wave function \psi=\left(\frac{2}{a}\right)^{1/2}\sin\left(\frac{\pi x}{a}\right). The walls are suddenly separated by infinite distance. Find the probability of the particle having momentum between p and p+dp.

Establish that: hc = 1240\ \mathrm{eV\,nm} = 1240\ \mathrm{MeV\,fm}