UPSC Physics Optional PYQs (CSE & IFoS)PYQs

The number of alpha particles emitted per gm of radium each second is 3.71 \times 10^{10}. Atomic weight of radium is 226. Calculate its half-life in years.

Give an account of Pauli's exclusion principle. Show how it leads to the building up of the Periodic Table of elements. The description must particularly emphasize shell structure and the placing of alkali metals, halogens and inert gases in the Periodic Table.

Write a brief note (about 200\text{ words}) on X-ray absorption edges.

Find the Fermi energy in eV of electrons in sodium({}_{11}^{23}\text{C Na}), given its density to be 0.97\text{ g cm}^{-3}. Treat the electrons as a free gas.

The stopping potential for electrons emitted from a metal, due to photoelectric effect, is found to be 1\text{ volt} for light of 2,500\text{ Angstrom units}. Calculate the work function of the metal in electron volts.

Construct solutions of Schrodinger equation for a particle moving the potential \begin{aligned} V(x) &= 0 & \text{for } x < 0 \\\\ &= V_0 & \text{for } x > 0 \end{aligned} Deduce the reflection coefficient for particles incident from left to right (i.e. from negative to positive x regions) with energy E > V_0. Do you expect any reflection for particles of same energy incident from right to left? Explain qualitatively.

Calculate the root-mean-square speed of smoke particles of mass 5\times 10^{-14}\text{ g} in air 0^{\circ}\text{C}.

Write a note on Super fluidity, explaining why it is a quantum phenomenon.

Write a note on Thermal ionization and its application.

Write a note on Brownian motion and the importance of its study.

Consider the following equation of state for a gas: P = \frac{RT}{v-b} - \frac{a}{Tv^{2}} where a and b are constants and other symbols have their usual meaning. Find the values of P_{c}, T_{c} and V_{c} in terms of a and h at the critical point.

Write a note on Physical significance of each of the four Maxwell's equation.

Write down the expression for the energy distribution of a black body radiation at temperature T and deduce. Wien's displacement law. \frac{h\omega_{m}}{kT} = \text{const.} Taking the constant to be equal to 3-\epsilon, where \epsilon is small (so that \epsilon can be neglected in comparison to 1). Find the value of \epsilon.

The parallel plates of a capacitor have an area of 2000\text{ cm}^2 each and are 1\text{ cm} apart. They are originally at a potential difference of 3,000\text{ volts}. When a dielectric is introduced covering the whole space between the plates, the potential difference becomes 1000\text{ volts}. Calculate the capacitance of the capacitor before and after insertion of the dielectric. What is the dielectric constant of the dielectric?

Obtain an expression for the impedance of an LCR circuit for the following cases:

L, C and R in series. Discuss the factors that determine sharpness of resonance in these cases.

L and R in series and C in parallel to them.

Two cells of emf 2 volts each and internal resistance 2 ohms rich are connected in parallel with each other and with a load resistance. Calculate the maximum power that can be dissipated in the load.

Calculate the power radiated by a tungsten filament 10 cm long and 0.010 mm in diameter, when it is heated to 2,500 K in an evacuated bulb. Assume that the filament radiates at 30% of the rate of a black body at the same temperature.

Two homogeneous isotropic dielectric media have a common plane boundary and ale otherwise infinite in extent. An electromagnetic wave is incident on the boundary. Establish the laws of reflection and refraction.