UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain the basic distinction between a perfect conductor and a superconductor.

Mention the conservation law violated in the following elementary particle reactions:

(i) \mu^- \rightarrow e^- + u_o

(ii) n \rightarrow p + e^-

(iii) k \rightarrow \pi^o + \pi^o

(iv) e^- + e^- \rightarrow \gamma

Explain the phenomenon of nuclear fission and obtain the expression for fissionability parameter. Show that the critical value of the fissionability parameter is 50.

Explain the physical meaning of each term, write semiempirical mass formula for a nucleus. Find the value of atomic number of most stable nucleus for a given mass number A.

Draw the energy level diagram and show the allowed transitions for Zeeman pattern for n = 3_1 \rightarrow 2_0 transition line of a hydrogen atom placed in a uniform magnetic field of 1\text{ kg}. Calculate the doublet splittings.

Draw the expression for Lande's g-factor for LS coupled state.

Write in brief the differences between the IR active and Raman active bands.

Explain the origin of continuous X-rays. Compare the phenomenon with photoelectric effect.

Write down the time independent Schrodinger equation for the x < 0 and x > 0 in case of a step potential V(x) = \begin{cases} 0, & x < 0 \\ V_o, & x > 0 \end{cases} Discuss the solutions thus obtained for the case E > V_o. Obtain the following relations. |R|^2 = \left(\frac{1-\mu}{1+\mu}\right)^2 \quad \text{and} \quad \frac{k}{k_o}|T|^2 = \mu \left(\frac{2}{1+\mu}\right)^2 There \mu = \sqrt{1 - \frac{V_o}{E}}, R and T are reflection and transmission coefficients respectively. Other symbols have their usual meaning. Plot the behaviour of |R|^2 and k/k_o |T|^2 with \mu.

Using Heisenberg Uncertainty principle, find the ground state energy and Bohar radius of hydrogen atom.

Using a Carnot cycle obtain the Clausius Clayperon equation. At normal pressure the ratio of densities of ice and water is 9 : 10. When 1 kilo-mole of ice is melted, the change in entropy is 22.2 \times 10^3\text{ JK}^{-1}. If the external pressure is increased by 10^5\text{ Nm}^{-2}, what will be the change in the melting point of ice?

A gas at a pressure P and temperature T has a density \rho. The velocity of sound in this gas is v. Obtain an expression for the degrees of freedom of the gas molecules. At STP, \rho = 1.3\text{ kg m}^{-3} and \text{v} = 330\text{ ms}^{-1}. Calculate the degrees of freedom.

Obtain an expression for the mean free path. Mention the correction introduced by Maxwell. Calculate the value of Avogadro's number if the mean free path of nitrogen molecules at STP is 6.85 \times 10^{-8}\text{ m}. The molecular diameter is 3.5\text{ \AA}.

Write a short note on Law of equipartition of energy.

Write a short note on Debye theory of specific heat of solids.

What is population inversion ? Mention the methods of achieving population inversion. Explain the concept of negative temperature.

Show the distribution of velocities for temperatures \text{T}_1, \text{T}_2 and \text{T}_3 (\text{T}_1 > \text{T}_2 > \text{T}_3) of gas molecules according to the Maxwell-Boltzmann law. Using this law prove that the most probable velocity is \sqrt{2/3} times the root-mean-square velocity.

Define Helmholtz free energy F and Gibbs free energy G. What does decrease in F and G signify ? Show that the internal energy U at temperature T is given by U = F - T \left( \frac{\partial F}{\partial T} \right)_V

Using Gauss law find the electric field inside a cylindrical capacitor and hence derive the expression for its capacitance. Find the dielectric constant of the material inside a 50\text{ mm} long capacitor of capacitance 40\ \mu\text{F} having inner conductor of radius 1\text{ mm}, outer conductor of radius 10\text{ mm}. Which of the materials has such a value of the dielectric constant ?

The self inductance of primary and secondary coils of a R.F. transformer is 10\text{ mH} each. When the coils are connected in series self resonating frequencies are 132.6\text{ kHz} and 108.3\text{ kHz}. Calculate the mutual inductance between the coils and the winding capacitance.