UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Derive diffraction conditions using reciprocal lattice concept. What are these conditions known as ?

Show that the Fermi level shifts upward, closer to the conduction band in an n-type semiconductor and shifts downward, closer to the valence band in a p-type semiconductor.

With a neat circuit diagram, explain the working of Wien-Bridge oscillator.

Explain classical theory of diamagnetism. Show that the susceptibility of diamagnetic substances is directly proportional to the atomic number. Why all the electrons in an atom contribute to diamagnetism ?

Derive an expression for the specific heat of a solid based on the Debye theory and show how it agrees with the experimental values. What is the most important assumption of Debye theory in comparison to Einstein theory ? Is there any drawback of Debye theory ?

(i) Determine the input and output impedances of the amplifier in given figure. The op-amp datasheet gives Z_{\text{in}} = 2\text{ M}\Omega, Z_{\text{out}} = 75\ \Omega and A_{\text{ol}} = 200,000 (open loop voltage gain). (ii) Find the closed-loop voltage gain.

What do you understand by nuclear forces ? Explain meson theory of exchange forces.

How could you establish that \nu_e and \bar{\nu}_e are two different particles ?

Establish the Rutherford's scattering cross section formula for \alpha-particle by considering the standard assumptions and symbols.

What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors.

What is the age of a fossil that contains 6\text{ g} of carbon {}^{14}\text{C} and has a decay rate of 27\text{ decays per minute} ? Given : Ratio \frac{{}^{14}\text{C}}{{}^{12}\text{C}} = 1\cdot 3 \times 10^{-13}, Half life (T_{1/2}) of {}^{14}\text{C} = 5730\text{ yrs}.

(i) K^+ \longrightarrow \Pi^+ + \Pi^+ + \Pi^- (ii) \Pi^+ + p \longrightarrow \Pi^+ + \Pi^+ + n (iii) \Pi^+ + p \longrightarrow \Delta^{++} \longrightarrow \Pi^+ + p (iv) \Sigma^\circ \longrightarrow \lambda^\circ + \gamma (v) \Sigma^+ \longrightarrow \lambda^\circ + e^+ + u_e (vi) K^- + p \longrightarrow K^+ + K^\circ + \Omega^- (vii) \Pi^\circ \longrightarrow \gamma + e^+ + e^- (viii) \Sigma^- \longrightarrow n + e^- + \bar{\nu}_e (ix) \lambda^\circ \longrightarrow p + e^- + \bar{\nu}_e (x) e^+ + e^- \longrightarrow \gamma + \gamma Name the interactions via which the above nuclear decays occur :

What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.

A beam of hydrogen atoms emitted from an oven at 400\text{ k} is sent through a Stern-Gerlach experiment having magnet of length 1\text{ m} and a gradient field of 10\text{ tesla/m}. Calculate the transverse deflection of an atom at the point where the beam leaves the magnet.

What is Lande's g factor ? Evaluate the Lande's g factor for the {}^3P_1 level in the 2p3s configuration of the {}^6\text{C} atom. Also calculate the splitting of the level when the atom is placed in an external magnetic field of 0\cdot 1\text{ tesla}.

What is Raman effect ? Explain Quantum theory of Raman effect and Rotational Structure of a Raman spectrum.

If an atom is placed in a magnetic field of strength 0\cdot 1\text{ weber/m}^2, then calculate the rate of precession and torque on an electron with l=3 in the atom. Given that the magnetic moment of the electron makes an angle of 30^\circ with the magnetic field.

What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?

A particle constrained to move along x-axis in the domain 0 \le x \le L has a wave function \psi(x) = \sin \left( \frac{n \pi x}{L} \right), where n is an integer. Normalize the wave function and evaluate the expectation value of momentum of the particle.

By assuming the nucleus as a cubical box of length equal to the nuclear diameter 10^{-12}\text{ cm}, calculate the kinetic energy of the highest level occupied nucleon of iron-56 nucleus.