UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What is the difference between neutrino and anti-neutrino ? How is helicity of neutrino determined ?

Calculate the binding energy per nucleon for {}_2^4\text{He} and {}_8^{16}\text{O}.

(i) State the quantum numbers I_z, Y and S for the uds quarks and antiquarks. What combination of these leads to the formation of (a) proton and (b) neutron ?

If x and p_x are two conjugate variables, show that [[UNCLEAR]] duce 4 watts and the amount of energy that is released in the complete fissioning of 1\text{ kg} of {}^{235}\text{U}. (Assume energy released per fission of {}^{235}\text{U} is 200\text{ MeV}.)

Describe Stern-Gerlach experiment and discuss its implications.

Obtain an expression for the vibration-rotation energy levels of a diatomic molecule in a given electronic state. The wave numbers of the vibrational transitions occuring in HF, HCl and HI molecules are 4141.3\text{ cm}^{-1}, 2988.9\text{ cm}^{-1} and 2309.5\text{ cm}^{-1} respectively. Compare the force constants of these three molecules.

(i) Calculate the Zeeman shift observed in the normal Zeeman effect when a spectral line of wavelength 5000\text{ \AA} is subjected to the magnetic field of 0.4\text{ Wb m}^{-2}. (ii) Show that for the ground state of hydrogen atom the mean value of r is 3/2\text{ a}_0, where \text{a}_0 being Bohr radius constant.

(i) Calculate the wavelength of neutrons at a temperature of 20^\circ\text{C}. (ii) What are the term symbols for atoms with the following S (total spin) and L (total orbital) quantum numbers, S = 1/2, L = 3 ?

A hydrogen atom is in the following state : \Psi_{nlm} (r, 0) = (\sqrt{1/14}) [2\psi_{100}(r) - 3\psi_{200}(r) + \psi_{322}(r)] (i) What is the probability of finding the system in the state (200) ? (ii) What are \langle H \rangle and \langle L_z \rangle ?

Set up the time-independent Schrodinger equation for an electron moving in Coulomb field, V(r) = \frac{Ze^2}{4\pi\varepsilon_0 r} in polar coordinates. Solve the radial equation to get the energy eigen values.

Show that the entropy of one gram molecule of an ideal gas is given by S = C_p \ln V + C_v \ln p + S_0

Show that for Fermi-Dirac distribution of electrons, the number of electrons N_i in the energy state \varepsilon_i are given by N_i = \frac{g_i}{A \exp(\varepsilon_i / kT) + 1} where g_i represents the number of quantum states in the energy level \varepsilon_i. Further state under what conditions this distribution law goes over to Maxwell-Boltzmann statistics. Show by drawing curves how the Fermi-Dirac distribution function varies with the energy at T = 0 and also at the other finite temperatures.

A gas expands isothermally from the pressure p_1 and volume V_1 to the pressure p_2 and the volume V_2. Calculate (i) the change in internal energy, (ii) the change in entropy, (iii) the change in enthalpy. What will be the corresponding quantities when the gas expands adiabatically ?

Given the temperature of the Sun's surface T = 5755\text{ K}, radius of the Sun 6.9 \times 10^5\text{ km}, distance between the Earth and the Sun 1.5 \times 10^8\text{ km}. Estimate the solar constant (i.e. the energy received per sec per unit area of the Eath's surface). Assume \sigma = 5.7 \times 10^{-8}\text{ W/m}^2\text{-K}^4.

Show that the Poynting vector \bar{S} = (\bar{E} \times \bar{H}) represents the energy flow per unit area per unit time both in magnitude and direction in case of a plane electromagnetic wave.

What are the vector and scalar potentials ? Derive Maxwell's wave equations in terms of these potentials.

A point charge q is held at a distance d in front of an infinite grounded conducting plane. What is the electric potential in front of the plane ?

Find out the magnetic field inside a long solenoid carrying current i and having n turns per unit length.

What is the volume density of the charge in a region of space, where the electrostatic potential is given by V = a - b (x^2 + y^2) - c \ln (x^2 + y^2), where a, b, c are constants ?

Define the strength of a magnetic shell and calculate the magnetic potential at any neighbouring point due to this shell. Does the potential depend on the shape of the shell ?