PYQ Bank

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

Describe in detail one experiment for the detection of neutrino.

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

(i) Write the Weizsacker mass formula and explain the significance of various terms. (ii) Determine the amount of {}_{84}^{210}\text{Po} necessary to provide a source of \alpha-particles of strength 5\text{ mC}_i. The half-life of {}_{84}^{210}\text{Po} is 138\text{ d}.

(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 ?

(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.

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.

Describe Stern-Gerlach experiment and discuss its implications.

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.

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 ?

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.

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

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 ?

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

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 ?

A network PQRS is connected as shown in the figure below. Apply Kirchhoff's law and show that the current flowing through the 20\ \Omega resistor PR is 0.029 A.

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 ?

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.

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