What are anti-Stokes lines? Do they occur in both Raman and Compton scatterings? Explain how they arise and how temperature affects their intensities.

Set up Schrodinger's equation for a one dimensional harmonic oscillator. Assuming that the solution is of the from \psi = A e^{-\alpha x^2} f(x) where \alpha is a constant and f(x) is a polynomial in x, find the energy eigen values and the ground state eigenfunction. Comment on the relation between the ground slate energy and Heisenberg's uncertainty principle.

State the important points in Bohr's theory of the hydrogen atom winch depart from classical ideas. Flow is the idea of Bohr orbits changed in Schrodinger's wave mechanics?

State de Brogue hpotliesis and use it to deduce the energy levels of a particle in a one-dimensional box. Calculate the mean energy per electron at 0\text{ K} if electrons arc enclosed in a long-chain molecule of length 50\text{ \AA}.

A system is composed of two-level atoms, the excited state 1, being 0.10\text{ eV} above the ground state 0. Find the fraction of all atoms which will be in state 1 if the system is in thermal equilibrium at temperature 300\text{ K}.

Write down the Maxwell-Boltzmann law for the distribution of speeds c of molecules in a gas. Show the distribution graphically for the temperatures T and 2T; also write down the expression for average value of c^3.

Calculate the mean free path of molecules of \text{H}_2 gas at 20^\circ\text{ C} at atmospheric pressure. Assume the molecular diameter to be 2.00 \times 10^{-10}\text{ m}.

Write a note on Dilution refrigeration.

Write a note on Enthalpy as a thermodynamic potential.

Thermal energy of a solid is given by the relation E = \int_0^{ u_m} \frac{h\nu g(\nu)d\nu}{e^{h\nu/k_B T} - 1} where $ u_m = k_B \theta_D/h$, \theta_D being the Debye temperature. Given g(\nu) = 6N h^2 \nu(k_B \theta_D)^2, deduce the expression for E for T \ll \theta_D and discuss the temperature variation of specific heat for T \ll \theta_D. \left( \int_0^\infty \frac{x^3 dx}{e^x - 1} = 2.404 \right)

Calculate the work done in compressing adiabatically 10^{-3}\text{ kg} of air initially at STP to one-half its original volume. (Give density of air at \text{STP}=1.293\text{ kg/m}^3 and \gamma = 1.4.

The components of an electrostatic field in vacuo are given as E_x = \frac{a}{r^3} + \frac{bx^2}{r^5} E_y = \frac{cxy}{r^5} E_z = \frac{fxz}{r^5} where a,b,c, and f are constants x,y,z, the rectangular cartesian coordinates and r^2=x^2+y^2+z^2. Using the basic equations obeyed by the electrostatic field in vacuo, find he relations between a,b,c and f and determine the charge density at a general point in space. Would that explain the observed field?

Starting from Biot-Savart law, calculate the magnetic field at the centre of a solenoid of length 1 meter, radius 2 cm and having 25 turns per centimeter, the current through the solenoid being 1 ampere.

Write a brief scientific note on Ferrimagnetism and ferrites.

Define solar constant and say which of the values 1.34\text{ W/m}^2, 1.34 \times 10^3\text{ W/m}^2, 1.34 \times 10^5\text{ W/m}^2 is valid for it. Calculate the total energy radiated by the sun in one second and hence the decrease in its mass per second.

A charged particle moving horizontally towards the east with a velocity of 10^{5}\text{ m/s} enters into a region where there is a horizontal electric field E intensity 100\text{ volt/cm} directed towards the north as also a magnetic field B. The particle continues to move in the same direction as before. What can you san about the field B? Is it completely determined? What will be the path, of particle if the magnetic Field be switched off?

A circular coil of wire having 100 turns and radius 10 cm is rotating about a vertical axis in its own plane uniformly at rate of 480 revolutions per minute. There is a horizontal magnetic field of intensity 0.01\text{ Wb/m}^2. The terminals of the coil are connected to the ends of an inductor having inductance 0.01 henry. Assuming that the resistance in the circuit can be neglected, find the current in the circuit at the instant the plane of the rotating coil is perpendicular to the magnetic field.

Write a note on Rayleighs criterion and resolving power of a telescope.

For a certain wave, system the angular velocity \omega and the wave vector k are related as follows: \omega = \omega_0 \left| \sin \frac{k a}{2} \right| \quad \text{for } -\frac{\pi}{a} < k < \frac{\pi}{a} Determine and plot the phase velocity and the group velocity for this system.

Two transverse sine waves each of amplitude 4\text{ mm} wavelength 2\text{m} and time period 1\text{ s} and in-phase at x=0, t=0 are travelling along the x-axis in opposite directions. Obtain the equation of the resultant wave and comment on its nature. Calculate the maximum displacement at x=2.3\text{ m}. Also locate the antinodes and nodes.