Given a rough sketch showing the variation of binding energy per nucleon with mass number of nuclei and hence explain how an enormous amount of energy is emitted in uranium fission. How it is that two blocks containing uranium of mass number 235 may remain quiet when separated but may explode when brought together into a single block? Explain the function of a moderator in a nuclear reactor.

Explain why a cyclotron is used for accelerating particles like Protons and deuterons but is not used for accelerating electrons. Mention the advantages and disadvantages of a linear accelerator compared to cyclic accelerators like the cyclotron.

Write an explanatory outline of thermal ionization of atoms and the spectra of stars, specifying what information we get from the latter.

What is meant by L-S coupling? Deduce the spectral terms which can arise from 3p4p electron configuration. Would all these terms exist in 3\mathrm{p}^2 configuration? Write expressions for the square of angular momentum for L=2 and also for the component of angular momentum for \mathrm{m}_j=2 as given by quantum mechanics.

What did the Stern-Gerlach experiment establish? Explain your answer. Would the experiment succeed if it were performed with a beam of free electrons?

In a hydrogen atom the electron is replaced by a muon whose mass is 200 times that of the electron and charge is the same as that of the electron. Calculate the Ionization potential on the basis of Bohr's model.

In a Compton scattering the angle of scattering was 30^\circ while the angle of recoil was 60^\circ. Calculate the energy of the incident photon taking the formulae you use as given.

Photoelectron are liberated by ultraviolet light of wavelength 3000\text{ \AA} from a metallic surface for which the photoelectric threshold is at 4000\text{ \AA}. Calculate the De Broglie wavelength of electrons emitted with maximum kinetic energy.

Write down Schrodinger's equation in one-dimension and explain the significance of the eigenvalues and eigenfunction of this equation. Solve the Schrodinger's equation if the potential function V is given as V(x) = V_e(\text{a constant}) for |x| < a/2 = 0 for |x| > a/2 State the boundary conditions you use along with their justification (In the solution consider particles incident from one side only.) If he total energy F < V_0 show that there is an important difference with classical mechanics. Explain with the help of the uncertainty principle that E < V_0 does not mean that the kinetic energy is negative.

Use the Maxwell relation \left(\frac{\partial s}{\partial v}\right)_T = \left(\frac{\partial p}{\partial T}\right)_v to show that the internal energy, U, of a thermodynamic system depends on the volume according to the expression \left(\frac{\partial U}{\partial v}\right)_T = T\left(\frac{\partial p}{\partial T}\right)_v - p where the symbols have their usual meanings. Use this result to derive Stefan's law for a black-body radiator.

Obtain the Clausius-Clapeyron equation. \frac{dp}{dt} = \frac{L}{T(v_2 - v_1)} where the symbols have their usual meanings

Explain, using the kinetic modal, why peaks in the curves showing Maxwell distribution of molecular speeds move towards higher speed at higher temperature.

Write a short note on Thermodynamic potentials.

How much faster does a cup of coffee cool when it is at 100^\circ\text{ C} than when it is at 30^\circ\text{ C}, if room temperature is 20^\circ\text{ C}?

1 kg of ice at 0^\circ\text{ C} is melted and converted to water at 0^\circ\text{ C}. Compute the change in entropy.

Three point charges are situated at the vertices of an equilateral triangle (one at each vertex); Show that the electric intensity vanishes at the centroid if and only if the charges are equal in magnitude and of the same sign.

Write down Maxwell's equations in vacuum. Show that in the source-free case, both the electric and magnetic vectors obey wave equations of identical form and considering a plane wave solution, prove dial the electric and magnetic vectors and the direction of propagation are mutually perpendicular. Show further that there is a propagation of energy given by the Poynting vector.

An electromotive force p_0 \sin pt + E_1 \sin 2 pt is impressed on a circuit containing an inductor and a resistor. Set up the differential equation obeyed by the current and show that in the steady state the current comprises two sinusoidal terms. Calculate the average power dissipation in the circuit. What is the difference, if any, between a varying current and an alternating current?

Two point charges each of magnitude +2\text{ millicoulomb} are at A and B in front of a infinite conducting plane which is grounded. The line OAB is the perpendicular to time plane with the point O on the plane. If \mathrm{OA}=1\text{ m} and \mathrm{OB}=2\text{ m} calculate the force on the charge at A

Write a short note on Wien's Law.