A vessel of mass 10^7\text{ kg} is gyrostabilised by a uniform circular disc of mass 5\times 10^4\text{ kg} and radius 2\text{m} which rotates at 15\text{ rev/sec}. What is the angular momentum of the stabilizer ?

What is the momentum of a proton having kinetic energy 1\text{ BeV} ? The energy equivalent to proton rest mass is 0.938\text{ BeV}.

Define Fermi energy. Show that the Fermi level lays half-way between the top of the valence band and the bottom of the conduction band of an intrinsic semiconductor. Explain why an extrinsic semiconductor, such as an N-type crystal, has more free electrons than holes but is found to be electrically uncharged.

Write a shout note (about 200 words) on super-conductors and the nature of revolution that may come up if superconductors with critical temperature well above the room temperatures are developed.

Draw the circuit diagrams suitable for measuring the voltage amplification of a triode valve with the following methods of connection: (a) Common cathode (b) Common grid (c) Common anode. Write down, without proofs, the expression for amplification in each case in terms of \mu and the relevant resistance values. Which of the three methods is usually employed in high frequency circuit practices and why ?

Write a brief note (about 200 words) on parity violation

Some amount of a radioactive substance (half-life=30\text{ days}) spread inside a room and consequently the level of radiation becomes 50 times the permissible level for normal occupancy of the room. After how many days the room would be safe for occupation?

Schematically draw the binding energy cone for atomic nuclei defining the parameters used. Explain how it indicates release of energy on fission of some nuclei and on fusion of other. Could one of these processes be the origin of solar energy?

Interpret the nuclear process described by the equation _{92}U^{235} + _{0}n^{1} \rightarrow _{92}n^{236} \rightarrow _{56}Ba^{141} + _{36}Kr^{92} + 3 _{0}n^{1} + Q The products of this kind of reaction vary widely, but the average Q is found to be 180 MeV. Compute the consumption rate of U^{235} per year if power generation is to be an average 100 MW. (Take efficiency = 1).

The series limit due Balmer series for hydrogen is given by 3.65 \times 10^{-5}\text{ cm.} and an element is found to give k-series wavelength down to 10 \times 10^{-10}\text{ cm,} Find the atomic number of the element.

In observing the Raman spectrum of a sample, using 2537\text{ \AA} as the exciting line, one gets a Stokes line at 2683\text{ \AA}. Deduce the Raman shift in \text{cm}^{-1} units. What information does it give? Compute the wavelength, in \text{\AA} units, for the corresponding Stokes and anti-Stokes tines if the exciting line is 5461\text{ \AA}.

Define Compton wavelength for an electron. Calculate in electron-volts the photon energy corresponding to radiations of the Compton wavelength. What light does the Compton effect throw on the nature of X-rays?

Compare the energy of a photon with that of a neutron when both are associated with wavelength of 1\text{\AA}.

State and explain Heisenberg uncertainty principle using situations where one of the parameters is (a) liner distance x (b) angle \phi (c) energy E. Prove that according to the principal the presence of an electron within the atomic nucleus is not possible.

Explain thermoionic emission. Discuss Richardson's derivation of the thermionic equation and show how the velocity distribution of the emitted electrons corroborates Fermi-Dirac distribution, Mention a few modern thermoionic emitters.

Find the density of hydrogen gas at temperature of 25^\circ\text{C} and pressure of 750\text{ mm Hg}.

For a Maxwell-Boltzmann gas derive the expression for (i) the most probable speed (ii) the average speed and (iii) the root mean square speed and find their ratio (taking the most probable speed as unity).

Write a note on Production of temperature below 1 K.

Starting from van der Waals equation for a gas, deduce expressions for its critical temperature, critical pressure and critical volume.

Mention some experiment which establishes that electrons in metals obey Fermi-Dirac statistics and justify your answer in some detail.