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.
Write a note on Production of temperature below 1 K.
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).
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.
Mention some experiment which establishes that electrons in metals obey Fermi-Dirac statistics and justify your answer in some detail.
Derive the expression for the energy distribution of particles according to Bose-Einstein statistics.
Find the density of hydrogen gas at temperature of 25^\circ\text{C} and pressure of 750\text{ mm Hg}.
Starting from van der Waals equation for a gas, deduce expressions for its critical temperature, critical pressure and critical volume.
Write down Maxwell s equations for the electromagnetic field in Free space and show that \vec{E} satisfies the wave equation. Hence obtain the expression for the velocity of e.m. waves in free space.
Obtain an expression for the force exerted on unit volume of a paramagnetic substance in a non-uniform magnetic field. How could you experimentally distinguish and diamagnetic and paramagnetic substance?
Derive an expression for the mean energy \varepsilon of a Planck oscillator in thermal equilibrium with the surroundings. How does the ratio h\nu / kT vary as the temperature T varies from \leqslant h\nu / k to \leqslant h\nu / k, the symbols having the usual meanings?
In an oscillatory circuit L = 0.30\text{ henry} and C = 1.2 \times 10^{-6}\text{ F,} determine the value of maximum resistance so that the circuit may remain oscillatory.
What is dielectric susceptibility? Describe how you can determine the radius of an atom from the measurement of the dielectric constant of a gas. A parallel plate condenser consists of two plates of area 400\text{ sq. cm.} each separated by a sheet of material of 0.10\text{ mm} thickness. Find the capacity in microfarads when the dielectric constant of the material is 5.0.
Write a note on Anomalous dispersion.
Fourier analyse the step-function f(x) = 1 \text{ for } 0 < x < \pi = -1 \text{ for } \pi < x < 2\pi and hence prove that 1 + \frac{1}{9} + \frac{1}{25} + \frac{1}{49} + \dots = \frac{\pi^2}{8}
State Huygen's principle and on its basis establish Snell's law of refraction of light. How does the result differ from what Newton's Corpuscular theory gave?
Plane waves pass through a slit whose plane is parallel to the wave fronts. Obtain an expression for the angular spread of the central maximum due to diffraction, and critically comment on the result.
Monochromatic light of wavelength 6.56 \times 10^{-7}\text{ m} falls normally on a grating 2.00\text{ cm} wide. The first order spectrum is produced at an angle of 18^\circ15' from the normal. Deduce the total number of lines in the grating.
A beam of light of wavelength 5.82 \times 10^{-7}\text{ m} falls normally on a glass wexge with the wedge angle of 20''. If the refractive index of glass is 1.5, find the number of dark interference fringes per centimetre of the wedge length.
The equation for displacement of point on a damped oscillator is given by x - 5e^{-0.2t} \sin \frac{\pi}{2}t \text{ metre} Find the velocity of the oscillating point at t = \frac{T}{4} and T_p where T is the time-period of the oscillator.
