State how Rutherford's experiments on alpha scattering by thin gold foils established that
(i) the positive charge in an atom is confined to a nucleus of radius far less than the atomic radii, and
(ii) the Coulomb law is valid down to such small distances. Why do the electrons not participate in the interactions appreciably?
What is a P.N. junction? Describe with energy level diagram the formation of double layer of charges which generates a potential difference (V) across, the junction. Hence show that the capacitance of the double layer. C=KV^{-1/2}, where K is a constant. State some practical use of this relation between C and V.
What is alpha decay? Deduce an expression for the potential barrier penetrability for alpha particle in a nucleus. Show how the penetrability is related to the alpha decay constant.
Discuss briefly the three types of interaction between elementary particles, and explain the relative strength of the various kinds of interaction between elementary particles.
What is deuterium? Is deuterium the same as hydrogen? Hon can you obtain deuteron from deuterium? Calculate the frequency of the oscillating potential applied to a cyclotron as to accelerate deuterons when the magnetic induction has a constant value of 2.5\text{ Wb/m}^{2}.
Discuss the origin of line spectrum and continuous spectrum of X-rays. What is Duance and Hunt limit for X-ray spectrum? Can you obtain the value of 'h' (Planck's const.) precisely from a knowledge of the Duane and Hunt limit. An X-ray tube is operated it 20\text{ kV}. Determine the wavelength limit of continuous X-rays.
State and explain Pauli's exclusion principle. Estimate the total number of electron states in a many electron atom for a given principal quantum number n.
Derive Schrodinger equation for a linear harmonic oscillator, and determine its eigenvalue and eigenfunctions. Discuss the significance zero point energy.
An electron moves with a speed of 10^{3}\text{ m/sec}, accurate to 0.008\%. Find the accuracy with which the position of the electron can be located.
State and explain Einstein's photoelectric emission equation, Distinguish between extrinsic and intrinsic photo electric effects. What is "quantum field"? On what factors does the quantum yield depend?
A Carnot’s engine is made to work between 0^\circ\text{C} and -200^\circ\text{C}. Calculate us efficiency. Derive the expression you use of calculation.
Write a short note on Production of low temperature using adiabatic demagnetisation.
A volume of one gm-mole of an ideal gas expands isothermally to four times its initial volume. Calculate the change in its entropy in terms of gas constant.
Write a short note on Negative temperature.
A gas possesses a Maxwellian velocity distribution function. Show that the fraction of molecules in a given volume that possess a velocity (+v_x) in one direction only and whose magnitude is greater than some selected value v_o is \int_{v_o}^{\infty} f(V_x) dv_x = \frac{1}{2} \left[ 1 - \frac{1}{\sqrt{\pi}} \text{erf} \left( \frac{1/4 m v_o^2}{KT} \right)^{1/2} \right] Symbols have their usual meanings.
Find the temperature at which root mean square velocity of nitrogen molecules in earth’s atmosphere equals the velocity of escape from the earth’s gravitational field. Mass of N_2 atom = 23.24 \times 10^{24}\text{ g}. Mean radius of earth = 6370\text{ km}.
Calculate the mean free path of helium atoms at NTP, the coefficient of viscosity being 190 \times 10^{-7}\text{ kg m}^{-1}\text{ s}^{-1}. 1\text{ atmospheric pressure} = 0.076 \times 136 \times 10^3 \times 9.81\text{ Nm}^{-2}.
Discuss briefly the various ways of modulation of electromagnetic waves for the purpose of communication through radio and television.
Write down the expression for energy distribution of a black- body radiation at temperature T and deduce Wien’s displacement law.
Derive an expression for the Poynting's vector and explain us significance A light source (one kilowatt) is radiating energy uniformly. Determine the intensity of the electric field at a distance of one metre from the sources.