1. Answer any five parts Obtain the velocity of a 100 MeV kinetic energy electron of rest mass 0·5/c^2 MeV. A ball of mass 92 g moves with a speed 72 ms^-l. Calculate the de Broglie wavelength associated with it. Would you be able to observe the ball's wave characteristics The average lifetime of an excited atom is about s. Calculate the uncertainty in the energy emitted. Write the electronic configuration for atoms having Z 20 and Z 31.
The wave function of a particle of mass m inside an infinite square well of width 2 L to is <img src='./qimages/12720-1e.jpg'>

Obtain expressions for A and B.
A rod of proper length 2 m measures only 1 m in a reference frame that is moving with respect to the rod. What is the speed of the moving reference frame?
Obtain an expression for the cyclotron frequency.

2. Answer any one part Derive an expression for the relativistic force law. Show that in the absence of external forces, relativistic momentum is conserved.
Show that the Lorentz transformation reduces to the Galilean transformation for v«c.

3. Answer any one part Discuss the statistical interpretation of wave function. Define Hermitian operator and show that its expectation value is real. If two non-commuting operators A and B commute with their commutator show that n where n is an integer. Hence obtain the value of px].

4. Answer any one part Write down the Schrodinger equation for a particle confined in a potential of the form <img src='./qimages/12720-4a.jpg'>

Write down the boundary conditions and obtain the general solution in all three regions.
State Hund's rules. Using Hund's rules obtain the spectral terms and ground state of the He atom.

5. Answer any one part
Define half-life period of a radioactive material. How long does it take for 60% of a sample of radon to decay Half-life of radon is 3·8 days.
Define multiplication factor. Obtain an expression for the time behaviour of a neutron chain reaction.

Physical Constants:

h 6·626 x 10^-34 Js

me =9·109 x 10^-31 kg

mp 1·672 x 10^-27 kg