Calculate the kinetic energy of an electron moving with a velocity of 0·999 c in the laboratory system where, c is the velocity of light.

Calculate the de Broglie wavelength of a 100 MeV electron.

Calculate the minimum uncertainty in the momentum of a proton confined to a nucleus of radius 10^-14 m. Also calculate the minimum kinetic energy of the proton.

Obtain the most probable value of r for the ground state of a hydrogen atom for which the wave function is



List all the spectral terms of a hydrogen-like atom in n 3 state.

The half-life of a radioactive element IS 26 days. Calculate the time required for 25% of the element to decay.

Explain whether the following reactions are possible:

A0 n

h e

An electron is moving with a speed of 0·85 c in a direction opposite to that of a photon. Calculate the relative velocity of the photon with respect to the electron.

A pion at rest decays into a muon and a neutrino (zero rest mass). Using the relativistic law of conservation of energy and momentum obtain the momentum of muon in terms of mn and mM

Write the time-dependent Schrodinger equation and deduce the time-independent Schrodinger equation.

Obtain the value of the commutator Ly].

State the properties of wave function.

The wave function of a particle confined in a length 0 x L is

A sin n n x/L

L Obtain the normalisation constant.

Give the selection rules for atomic transitions that yield a characteristic X-ray spectrum. Draw the approximate energy levels for the Land M shells and show all the allowed transitions. Use Moseley's law to obtain the frequency of an X-ray line when an L to K transition takes place in an Ag atom for =3.

Write down the time-independent Schrodinger equation for a one-dimensional harmonic oscillator which has an angular frequency 0). Also calculate the mean kinetic energy and potential energy of the oscillator in the ground state given by the wave function



where a mw/h

Define mass defect and binding energy. The energy released when two 2 1 H nuclei fuse together to form 4 2 He nucleus is 23·6 MeV. Given that the binding energy per nucleon in 2 1 H is 1·1 MeV, calculate the binding energy per nucleon for 4 2 He

Explain the working of Wilson cloud chamber.