Determine the commutator [Lz ,Ly ] .

State Moseley’s law. Using this law, obtain the frequency of an X-ray line when an L to K transition takes place in a silver atom. Take σ = 3.

A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship emits light of wavelength λ = 4500 Å which appears blue to a passenger on the spaceship. What colour would the light appear to a person on earth?

The energy of a particle of mass m bound by a special kind of spring is

  E = p²/2m + kx⁴

where k is a positive constant. Use the Heisenberg’s Uncertainty Principle to calculate the minimum possible energy of the particle.

If σ _x, σ _y and σ_z are three components of a Pauli spin matrix σ, then show tha

[σ _x , σ _y ] = 2i σ z ; [σ _y , σ _z ] = 2iσ _x

In a circular accelerator a proton is accelerated to an energy of 10¹² eV, as measured in the laboratory frame. If the rest energy of the proton is 10⁹ eV, calculate

the speed of the proton as measured in the laboratory frame

ii) the force that must be applied by the magnets in the accelerator to keep the

protons moving at this speed in a circle of radius 1000 m.

Two events happen simultaneously in the frame S at a distance of 3.0 light years apart. In the frame S′, which is moving with a speed v relative to S, the distance between these events is 3.5 light years. Calculate (i) v and (ii) the time interval between these events in the frame S′