IGNOU PHE-11
- Modern Physics,
Latest Solved Assignment
(January 2024 - December 2024)

1. a) The mean lifetime of a muon is . If the muons are travelling with a speed of 0.95c, calculate the observed lifetime of the muon.

b) Two rockets of rest length L0 are approaching the earth from opposite directions with velocities of ±c/ 4. How long would one of them appear to the other?

c) How fast and in what direction must a galaxy S be moving, if an absorption line observed at a wavelength of 550 nm for a stationary galaxy is shifted to 480 nm for S.

d) Electrons in a television set are accelerated through a potential difference of 40 kV. Assuming that the electrons start from rest, calculate their velocity using the relativistic equation for the kinetic energy.

e) A particle of mass M, initially at rest, decays into two particles with rest masses m1 and m2 respectively. Show that the total energy of the mass m1 is:

2. a) Calculate the de Broglie wavelength of an electron which is accelerated through a potential difference of 15 kV.

b) Determine the normalization constant N for the following wave function:

where Ψ(r, t) is defined over 0 ≤ r ≤ ∞, E is the energy, Z is a constant, q is the charge of the electron, and m is the mass of the particle.

c) Estimate the minimum kinetic energy a proton confined to a nucleus of diameter 2.0×10-15 m may have.

d) Show that
[Ly, Lz ] = i h Lx

e) The normalized eigenfunction for a particle of mass m and energy E is where N and a are real constants. Given that V(x) = 0 at x = 0, determine E.

3. a) Calculate < px > for the ground state harmonic oscillator eigen function.

b) X-rays from a cobalt (Z = 27) tube have a strong K line of wavelength 1.785 Å and a weak line due to chromium impurity (Z = 24). Using Moseley’s law, calculate the wavelength of the weak line.

c) Determine the average kinetic energy of the hydrogen atom in its ground state.

4. a) A radioactive sample emits n β-particles in 2s. In next 2s it emits 0.75 n β-particles. Calculate the mean life of the sample?

b) In a nuclear reactor 235U undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 years, find the total mass of uranium required.

c) Describe the principle and working of a cyclotron. Derive an expression of the maximum kinetic energy of the particle when it reaches the outermost radius of the cyclotron.

d) Write the charge, baryon number and spin of a photon and a proton.