UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Predict the spin and parity of ground states of the following nuclei on the basis of shell model:

(i) {}_{8}\mathrm{O}^{15}

(ii) {}_{8}\mathrm{O}^{16}

(iii) {}_{17}\mathrm{Cl}^{38}

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega = 41\,A^{-1/3}\,\mathrm{MeV}.

State the basic assumption of single particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of a three-dimensional spherical harmonic oscillator?

Write down the following decays in terms of quarks:

(i) \Omega^- \to \Lambda^0 + K^-

(ii) \Lambda^0 \to p + \pi^-

(iii) K^- \to \mu^- \bar{\nu}_\mu

Discuss the four basic types of fundamental interactions in nature and compare them.

Describe the quark model. Obtain the quark composition of baryons and mesons.

Obtain the ground-state wave function, depth of potential and range of nuclear force in deuteron and discuss. Also prove that no bound state exists for l \neq 0.

Compute the density of a typical nucleus and find the resultant mass, if we could manufacture a nucleus with a radius of 1\text{ cm}.

Discuss the shell model of the nucleus. What are its merits ?

What is kinematics of nuclear reaction ? What is the Q-value and its significance ?

Describe grand unification theories (GUT).

It is possible to estimate the nuclear radius from the study of alpha decay? Explain how.

Explain why stable light nuclei have equal number of protons and neutrons whereas heavy nuclei have excess of neutron.

Explain how the nuclear spin I depends on the mass number A and atomic number Z of atoms.

What are the limitations of shell model?

How does liquid drop model explain fission?

Briefly explain the meson theory of nuclear force.

What are the major components of a fission reactor ? With a schematic diagram explain its working.

How does the semi-empirical mass formula explain the stability of a nucleus against beta decay ?

Explain why each of the following reactions is forbidden :

(i) p + p \rightarrow p + p + n

(ii) p + p \rightarrow p + \pi^+ + \gamma

(iii) \Xi^0 \rightarrow n + \pi^0

(iv) \Lambda \rightarrow p + \pi^0

(v) u_e + p \rightarrow n + e^+