Estimate the order of nuclear radius of lead (Z = 82) using the large angle (back) scattering of alpha particles of energy 10\,\mathrm{MeV} incident on a target (lead). [Given: (4\pi\epsilon_0)^{-1} = 9 \times 10^{9}\,\mathrm{N\,m^2\,C^{-2}}]

Given that the deuteron magnetic moment operator (in units of nuclear magneton) can be expressed as \vec{\mu}_d = \mu_n\vec{\sigma}_n + \mu_p\vec{\sigma}_p + \frac{1}{2}\vec{l} where \vec{l} is the relative angular momentum between neutron and proton, \vec{\sigma}_n and \vec{\sigma}_p are the Pauli spin operators and \mu_n and \mu_p are the respective magnetic moments. Find out the D-state probability of deuteron wave function. [Given: \mu_d = 0.857\mu_N, \mu_n = -1.913\mu_N and \mu_p = 2.793\mu_N; \mu_N (nuclear magneton)]

State the three characteristic properties of strong, weak and electromagnetic forces distinguishing one from the other.

Write down the quark constituents of each of the following:

(i) \pi^+

(ii) K^+

(iii) \Delta^{++}

(iv) \Sigma^0

(v) \Omega^-

How does one explain the approximate constancy of average binding energy per nucleon (\mathrm{BE}/A) of nuclei in the region 30 \leq A \leq 170 in the plot of \mathrm{BE}/A versus mass number A?

Point out the interactions in which the following conservation laws are obeyed or violated

(i) Isotopic spin

(ii) Hyper charge

(iii) Lepton number

(iv) Charge conjugation

Write the semi-empirical mass formula pointing out the role of volume term, surface energy term, coulomb and symmetry energy correction terms.

Write down the quark structure of the following hadrons: \Delta^{++}, \Omega^-, \Sigma^- and \Lambda^0 Write down the following decays in terms of quarks:

(i) n \to p + e^- \bar{\nu}_e

(ii) \Delta^+ \to \pi^+ + n

(iii) \Sigma^+ \to p + \pi^0

Explain unification of electromagnetic and weak interactions. What is Z^0-boson? What is its relevance in electroweak unification?

Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, state whether the following reactions are possible or not:

(i) \pi^- \to \mu^- \bar{\nu}_\tau

(ii) n \to p + e^- \bar{\nu}_e

What are elementary particles and how are they classified? Describe in brief the different types of interactions that can occur between the elementary particles.

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?

Explain why the deuteron has no excited state.

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

Describe grand unification theories (GUT).

How does liquid drop model explain fission?

Discuss Yukawa’s theory of nuclear forces.

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