By considering a suitable nuclear potential well for the deuteron ground state, show that it is a loosely bound nucleus.

What do you understand by \text{SU}(3) symmetry for the quark model? On the basis of it, explain that the baryons can have +2 charge but mesons cannot have the same.

Calculate the minimum energy (E_\gamma) required for a gamma ray photon to disintegrate a deuteron of mass M and binding energy B into a neutron and a proton. (Assume B \ll Mc^2)

What were the difficulties faced by the initial theory of \beta-decay? How did Pauli eliminate the difficulties? What were the expected properties of the new particle proposed by Pauli?

Assume that the range of the interaction of nuclear force and of meson is 2 \times 10^{-15}\text{ m}. Estimate the mass of the meson.

Apply the meson theory of nuclear forces to write the interaction between protons, neutrons, proton to neutron and neutron to proton.

In the case of deuterons, answer the following : (i) What percentage of the time do the nucleons of a deuteron spend within the range of the nuclear forces?

(ii) From a study of the radial part of the Schr"{o}dinger equation of a deuteron for any angular momentum l, what do we conclude?

A radionuclide (N_1) decays to a radioactive daughter (N_2) that subsequently decays to a third daughter (N_3). If at t = 0, the initial concentrations of N_1, N_2 and N_3 are N_1^0, 0 and 0 respectively, and the decay constants are \lambda_1 (from N_1 \rightarrow N_2) and \lambda_2 (from N_2 \rightarrow N_3), then derive the expression for N_2 at time t. Given that the daughter N_3 is stable.

Write the decay reactions of the neutral pions (\pi^0) and the charged pions (\pi^+, \pi^-).

A sample contains 4\text{ mg} of ^{210}\text{Bi}. If the half-life of radioactive ^{210}\text{Bi} is 5\text{ days} and the average energy of the \beta-particles emitted is 0\cdot 34\text{ MeV}, then at what rate does the sample emit energy?

What do you understand by the critical size of a nuclear reactor? Write down the common features of nuclear reactors used for the production of electricity.

The nature of curves of binding energy and packing fraction are complementary to each other. Explain.

Justify the fact that the electrons are emitted from nuclei in \beta-decay but they cannot be contained inside the nuclei.

On the basis of conservation laws, explain whether the following reactions are allowed or forbidden : (i) \pi^- + \text{p} \longrightarrow \Sigma^+ + \text{K}^- (ii) \text{K}^- + \text{p} \longrightarrow \Omega^- + \text{K}^+ + \text{K}^0 (iii) \Omega^- \longrightarrow \Xi^0 + \pi^- (iv) \pi^+ + \text{p} \longrightarrow \text{p} + \text{p} + \bar{\text{n}} (v) \Sigma^+ \longrightarrow \Lambda^0 + \text{K}^+

Why does a neutron star have a magnetic field if it is composed of neutrons?

Derive an expression for \alpha-disintegration energy for a nucleus in a radioactive decay process.

Explain Gell-Mann and Ne'eman SU(3) symmetry for the classification of elementary particles — baryons and mesons.