Explain the Mössbauer effect.

Calculate in terms of the nuclear magneton, \mu_{\mathrm{N}}, the magnetic dipole moment of ^{3}S_{1} state of deuteron. Given, \mu_{\mathrm{p}}=2\cdot792847\mu_{\mathrm{N}} and \mu_{\mathrm{n}}=-1.913042\mu_{\mathrm{N}}.

List in two separate columns, the quantities that are conserved and not conserved in the weak interaction of particles.

Assuming equal masses for up (u) and down (d) quarks, find the ratio (\mu_n/\mu_p) of the magnetic moments of neutron and proton.

For a system consisting of one proton and one neutron (not necessarily a deuteron), write down the various possible states specifying clearly its isospin, spin and orbital quantum numbers.

Explain the origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.

Why is it not possible to detect the parity violation in weak interaction by observing only the beta decay rate? Justify your answer.

Given that the single particle energy separation between 1d_{5/2} and 1d_{3/2} in ^{17}\mathrm{O} is 5\,\mathrm{MeV}. Calculate the strength of spin-orbit interaction. It is observed that 1d_{5/2} level is lower than 1d_{3/2} level.

Explain the various methods of finding the size of the nucleus. How will you determine the nuclear radius from the observation of beta rays resulting from nuclear transition when the initial and final nuclei are mirror nuclei?

Stable light nuclei have equal number of protons and neutrons, whereas heavy nuclei have excess of neutrons. Explain why.

Which of the following elementary particle reactions/decays are allowed under various conservation laws? If allowed, write down the type of interaction and the characteristic time by which it would proceed:

(i) p + n \to \Lambda^0 + \Sigma^+

(ii) \pi^+ + n \to \Lambda^0 + K^+ \setcounter{enumi}{2}

(iii) p+n\to K^{+}+\Sigma^{+}

(iv) \pi^{0}\to\gamma+

(v) \bar{n}\to\bar{p}+e^{+}+\nu_e

Obtain an expression for the magnetic moment of a nucleus having one nucleon outside the closed core. Use this to calculate the magnetic moment of \,_{8}^{17}\mathrm{O} nucleus.

Write the semi-empirical mass formula for nuclei and on its basis draw mass parabolas for odd and even isobars. What would be the most stable isobar in each case?

The maximum energy of a positron (e^+) released in the decay of \,_{6}^{13}\mathrm{C} atom into a \,_{7}^{13}\mathrm{N} atom is 1.202\,\mathrm{MeV}. If the mass of the \,_{6}^{13}\mathrm{C} atom is 13.003354\,\mathrm{u}, calculate the mass of the \,_{7}^{13}\mathrm{N} atom.

Nuclear forces are mediated by exchange of \pi-mesons of rest mass 140\,\mathrm{MeV}. Estimate the range of nuclear forces.

A \pi^--meson at rest decays into a \mu^--meson: \pi^-\to\mu^-+\bar{\nu}_{\mu} Calculate the kinetic energy of the \mu^--meson emitted in the reaction.

Assuming that the neutron-proton interaction has a square well form V(r)=-V_0\quad\text{for }r\leq b =0\quad\text{for }r>b, the ground state wave function of deuteron nucleus is given as \psi(r)=A\sin kr\quad\text{for }r\leq b =Ce^{-\gamma r}\quad\text{for }r>b where k=\sqrt{\frac{M}{\hbar^2}(V_0+W)} and \gamma=\sqrt{\frac{MW}{\hbar^2}}. Here M is the nucleon mass, W is the binding energy of deuteron and A and C are constants.

(i) Show that for a just bound state of deuteron V_0b^2=\frac{\pi^2\hbar^2}{4M}.

(ii) Explain why deuteron is a loosely bound extended structure.

Distinguish between charge independence and charge symmetry of nuclear force. Give one example of each of these.

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}}]

Describe briefly how parity violation in \beta-decay was experimentally observed? What do you understand by the statement, 'neutrinos are left-handed'?