Find the total kinetic energy of electron and antielectron neutrino emitted in beta decay of free neutron. (The neutron-proton mass difference is 1.30\,\mathrm{MeV} and mass of electron is 0.51\,\mathrm{MeV})

What are magic numbers? Discuss shell structure of a nucleus. How is this model able to explain various properties of nuclei? Discuss the limitations of this model.

A star converts all its hydrogen to helium, achieving 100% helium. It then converts the helium to carbon via the reaction {}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}\rightarrow{}^{12}_{6}\mathrm{C}+7\cdot27\mathrm{MeV} The mass of the star is 5.0\times10^{32}\,\mathrm{kg} and it generates energy at the rate of 5\times10^{30}\,\mathrm{W}. How long will it take to convert all Helium to carbon at this rate?

Predict from the single particle shell model the shell configuration, ground state spin and parity for the following nuclei: {}^{13}_{7}\mathrm{N};\ {}^{17}_{8}\mathrm{O}

Calculate the packing fraction and the binding energy per nucleon for ^{16}_{8}\mathrm{O} and ^{87}_{38}\mathrm{Sr} nuclei.

Explain parity violation in \beta-decay. Describe how parity violation was experimentally detected in the decay of ^{60}\mathrm{Co}.

Write down the Yukawa potential and derive an expression for the mass of \pi-meson in terms of range of nuclear force. What part of the Nucleon – Nucleon interaction is explained by this potential ?

What is the simplest two-nucleon bound system ? How does its study help in obtaining information about nuclear forces ? Indicate clearly how the non-central forces can be explained by the observed magnetic moment of this system.

Compare the methods of electron scattering and neutron scattering experiments to obtain information about nuclear size.

At what energies, do we anticipate the unification of strong and electroweak interactions ? What will happen to coupling constants of these interactions in this situation ? How does unification indicate the decay of proton and existence of leptoquark ?

What are the field quanta of weak and electromagnetic interactions ? Show that weak interaction is a short range force while electromagnetic interaction is a long range one.

Identify all the spin-half particles in the following list : Antineutron, Antiproton, Muon, Muon Neutrino, Neutral Kaon, Neutral Sigma, Neutral Xi, Neutron, Photon, Positive Pion, Positron, Proton, u-quark.

Which of the following \alpha decay processes is expected to have a large Q value ? {}_{84}^{211}\text{Po}_0 \rightarrow {}_{82}^{207}\text{Po}_0 + \alpha {}_{84}^{212}\text{Po}_0 \rightarrow {}_{82}^{208}\text{Po}_0 + \alpha Which of these processes will have a longer lifetime ? Explain your answer briefly.

What is \beta-decay ? Give three examples of \beta-decay of nuclei. Explain how neutrino hypothesis helped in explaining conservation of energy-momentum and angular momentum. What is Kurie plot ? How can one use Kurie plot to set limits on mass of the neutrino ?

Explain lepton number conservation and why it is necessary to distinguish between different types of neutrinos ?

In the Lorentz model for dispersion, the uniform dielectric medium is assumed to be a collection of oscillators with number density N, natural frequency $ \omega_0 $ and decay constant $ \gamma $. Find the complex susceptibility $ \chi $ of such a medium. In the frequency dependence of the real part of $ \chi $ identify the regions of normal and anomalous dispersion.

Explain why the decay process n \rightarrow p + e + \bar{\nu} is observed but the decay p \rightarrow n + e^+ + \nu is not observed.

Give the hypercharge and isospin of the quarks and antiquarks. What are the quark contents of the mesons: \pi^+, \pi^\circ, \pi^-, K^+, K^\circ, K^- \text{ and } \eta ?

What is nuclear isomerism ? Give two examples and explain how this can be understood from single particle shell model.

(i) Calculate the Q-value of the reaction ^9_4\text{Be} (^4_2\text{He}, n) ^{12}_6\text{C} Given \text{Mass } (^9\text{Be}) = 9.012183\text{ u} \text{Mass } (^4\text{He}) = 4.002603\text{ u} \text{Mass } (^{12}\text{C}) = 12.000\text{ u} Write down the nucleonic configuration of {}^{7}\text{Li}, {}^{12}\text{C}, {}^{17}\text{O} and {}^{27}\text{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of the shell model ?