PYQ Bank

Write the quark composition of the following :

(i) Neutron

(ii) Proton

(iii) \Lambda

(iv) \text{K}^-

(v) \pi^+

Predict from the single particle shell model, the shell configuration, ground state spin and parity for the following nuclei : ^7_3\text{Li}, \quad ^{13}_7\text{N}, \quad ^{17}_8\text{O}, \quad ^{27}_{13}\text{Al}

What are magic numbers ? Discuss the 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 into helium, achieving 100\% helium. It then converts the helium into carbon via the reaction ^4_2\text{He} + ^4_2\text{He} + ^4_2\text{He} \xrightarrow{\quad} ^{12}_6\text{C} + 7.27\text{ MeV} The mass of the star is 5.0 \times 10^{32}\text{ kg} and it generates energy at the rate of 5 \times 10^{30}\text{ W}. How long will it take to convert all helium to carbon at this rate ?

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?

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

Calculate the binding energy per nucleus for ^{87}_{38}\text{Sr}.

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

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}

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.

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.

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 ?

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 ?

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.

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

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

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 \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 ?

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