UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

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.

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}

Write the quark composition of the following :

(i) Neutron

(ii) Proton

(iii) \Lambda

(iv) \text{K}^-

(v) \pi^+

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 ?

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 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.

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

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

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 ?

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.

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.

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 ?

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.

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