UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write down the basic weak interaction processes in the nuclei. Also illustrate the beta decays of (i) neutron and (ii) proton.

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

List the main reactions in the pp chain leading from hydrogen to helium during stellar nucleosynthesis. Also mention the net effect of the reactions.

(i) Plot proton number (Z) versus neutron number (N). What is the inference from the plot with regards to light and heavy nuclides ? (ii) Which nucleus would you expect to be more stable, {}^{7}_{3}\text{Li} or {}^{8}_{3}\text{Li} ? 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 origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.

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 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?

On the basis of liquid-drop model, write the semi-empirical mass formula for the total binding energy. Also explain their each term.

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

What do you understand by the reproduction factor of a fission reactor? What is the maximum value of the reproduction factor in a uranium fission reaction?

In the following nuclear reactions, what particles are possible for the unknown particle X?

(i) \pi^- + p \rightarrow K^0 + X

(ii) p + p \rightarrow \pi^+ + n + \Lambda^0 + X

Calculate the decay rate of {}^{14}\text{C} per gram of carbon in a living organism, assuming the ratio {}^{14}\text{C} / ^{12}\text{C} = 1\cdot 35 \times 10^{-12}. The half-life of {}^{14}\text{C} is 5730 years.

What are the properties of the particles made up of the following quarks? Also write the names of particles :

(i) u\bar{d}

(ii) \bar{u}d

(iii) dds

(iv) uss

By applying the conservation laws, state about the following decay equations, whether they are allowed or not allowed :

(i) \Sigma^+ \rightarrow p + \pi^0

(ii) \Sigma^0 \rightarrow \Lambda^0 + \gamma

(iii) \Lambda^0 \rightarrow n + \pi^0

Explain the salient features of nuclear shell model. What are the magic numbers? Write the experimental facts in support of shell model of nuclei.

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.

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

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?

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^+

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

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

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