UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write two properties of deuteron which support the existence of non-central tensor force.

Given that the deuteron magnetic moment operator (in units of nuclear magneton) can be expressed as \vec{\mu}_d = \mu_n\vec{\sigma}_n + \mu_p\vec{\sigma}_p + \frac{1}{2}\vec{l} where \vec{l} is the relative angular momentum between neutron and proton, \vec{\sigma}_n and \vec{\sigma}_p are the Pauli spin operators and \mu_n and \mu_p are the respective magnetic moments. Find out the D-state probability of deuteron wave function. [Given: \mu_d = 0.857\mu_N, \mu_n = -1.913\mu_N and \mu_p = 2.793\mu_N; \mu_N (nuclear magneton)]

State the three characteristic properties of strong, weak and electromagnetic forces distinguishing one from the other.

Point out the interactions in which the following conservation laws are obeyed or violated

(i) Isotopic spin

(ii) Hyper charge

(iii) Lepton number

(iv) Charge conjugation

How does one explain the approximate constancy of average binding energy per nucleon (\mathrm{BE}/A) of nuclei in the region 30 \leq A \leq 170 in the plot of \mathrm{BE}/A versus mass number A?

Write down the quark constituents of each of the following:

(i) \pi^+

(ii) K^+

(iii) \Delta^{++}

(iv) \Sigma^0

(v) \Omega^-

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}}]

Explain unification of electromagnetic and weak interactions. What is Z^0-boson? What is its relevance in electroweak unification?

Write down the quark structure of the following hadrons: \Delta^{++}, \Omega^-, \Sigma^- and \Lambda^0 Write down the following decays in terms of quarks:

(i) n \to p + e^- \bar{\nu}_e

(ii) \Delta^+ \to \pi^+ + n

(iii) \Sigma^+ \to p + \pi^0

Predict the spin and parity of ground states of the following nuclei on the basis of shell model:

(i) {}_{8}\mathrm{O}^{15}

(ii) {}_{8}\mathrm{O}^{16}

(iii) {}_{17}\mathrm{Cl}^{38}

What are elementary particles and how are they classified? Describe in brief the different types of interactions that can occur between the elementary particles.

Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, state whether the following reactions are possible or not:

(i) \pi^- \to \mu^- \bar{\nu}_\tau

(ii) n \to p + e^- \bar{\nu}_e

State the basic assumption of single particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of a three-dimensional spherical harmonic oscillator?

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega = 41\,A^{-1/3}\,\mathrm{MeV}.

Explain why the deuteron has no excited state.

Describe grand unification theories (GUT).

Write down the following decays in terms of quarks:

(i) \Omega^- \to \Lambda^0 + K^-

(ii) \Lambda^0 \to p + \pi^-

(iii) K^- \to \mu^- \bar{\nu}_\mu

How are elementary particles classified on the basis of their participation in fundamental interaction?

What are the magic numbers in nuclei? List the experimental evidences indicating their existence.

What are salient features of nuclear forces?