UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe briefly how parity violation in \beta-decay was experimentally observed? What do you understand by the statement, 'neutrinos are left-handed'?

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)]

Distinguish between charge independence and charge symmetry of nuclear force. Give one example of each of these.

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?

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}}]

Write down the semiempirical mass formula for nuclei and sketch the variation of isobaric masses with atomic number for both odd and even values of A. How many stable isobars would be there in each case ?

Describe the main features of the shell model of the nucleus. Explain how it can account for the magic numbers of nuclei.

What is the main inference drawn from the Stern Gerlach experiment ? What would be the change in the result in the following cases :

(i) electron spin is \frac{3}{2}\hbar instead of \frac{\hbar}{2}.

(ii) a beam of neutral atoms is passed through a homogeneous magnetic field.

What are Stokes and anti-Stokes lines ? What is their importance in understanding the molecular structure ?

What is meant by Larmour precession ? Calculate the Larmour frequency for protons in a magnetic field of 1 Tesla.

Consider two electrons system in (3p)^1(4s)^1 configuration. Derive the allowed energy states of the system in (i) LS coupling and (ii) jj coupling sketching the energy level diagram in each case. Name the interactions which are responsible for different splittings.

The first rotational line in the rotational spectrum of CO is observed at 3\cdot84235\text{ cm}^{-1}. Calculate the rotational constant B and the bond length.

In an NMR experiment, hydrogen atoms are subjected to a magnetic field of 5.0\ \mathrm{T}. Determine the difference in energy (\mathrm{kJ/mol}) between two spin states of the nuclei of hydrogen atom and the frequency of radiation required for NMR.

State Franck-Condon principle. Define Franck-Condon factors. Using schematic diagram, explain the decay of excited states leading to the phenomena of fluorescence and phosphorescence.

Given the force constant of HCl molecule = 516\ \mathrm{N\,m}^{-1}, determine the wave number of the fundamental mode of vibration of the molecule. How many transition lines one can expect in the vibration spectra of HCl molecule at room temperature?

Explain Stokes and anti-Stokes Raman scattering with the help of energy level diagram. For a diatomic molecule, obtain expressions for transition energies of its Raman spectra with rotational fine structure and hence the wave numbers of the Stokes lines.

Explain why lines in some Raman spectra are found to be plane polarized to different extents even though the exciting radiation is completely unpolarized?

Show that the lines in the absorption spectra corresponding to the rotational transitions from two adjacent energy levels of a medium sized molecule at room temperature have comparable intensities.

Explain the principle of Nuclear Magnetic Resonance (NMR) with the help of an energy level diagram. Give examples of nuclei which exhibit NMR. What major inferences can be drawn from an NMR spectra?