UPSC Physics Optional PYQs (CSE & IFoS)PYQs

An amplifier in common-emitter configuration is shown in the above figure. If the current gain \beta=100 and the a.c. emitter resistance =25.0\,\Omega, determine the input impedance and the voltage gain of the amplifier:

A system of paramagnetic atoms (N per unit volume) which can occupy only two energy levels in a uniform external magnetic field H is at a temperature T. If this system follows Boltzman's distribution, find the magnetisation and susceptibility of the system.

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?

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)]

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

Write the semi-empirical mass formula pointing out the role of volume term, surface energy term, coulomb and symmetry energy correction terms.

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

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

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}}]

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

Write down the quark constituents of each of the following:

(i) \pi^+

(ii) K^+

(iii) \Delta^{++}

(iv) \Sigma^0

(v) \Omega^-

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

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?

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.

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.

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.

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.

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?

Calculate the probability of transmission of an electron of 1.0\,\mathrm{eV} energy through a potential barrier of 4.0\,\mathrm{eV} and 0.1\,\mathrm{nm} width.