UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain parity violation in \beta-decay. Describe how parity violation was experimentally detected in the decay of {}^{60}\mathrm{Co}. Mention any other decay process in which the parity violation has been demonstrated.

Write down the nucleonic configuration of {}^{7}\mathrm{Li}, {}^{12}\mathrm{C}, {}^{17}\mathrm{O} and {}^{27}\mathrm{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of shell model?

Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation of Hooke's law type of interaction.

Explain why the separation between vibrational levels is smaller in an excited electronic state than in the ground electronic state.

Explain the concept of shared pair of electrons with antiparallel spins forming a covalent bond in \text{H}_2-like molecule with reference to total energy.

A substance shows a Raman line at 4567\text{ \AA} when exciting line 4358\text{ \AA} is used. Estimate the positions of Stokes and anti-Stokes lines for the same substance when exciting line 4047\text{ \AA} is used.

In a Raman spectrum of a linear triatomic molecule, the first three lines are 4.86, 8.14 and 11.36\ \mathrm{cm^{-1}}. Calculate the rotational constant, B and the moment of inertia of the molecule. (Given h = 6.626 \times 10^{-27}\ \mathrm{J\,s}, C = 3.0 \times 10^{10}\ \mathrm{cm/sec.})

With proper selection rules, construct the energy level diagram and allowed transitions for ESR spectrum of hydrogen atom.

What do you understand by H-one (HI) interstellar clouds and their importance to understand the universe.

Discuss the fine structure of sodium D line. Draw D_1 and D_2 lines due to the transitions between {}^2P and {}^2S levels.

The term symbol for atomic states are quoted as {}^3P_2 and {}^2D_{5/2}. What are the values of L, S and J?

How are electrons distributed in the various sub-shells for n=3? Give the quantum numbers for the electrons in the second shell.

Why are Raman active vibrations and infrared vibrations in \mathrm{CO_2} molecule complementary to each other?

(i) Enumerate the possible values of quantum numbers j and m_j for state in which l = 2 and s = 1/2.

(ii) Draw the corresponding vector model diagram.

The particle in a box has a ground state wave function given as \psi(x) = \frac{1}{\sqrt{l}} \cos \frac{\pi x}{2l} The box width is 2l and the particle is confined within (-l, +l). Calculate the expectation value of x^2.

A particle is bound in a potential well given by V(x) = \begin{cases} \infty & \text{for } x \le 0 \\ cx & \text{for } x > 0 \end{cases} Estimate the ground state energy of the system from uncertainty principle.

Write down Schrödinger equations for a particle of energy E < V_0, incident on a step potential height V_0. Solve them to find out the transmission and reflection coefficients in terms of k and k', where k = \sqrt{\frac{2mE}{\hbar^2}} and k' = \sqrt{\frac{2m(V_0 - E)}{\hbar^2}}. Show that in this case, there is a finite probability of finding the particle in a classically forbidden region.

Show that the spherical harmonics Y_{lm}(\theta, \phi) are simultaneous eigenfunctions of L^2, L_z and L_z^2. What are their corresponding eigenvalues?

Develop and write down the expressions of L^2, L_z and L_z^2 in angular momentum operator algebra.

The normalized wave function for the electron in the ground state of the hydrogen atom is given by \psi(r)=\dfrac{1}{\sqrt{\pi a_0^3}}e^{-r/a_0}, where a_0 is the radius of the first Bohr orbit. Calculate the probability of finding the electron within a distance r_0 of the proton in the ground state.