UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain lepton number conservation and why it is necessary to distinguish between different types of neutrinos ?

Give the hypercharge and isospin of the quarks and antiquarks. What are the quark contents of the mesons: \pi^+, \pi^\circ, \pi^-, K^+, K^\circ, K^- \text{ and } \eta ?

What is \beta-decay ? Give three examples of \beta-decay of nuclei. Explain how neutrino hypothesis helped in explaining conservation of energy-momentum and angular momentum. What is Kurie plot ? How can one use Kurie plot to set limits on mass of the neutrino ?

What is nuclear isomerism ? Give two examples and explain how this can be understood from single particle shell model.

Which of the following \alpha decay processes is expected to have a large Q value ? {}_{84}^{211}\text{Po}_0 \rightarrow {}_{82}^{207}\text{Po}_0 + \alpha {}_{84}^{212}\text{Po}_0 \rightarrow {}_{82}^{208}\text{Po}_0 + \alpha Which of these processes will have a longer lifetime ? Explain your answer briefly.

Explain why the decay process n \rightarrow p + e + \bar{\nu} is observed but the decay p \rightarrow n + e^+ + \nu is not observed.

In the Lorentz model for dispersion, the uniform dielectric medium is assumed to be a collection of oscillators with number density N, natural frequency \omega_0 and decay constant \gamma. Find the complex susceptibility \chi of such a medium. In the frequency dependence of the real part of \chi identify the regions of normal and anomalous dispersion.

On the basis of electronic spectra of molecules explain, how fluorescence and phosphorescence occur. Distinguish between the two.

What do you understand by Raman effect ? Explain with help of a diagram, how it can be observed experimentally.

Write full form of acronyms EPR and NMR. Give underlying principle of EPR.

Assume a diatomic molecule consisting of two at- oms of masses m_1 and m_2, separated by a distance \vec{r}. Write down the Hamiltonian operator for the molecule. Determine the rotational energy levels of the molecule.

Draw the potential energy of a diatomic molecule as a function of interatomic distance. Mark the vibrational and rotational energy levels. Explain the selection rule for transition between vibrational states.

For transition to the ground state what is the longest wavelength that can be emitted by hydrogen ?

Show that for the one dimensional wave function \psi(x) = \begin{cases} \frac{1}{\sqrt{2a}} & , \quad |x| < a \\ 0 & , \quad |x| > a \end{cases} where a is a real constant, the rms uncertainty in momentum is infinite.

An electron is moving freely in a one-dimensional infinite potential box with walls at x = 0 and x = a. If the electron is initially in the ground state of the box and if suddenly the wall at x = a is moved x = 4a, calculate the probability of finding the particle in the ground state of the new box.

Write the commutation relations of angular momentum operator \hat{L}_x, \hat{L}_y and \hat{L}_z and calculate the commutators [\hat{L}_+, \hat{L}_z] and [\hat{L}_-, \hat{L}_z]. Show that \hat{L}_+ |l, m\rangle = \sqrt{l(l+1) - m(m+1)} |l, m+1\rangle, where |l, m\rangle is the state with definite values for L^2 and L_z.

An electron is in the spin state \chi = A \begin{pmatrix} 3i \\ 4 \end{pmatrix}. Determine the normalization constant A. Find the expectation value of the spin operator \hat{S}_x and also the uncertainty in the value of S_x in this state.

Show that the probability of transmission across the step barrier represented by the potential V(x) = \begin{cases} 0 & \text{for } x < 0 \\ V_0 & \text{for } x > 0 \end{cases} is T = \frac{4 k_1 k_2}{(k_1 + k_2)^2}, where k_1 and k_2 are wave numbers in regions x < 0 and x > 0, respectively.

The Hamiltonian of a particle moving along the x-axis is given by \hat{H} = -\alpha \frac{d^2}{dx^2} + 16\alpha \hat{x}^2, where \alpha is a real and positive constant having dimensions of energy. (i) If \psi(x) = A e^{-2x^2}, find the normalization constant A. Check whether \psi is an eigen function of \hat{H}. If yes, find the corresponding eigen value. (ii) Calculate the probability of finding the particle anywhere along the negative x-axis. (iii) Find the eigen value of \hat{H} corresponding to the eigen function \phi(x) = x\psi(x), where \psi(x) is the same as in part (i). (iv) Are the wave functions \psi(x) and \phi(x) orthogonal ?

Write (do not derive) the formula for the energy levels of a particle in a three dimensional cubical box of side L. How many electrons can occupy the level having energy 66h^2/8mL^2 ?