UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Discuss Yukawa’s theory of nuclear forces.

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

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

Explain how the nuclear spin I depends on the mass number A and atomic number Z of atoms.

Explain why stable light nuclei have equal number of protons and neutrons whereas heavy nuclei have excess of neutron.

It is possible to estimate the nuclear radius from the study of alpha decay? Explain how.

What are salient features of nuclear forces?

What are the limitations of shell model?

How does liquid drop model explain fission?

A sample of a certain element is placed in a magnetic field of flux density 0.3 tesla. How far apart is the Zeeman component of a spectral line of wavelength 4500\mathring{\mathrm{A}}? Given : e/m = 1.76 \times 10^{11}\ \mathrm{c/kg}, c = 3.0 \times 10^8\ \mathrm{m\,s^{-1}}.

Obtain an expression for the normal Zeeman shift. Illustrate the Zeeman splitting of spectral lines of H atom and the allowed transitions for the l = 1 and l = 2 states.

Explain the relaxation processes in NMR spectroscopy.

Given that the spacing between vibrational levels of CO molecules is 8.45 \times 10^{-2}\ \mathrm{eV} of energy. Find the force constant of the molecule.

Discuss the vibrational spectra of a diatomic molecule treating it as an anharmonic oscillator.

Obtain an expression for the resonance condition in NMR.

Using the commutation relations [x,p_x]=[y,p_y]=[z,p_z]=i\hbar deduce the commutation relation between the components of angular momentum operator \mathbf{L}. [L_x,L_y]=i\hbar L_z [L_y,L_z]=i\hbar L_x\quad\text{and}\quad [L_z,L_x]=i\hbar L_y.

Solve the Schrödinger equation for a particle of mass m confined in one dimensional potential well of the form: V(x)= \begin{cases} 0; & 0 \leq x \leq L,\\ \infty; & x<0,\ x>L. \end{cases} Obtain the discrete energy values and the normalized eigen functions.

An electron is moving in a one-dimensional box of infinite height and width 1\,\mathring{\mathrm{A}}. Find the minimum energy of electron.

If \hat{x} and \hat{p} are the position and momentum operators, prove the commutation relation [\hat{p}^{2},\hat{x}]=-2i\hbar\hat{p}.

The mean life of Lambda (\Lambda^0) particle is 2.6 \times 10^{-10}\,\mathrm{s}. What will be the uncertainty in the determination of its mass in \mathrm{eV}?