UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Justify the fact that the electrons are emitted from nuclei in \beta-decay but they cannot be contained inside the nuclei.

The nature of curves of binding energy and packing fraction are complementary to each other. Explain.

If an atom is placed in a magnetic field of strength 0\cdot 1\text{ weber/m}^2, then calculate the rate of precession and torque on an electron with l=3 in the atom. Given that the magnetic moment of the electron makes an angle of 30^\circ with the magnetic field.

What is Lande's g factor ? Evaluate the Lande's g factor for the {}^3P_1 level in the 2p3s configuration of the {}^6\text{C} atom. Also calculate the splitting of the level when the atom is placed in an external magnetic field of 0\cdot 1\text{ tesla}.

What is Raman effect ? Explain Quantum theory of Raman effect and Rotational Structure of a Raman spectrum.

Often the intensity of rotational transition J = 0 \to J = 1 is not the most intense. Explain.

Evaluate the Landé g-factor for the {}^3\mathrm{P}_1 level in the 2p 3s configuration of the {}^6\mathrm{C} atom, and then calculate the splitting of the level in eV, when the atom is in an external magnetic field of 0.2 tesla.

What is vector model of the atom? On the basis of it, explain the L-S and j-j coupling under external magnetic field.

An atomic state is denoted by {}^4\mathrm{D}_{5/2}. What should be the minimum number of electrons involved for this state? Give a possible electron configuration.

What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?

Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.

(i) Homonuclear diatomic molecules do not give any pure rotational or vibrational spectra, whereas they do give a rotational Raman spectra. Comment. (ii) The separation between the adjacent rotational Raman lines is 4B in hydrogen molecule, whereas in oxygen molecule it is 8B. Why?

A beam of hydrogen atoms emitted from an oven at 400\text{ k} is sent through a Stern-Gerlach experiment having magnet of length 1\text{ m} and a gradient field of 10\text{ tesla/m}. Calculate the transverse deflection of an atom at the point where the beam leaves the magnet.

How does the Stern-Gerlach experiment explain the concept of electron spin and its angular momentum quantization?

The rotational and centrifugal distortion constants of a diatomic molecule are 10\cdot 59\text{ cm}^{-1} and 5\cdot 3 \times 10^{-4}\text{ cm}^{-1}, respectively. Obtain an estimate each for the vibrational frequency and force constant of the molecule. [\text{Given } : \text{The reduced mass of the molecule is } 1\cdot 626 \times 10^{-27}\text{ kg}]

What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.

Calculate the zero point energy for a particle in an infinite potential well for the following cases : (i) a 100\text{ g} ball confined on a 5\text{ m} long line. (ii) an oxygen atom confined to a 2 \times 10^{-10}\text{ m} lattice. (iii) an electron confined to a 10^{-10}\text{ m} atom. Why zero point energy is not important for macroscopic objects ? Comment.

(i) Derive an expression for the period of Bloch oscillation for a one-dimensional crystal having lattice period a and electric field \varepsilon. (ii) Consider an electron in a perfectly periodic lattice, wherein the energy-wavenumber relationship in the first Brillouin zone is expressed as E = \frac{\hbar^2 k^2}{5\mathrm{m}_e} where \mathrm{m}_e is the mass of an electron in free space. Find the effective mass of the electron and hence write down the time-independent Schrodinger equation for the electron. Also determine the velocity of the electron. Ignore all interactions except between the electron and the lattice.

Consider a particle of mass m and charge q moving under the influence of a one dimensional harmonic oscillator potential. Assume it is placed in a constant electric field E. The Hamiltonian of this particle is therefore given by H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 X^2 - qEX. Obtain the energy expression and the wave function of the n\text{th} excited state of the particle.

Find the condition at which de Broglie wavelength equals the Compton wavelength for a particle.