PYQ Bank

What are elementary particles and how are they classified? Describe in brief the different types of interactions that can occur between the elementary particles.

What is Raman effect? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6\ \mathrm{cm}^{-1}. Find the internuclear distance between the atoms forming the molecule.

Obtain the frequency $ u_r$ of the spectral line of rotation spectra of a diatomic molecule and discuss the characteristics of its spectrum.

What is Lamb shift? What is its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom?

Consider a hydrogen atom in Bohr atomic model. Outline its importance in the context of spatial quantization and the spin of the electron.

Outline elementary theory of Nuclear Magnetic Resonance (NMR) and discuss its applications.

Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli’s exclusion principle.

In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 K, l \approx 25\ \mathrm{cm} and \frac{\partial B_z}{\partial z} \simeq 10^{+3}\,\text{Tesla/m}. Calculate the separation of the two components.

The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646\,\mathring{\mathrm{A}}. Find the wavelength of the first line of this series.

Outline the Stern-Gerlach experiment and discuss its importance in the context of quantum nature of atom.

Explain in detail L-S coupling and j-j coupling schemes.

Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum \vec{S} and its z-component of an electron moving along the external magnetic field \vec{B}.

In a nuclear experiment, beams of electrons and protons are moving with velocities c / 10 and c / 20 respectively. Calculate the de Broglie wavelengths of both the particles in metre (c is the speed of light = 3 \times 10^8\text{ m / s}).

A typical atomic radius is about 5 \times 10^{-15}\,m and the energy of \beta-particle emitted from a nucleus is at most of the order of 1\,\mathrm{MeV}. Prove on the basis of uncertainty principle that the electrons are not present in nuclei.

Explain the phenomenon of Zeeman effect of atomic physics.

Using uncertainty principle, calculate the size and energy of the ground state hydrogen atom.

Consider a two-electron system in ground state with orbital quantum number zero (l = 0). Use Pauli's exclusion principle to obtain orientations of the two electrons.

Write down the matrix representation of the three Pauli matrices \sigma_x, \sigma_y and \sigma_z. Prove that these matrices satisfy the following identities:

(i) [\sigma_x,\sigma_y]=2i\sigma_z

(ii) [\sigma^2\cdot\sigma_x]=0

(iii) (\vec{\sigma}\cdot\vec{A})(\vec{\sigma}\cdot\vec{B})=\vec{A}\cdot\vec{B}+i\vec{\sigma}\cdot(\vec{A}\times\vec{B}) if \vec{A} and \vec{B} commute with Pauli matrices.

Calculate the density of states for an electron moving freely inside a metal with the help of quantum mechanical Schrodinger's equation for free particle in a box.

Obtain the solution of one-dimensional free particle Schrödinger equation. Show that it corresponds to plane monochromatic (constant angular frequency) wave.