PYQ Bank

Discuss the different coupling schemes in atomic spectroscopy with suitable diagrams.

How is proton magnetic resonance applied to determine the chemical shifts in molecules containing hydrogen atom ? Illustrate your answer with a suitable example.

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 resonance condition in NMR.

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 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.

What is Lamb shift ? How is it measured ?

An atom in an excited state of 4\cdot 7\text{ eV} emits a photon and ends up in the ground state. The lifetime of the excited state is 10^{-13}\text{ s}. Calculate the energy uncertainty and obtain the spectral line width in wavelength of photon.

Given that the rotational inertia of \text{HCl} molecule has the value I = 2\cdot 66 \times 10^{-47}\text{ kg-m}^2, estimate the energy difference between the lowest and first excited state of \text{HCl}.

Find the de Broglie wave length of

(i) a neutron

(ii) an electron moving with kinetic energy of 500\,eV (1\,eV = 1.602 \times 10^{-19}\,J)

=-2i\hbar\hat{p}$.

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

Obtain the time-dependent Schrödinger equation for a particle. Hence deduce the time independent Schrödinger equation.

Write down Pauli spin matrices. Express J_x,J_y and J_z in terms of Pauli spin matrices.

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}?

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.

Show that

(i) no two of the three components of angular momentum operator commute and

(ii) the third component of the angular momentum operator commutes with the square of angular momentum operator.

What is the de Broglie wavelength of an electron whose kinetic energy is 100\text{ eV} ?

Explain the origin of the anomalous Zeeman effect.