A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600\text{ \AA} when excited by light of wavelength 4358\text{ \AA}. Calculate the wavelength of the corresponding infrared band.

Write down the characteristics of Raman spectral lines. Explain why Stokes lines are more intense than anti-Stokes lines. With exciting line at 2536~\text{\AA}, a Raman line for a sample is observed at 2612~\text{\AA}. Calculate the Raman shift in wave number.

Write down the Franck-Condon principle and explain how it accounts for the intensities of spectral lines in vibrational-electronic spectra with suitable illustrations.

Discuss the anomalous magnetic splitting of sodium D-lines with necessary illustration (no deduction is required). Identify the polarization of each component line. What condition needs to be satisfied for this splitting to take place?

What is Lamb shift? Why does the study of Lamb shift enjoy so much attention?

If the state of the hydrogen atom is 2p state, calculate the energy levels of the spin-orbit interaction Hamiltonian A \vec{L} \cdot \vec{S}, where A is a constant.

Draw the schematic diagram of a nuclear magnetic resonance (NMR) spectrometer. Discuss nuclear magnetic resonance imaging.

The first rotational line of ^{12}\text{C}^{16}\text{O} is observed at 3\cdot 84235~\text{cm}^{-1} and that of ^{13}\text{C}^{16}\text{O} at 3\cdot 67337~\text{cm}^{-1}. Assuming the mass of ^{16}\text{O} to be 15\cdot 9949~\text{u}, calculate that of ^{13}\text{C}.

In an atomic physics experiment a beam of p-state atoms is passed through a non-uniform magnetic field. After passing through the magnetic field the atomic beam strikes at the screen and is detected as shown in the given figure. Obtain an expression of the force acting on the p-atoms beam due to gradient in the magnetic field acting along z-axis as shown. Also comment on the number of spots that are found on the screen as an outcome and explain.

Show that for pure rotational spectrum of a diatomic molecule the wave number difference between the consecutive lines \Delta \bar{\nu} = \frac{\hbar}{2\pi Ic}, where I is the moment of interia.

The most intense vibrational bands of CO and HCl molecules have the wave numbers 2\cdot 143 \times 10^5\text{ m}^{-1} and 2\cdot 886 \times 10^5\text{ m}^{-1} respectively. Calculate the force constants of these molecules.

How many different wavelengths may be observed in the spectrum from a hydrogen sample, if the atoms are excited to states with principle quantum number n ?

Consider an electron circulating around a proton (as shown in figure) in a circular orbit of radius, r. Assuming the motion of orbiting electron equivalent to an electrical current loop, find the expression for the ratio of magnetic moment to the angular momentum of the system and estimate the numerical value of this ratio.

What are Stokes and anti-Stokes lines ? What is their importance in understanding the molecular structure ?

The first rotational line in the rotational spectrum of CO is observed at 3\cdot84235\text{ cm}^{-1}. Calculate the rotational constant B and the bond length.

What is meant by Larmour precession ? Calculate the Larmour frequency for protons in a magnetic field of 1 Tesla.

Consider two electrons system in (3p)^1(4s)^1 configuration. Derive the allowed energy states of the system in (i) LS coupling and (ii) jj coupling sketching the energy level diagram in each case. Name the interactions which are responsible for different splittings.

What is the main inference drawn from the Stern Gerlach experiment ? What would be the change in the result in the following cases :

(i) electron spin is \frac{3}{2}\hbar instead of \frac{\hbar}{2}.

(ii) a beam of neutral atoms is passed through a homogeneous magnetic field.

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