In an NMR experiment, hydrogen atoms are subjected to a magnetic field of 5.0\ \mathrm{T}. Determine the difference in energy (\mathrm{kJ/mol}) between two spin states of the nuclei of hydrogen atom and the frequency of radiation required for NMR.

Explain Stokes and anti-Stokes Raman scattering with the help of energy level diagram. For a diatomic molecule, obtain expressions for transition energies of its Raman spectra with rotational fine structure and hence the wave numbers of the Stokes lines.

Show that the lines in the absorption spectra corresponding to the rotational transitions from two adjacent energy levels of a medium sized molecule at room temperature have comparable intensities.

Explain the principle of Nuclear Magnetic Resonance (NMR) with the help of an energy level diagram. Give examples of nuclei which exhibit NMR. What major inferences can be drawn from an NMR spectra?

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.

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

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

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

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.

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 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.

Two successive lines in the rotational emission spectrum of HCl molecule appear at wave numbers 83.5\ \mathrm{cm^{-1}} and 104.1\ \mathrm{cm^{-1}}. Calculate the position of the next line appearing at the higher wave number.

Find the magnetic moment of an atom in {}^3P_2 state, assuming that LS coupling holds for this case.

Obtain Zeeman splitting for sodium D-lines.

If K, L and M energy levels of platinum are approximately 78, 12 and 3\ \mathrm{keV}, respectively, below the vacuum level, calculate the wavelengths of K_\alpha and K_\beta lines.

The energy levels of a hydrogen atom are given by E_n = \left(\frac{-1}{n^2}\right)R_{\mathrm{yd}} where 1R_{\mathrm{yd}} = hcR. Show that R = 1.097 \times 10^7\ \mathrm{m^{-1}}.

Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode.

The observed vibrational frequency of CO molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of the molecule?

Obtain an expression for the resonance condition in NMR.

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.