Explain how Pauli's exclusion principle helps in determining the electronic configuration in a many-electron system.

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Why is the relaxation process so important in nuclear magnetic resonance (NMR)?

The OH-radical has a moment of inertia of 1\cdot 48 \times 10^{-46}\text{ kg}\cdot\text{m}^2. For J = 6, calculate its angular velocity and angular momentum. Find the energy absorbed in the J = 6 \rightarrow J = 7 transition.

Calculate the number of permitted electrons in a sub-shell and a shell in an atom.

Why can the experimental observation of the Lamb shift not be explained by the Dirac theory?

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Why does the electron paramagnetic resonance (EPR) spectroscopy utilize the microwave region of the electromagnetic spectrum, while nuclear magnetic resonance (NMR) uses radio waves?

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What are hot bands in vibrational spectroscopy? Why are they called so?

Explain why the rotational transition J = 0 \rightarrow J = 1 is often not the most intense.

Why are ^{12}\text{C} and ^{16}\text{O} nuclei not suitable for the study of NMR?

From the pure rotational absorption spectra of a diatomic molecule (HF), the wave number difference between the consecutive rotational lines is found to be \Delta \bar{\nu} = 4050 \text{ m}^{-1}. Calculate the following : (1) Rotational constant (2) Moment of inertia (3) Distance between two atoms (bond length) [ Given, M_{\text{H}} = 1 \text{ u}, M_{\text{F}} = 19 \text{ u} ]

Find out the difference in frequencies of Lyman-alpha line in hydrogen and deuterium atoms.

The force constant of \text{HCl} molecule is 4\cdot 8 \times 10^5 \text{ dyne/cm}. Calculate the wave numbers of Stokes and anti-Stokes lines, when excited with a radiation of wavelength 4358 \text{ \AA}. [ Given, \mu_{\text{HCl}} = 1\cdot 61 \times 10^{-24} \text{ g} ]

The quantum numbers of two electrons in a two-valence electron atom are n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} Assuming L\text{-}S coupling, find the possible values of L and J.

Draw the normal Zeeman pattern for {}^1\text{F}_3 - {}^1\text{D}_2 transition.

The Stern-Gerlach experiment is a landmark experiment in quantum mechanics. Discuss about the most important findings of this experiment.

In case of pure rotational states, if the temperature will be doubled, then calculate the rotational quantum number corresponding to maximum population density. [ Assume that temperature is high ]

Distinguish between fluorescence and phosphorescence. Explain the mechanisms responsible for these phenomena. Discuss the applications of fluorescence and phosphorescence in the fields such as biochemistry, material science, etc.