Explain the mechanism of phosphorescence emission of radiation. Distinguish between fluorescence and phosphorescence.

Discuss the main features of the vibrational and the rotational Raman spectra of diatomic molecules. How is it used to explain the structure of a molecule?

The quantum numbers of the two optical 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 j-j coupling, find the possible values of J.

The fine-structure lines of CN band at 3883\cdot 4\text{ \AA} can be represented by the following equation : \nu = 25798 + 3\cdot 85m + 0\cdot 068m^2\text{ cm}^{-1} Calculate the separation between the null-line and the band-head, and state the direction of degradation of the band.

Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.

Distinguish between normal and anomalous Zeeman effects. Explain the Zeeman pattern of the resonance (D_1, D_2) lines of sodium.

Define Franck-Condon principle. How does it help in explaining the intensity distribution of vibrational-electronic spectra of diatomic molecules.

Show that the Landé g-factor for pure orbital angular momentum and pure spin angular momentum are 1 and 2 respectively. Further, evaluate the g-factor for the state {}^3P_1.

(i) Why does Stern-Gerlach experiment enjoy so much importance in atomic physics?

(ii) Draw the schematic diagram of this experiment and comment on the shapes of the magnet pole pieces.

(iii) Why was the atomic beam of silver used in this experiment?

An atomic state is denoted by {}^4D_{5/2}. Find the values of L, S and J. For this state, what should be the minimum number of electrons involved? Suggest a possible electronic configuration.

Set up the Schrodinger's wave equation for one dimensional potential barrier and obtain the probability of tunnelling.

Find the values of the following : (i) \vec{L} \times \vec{L} (ii) L_+ L_- (iii) [L_z, L_+] where \vec{L} is the angular momentum operator. L_+ and L_- are raising and lowering operators respectively.

An electron is confined to an infinite well whose width L (= 100\text{ pm}) is roughly the size of an atom. (i) What are the energies of four least energetic quantum states? (ii) What energy must be imparted to the electron to raise it from a state with n = 12 to a higher energy state with n = 25?

The components of the angular momenta \vec{J}_1 and \vec{J}_2 satisfy commutation rules. Show that the components of the sum \vec{J} = \vec{J}_1 + \vec{J}_2 also satisfy the commutation rules. Whether the difference \vec{J}_1 - \vec{J}_2 satisfies an angular momentum?

Show that for a given principal quantum number n, there are n^2 possible states of the atom.

What is the spin wave function (for s=\frac{1}{2}) if the spin component in the direction of unit vector \eta has a value of \frac{1}{2}\hbar?

An electron in a one-dimensional infinite potential well, defined by V(x)=0 for -a\leq x\leq a and V(x)=\infty otherwise, goes from n=4 to n=2 level and emits photon of frequency 3.43\times10^{14}\,\mathrm{Hz}. Calculate the width of the well. (Assume Plank's constant h=6.626\times10^{-34}\,\mathrm{J.S.} and mass of electron m=9.11\times10^{-31}\,\mathrm{kg})