How do Stokes lines appear in Raman spectrum as per classical and quantum theory of Raman effect ?

What is Lamb shift in the fine structure of hydrogen spectrum ? Discuss its theory based upon second quantization.

Explain how the hydrogen spectrum is used for imaging the universe.

How is Rydberg constant related to emission wavelength of hydrogen spectrum ?

Differentiate between L-S coupling and J-J coupling. What are the possible orientations of \vec{J} for the J = \frac{3}{2} and J = \frac{1}{2} states that correspond to l = 1 ?

(i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume that sodium has one free electron per atom and its density is 0\cdot 97\text{ gm/cm}^3. (ii) Draw the energy level diagram and mathematical expressions for the following : I. E_n of an electron confined in a one-dimensional box II. Linear harmonic oscillator Make a qualitative comparison of the above two cases.

Describe Electron Paramagnetic Resonance. Highlight its differences with NMR and discuss its applications.

Show that for a diatomic molecule with two nuclei of mass 'M' separated by a distance 'a', the rotational energy of nuclear motion is lower than electronic energy by a factor of \frac{m_e}{M}.

What is Lande's g factor ? Evaluate the Lande's g factor for the {}^3P_1 level in the 2p3s configuration of the {}^6\text{C} atom. Also calculate the splitting of the level when the atom is placed in an external magnetic field of 0\cdot 1\text{ tesla}.

What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?

If an atom is placed in a magnetic field of strength 0\cdot 1\text{ weber/m}^2, then calculate the rate of precession and torque on an electron with l=3 in the atom. Given that the magnetic moment of the electron makes an angle of 30^\circ with the magnetic field.

A beam of hydrogen atoms emitted from an oven at 400\text{ k} is sent through a Stern-Gerlach experiment having magnet of length 1\text{ m} and a gradient field of 10\text{ tesla/m}. Calculate the transverse deflection of an atom at the point where the beam leaves the magnet.

What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.

What is Raman effect ? Explain Quantum theory of Raman effect and Rotational Structure of a Raman spectrum.

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.

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.

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