PYQ Bank

Obtain the resonance condition of nuclear magnetic resonance spectroscopy. Write down at least three important applications.

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} ]

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.

(i) With suitable diagrams, explain the intensity distribution of spectral lines in vibrational-electronic spectra by using the Franck-Condon principle. (ii) Calculate the positions of the first two rotational Raman lines in the spectrum of \text{H}_2, if its bond length is 0\cdot 074\text{ nm}. [Given : ^{1}\text{H} = 1\cdot 673 \times 10^{-27}\text{ kg}]

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} ]

Why were silver atoms used in Stern-Gerlach experiment? Also, write the importance of this experiment.

(i) Discuss the importance of studying the isotope effect in rotational spectroscopy. (ii) If hydrogen is substituted by deuterium in hydrogen molecule, calculate the change in rotational constant B.

Experimental observation for the line spectrum of an atom shows that the separations between adjacent energy levels of increasing energy in a multiplet are in the ratio 3:5. By using the Landé interval rule, assign the quantum numbers L, S and J to these levels.

(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 in brief the Raman effect.

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

Calculate the possible angles between \vec{L} and \vec{S} for a d-electron in one-electron atom.

A beam of hydrogen atoms in a Stern-Gerlach experiment obtained from an oven heated to a temperature of 400\text{ K} passes through a magnetic field of length 1\text{ m} and having a gradient of 10\text{ T/m} perpendicular to the beam. Calculate the transverse deflection of an atom of the beam at a point where the beam leaves the field. The value of Bohr magneton \mu_B is 9\cdot 27 \times 10^{-24}\text{ A m}^2 and the Boltzmann constant k is 1\cdot 38 \times 10^{-23}\text{ J/K}.

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 ?

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 ?

Discuss the rotational fine structure of electronic bands of molecule.

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}.

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