PYQ Bank

State and discuss the Franck-Condon principle giving special reference to its applications.

Explain and discuss the basic principle of nuclear magnetic resonance (NMR).

What are the gyromagnetic factors of the three cases, viz., a spinning electron, an orbiting electron and a free proton ?

Determine the order of magnitude of the energy involved in the spin-orbit interaction of 2p state of an atom with an electron. Given the magnetic field due to the state is 0.28 T.

(i) How many lines occur in the multiplet arising from ^{2}\text{P}_{3/2} \rightarrow {^{2}\text{S}_{1/2}} and ^{2}\text{P}_{1/2} \rightarrow {^{2}\text{S}_{1/2}} transitions of alkali metal atoms placed in a weak magnetic field, why ? (ii) The wavefunction of a particle confined in a cube of volume L^3 is given by \Psi (x,y,z) = \left( \frac{2}{L} \right)^{3/2} \sin \frac{\pi x}{L} \sin \frac{\pi y}{L} \sin \frac{\pi z}{L} Calculate the average values of p_x and p_x^2 in the region 0 < x < L.

Describe Stern-Gerlach experiment and discuss its implications.

(i) Explain the molecular phenomenon of spontaneous emission between two electronic states of the same multiplicity and differentiate it form that of different multiplicity. (ii) The constants B and V_0 for a KCl molecule have values 1 \cdot 43 \times 10^{-5} \text{ eV} 8 \cdot 4 \times 10^{12} \text{ s}^{-1} respectively. Determine the number of rotational levels between the vibrational levels v = 0 and v = 1.

Obtain an expression for the vibration-rotation energy levels of a diatomic molecule in a given electronic state. The wave numbers of the vibrational transitions occuring in HF, HCl and HI molecules are 4141 \cdot 3 \text{ cm}^{-1}, 2988 \cdot 9 \text{ cm}^{-1} and 2309 \cdot 5 \text{ cm}^{-1} respectively. Compare the force constants of these three molecules.

Describe Stern-Gerlach experiment and discuss its implications.

(i) Calculate the wavelength of neutrons at a temperature of 20^\circ\text{C}. (ii) What are the term symbols for atoms with the following S (total spin) and L (total orbital) quantum numbers, S = 1/2, L = 3 ?

(i) Calculate the Zeeman shift observed in the normal Zeeman effect when a spectral line of wavelength 5000\text{ \AA} is subjected to the magnetic field of 0.4\text{ Wb m}^{-2}. (ii) Show that for the ground state of hydrogen atom the mean value of r is 3/2\text{ a}_0, where \text{a}_0 being Bohr radius constant.

Obtain an expression for the vibration-rotation energy levels of a diatomic molecule in a given electronic state. The wave numbers of the vibrational transitions occuring in HF, HCl and HI molecules are 4141.3\text{ cm}^{-1}, 2988.9\text{ cm}^{-1} and 2309.5\text{ cm}^{-1} respectively. Compare the force constants of these three molecules.

Define the gyromagnetic ratio and obtain an expression for the Lande g factor. What is the importance of g factor in spectroscopy?

(i) What are the typical energies (eV) of the radiations, required to excite (i) electronic transitions. (ii) vibrational transitions and (iii) rotational transitions in a molecule ? (ii) The rotational spectrum of HI consists of equidistant lines with a separation of 12.8\text{ cm}^{-1}. Calculate the (a) M.I. and (b) bond length of HI molecule.

Discuss the salient features of O, P, Q, R and S branches of electronic spectrum of diatomic molecules. Which spectrum contains only branches, both branches and bands, branches and progressions ?

A diatomic gas is found to have a number of absorption bands in the ultraviolet region. Each band is also observed to have a fine structure. How can the observed spectrum be explained and analyzed?

Derive an expression for the spin-orbit interaction energy in one electron system. Calculate the energy separation between the levels ^2P_{1/2} and ^2P_{3/2}.

Calculate the change in rotational constant (B_v) when deuterium is substituted for hydrogen in a hydrogen molecule.

Explain the nature, origin and significance of 21 cm hydrogen line.

(i) A sample is irradiated by a 5000 \AA\ radiation to give a Raman line at 5050.5 \AA. Calculate the Raman frequency. (ii) Explain, both red and violet degraded bands have been observed in electronic band systems, but rotation-vibration spectra show bands degraded to red only.