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State the postulates of Bohr regarding his atom model. Obtain the expressions for the radius and electron-energy of the n^\text{th} orbit. Explain how Bohr's atom model successfully accounts for the hydrogen spectrum.
Use Hund's rules to find the ground-state quantum numbers, L and S of (i) Carbon and (ii) Oxygen atoms.
Find the magnetic moment of an atom in {}^3P_2 state, assuming that LS coupling holds for this case.
Explain Russel Saunders coupling. Discuss the summation rules for orbital angular momentum, spin angular momentum and total angular momentum quantum numbers.
Two successive lines in the rotational emission spectrum of HCl molecule appear at wave numbers 83.5\ \mathrm{cm^{-1}} and 104.1\ \mathrm{cm^{-1}}. Calculate the position of the next line appearing at the higher wave number.
Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode.
The observed vibrational frequency of CO molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of the molecule?
What are the characteristics of a Raman spectrum ? How do you study Raman spectra in the laboratory ? Give two applications of Raman effect.
Given that the spacing between vibrational levels of CO molecules is 8.45 \times 10^{-2}\ \mathrm{eV} of energy. Find the force constant of the molecule.
Discuss the vibrational spectra of a diatomic molecule treating it as an anharmonic oscillator.
Given that the rotational inertia of \text{HCl} molecule has the value I = 2\cdot 66 \times 10^{-47}\text{ kg-m}^2, estimate the energy difference between the lowest and first excited state of \text{HCl}.
Explain spin-spin and spin-lattice relaxation times in NMR spectroscopy. How do they influence the line width of the NMR line ?
How is proton magnetic resonance applied to determine the chemical shifts in molecules containing hydrogen atom ? Illustrate your answer with a suitable example.
Discuss the different coupling schemes in atomic spectroscopy with suitable diagrams.
What is Lamb shift ? How is it measured ?
Explain the relaxation processes in NMR spectroscopy.
An atom in an excited state of 4\cdot 7\text{ eV} emits a photon and ends up in the ground state. The lifetime of the excited state is 10^{-13}\text{ s}. Calculate the energy uncertainty and obtain the spectral line width in wavelength of photon.
Obtain an expression for the normal Zeeman shift. Illustrate the Zeeman splitting of spectral lines of H atom and the allowed transitions for the l = 1 and l = 2 states.
A sample of a certain element is placed in a magnetic field of flux density 0.3 tesla. How far apart is the Zeeman component of a spectral line of wavelength 4500\mathring{\mathrm{A}}? Given : e/m = 1.76 \times 10^{11}\ \mathrm{c/kg}, c = 3.0 \times 10^8\ \mathrm{m\,s^{-1}}.
Obtain an expression for the resonance condition in NMR.