The zero point energy of the ground state of \text{N}_2 is 1176\text{ cm}^{-1} and that of its lowest excited state is 727\text{ cm}^{-1}. The energy difference between the minima of the two potential energy curves is 50,206\text{ cm}^{-1}. What is the energy of the v' = 0 \rightarrow v'' = 0 transition and its corresponding wavelength in cm ?
The calcium line of wavelength \lambda = 4226\cdot 73\text{ \AA} (\text{P} \rightarrow \text{S}) exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4\text{ Weber/metre}^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.
Explain the principle and working of Stern-Gerlach Experiment.
Determine the normal Zeeman splitting of the cadmium red line of 6438\,\mathring{\mathrm{A}}, when the atoms are places in a magnetic field of 0.009\,\mathrm{T}.
Explain how the magnetic moments of atoms, the space quantization of angular momentum and the spin of electron are measured using Stern–Gerlach experiment.
Write the principle of nuclear magnetic resonance (NMR). Explain the design and working of NMR, and write its important applications.
Calculate the frequency of the first Bohr orbit of hydrogen atom.
A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600\text{ \AA} when excited by light of wavelength 4358\text{ \AA}. Calculate the wavelength of the corresponding infrared band.
Obtain an expression for the rotational energy levels of a diatomic molecule, taking it as a rigid rotator. Discuss its spectrum and the selection rule.
Explain the mechanism of Fluorescent emission of radiation. Distinguish between Fluorescence spectra and Raman spectra of a diatomic molecule.
The potential energy of a diatomic molecule in terms of the interatomic spacing R is given by U(R)=-\frac{A}{R^2}+\frac{B}{R^{10}} where A=1.44\times10^{-3}\,\mathrm{J\,m^2} and B=2.19\times10^{-115}\,\mathrm{J\,m^{10}}. Calculate the equilibrium spacing, R_e and the dissociation energy.
Write down the characteristics of Raman spectral lines. Explain why Stokes lines are more intense than anti-Stokes lines. With exciting line at 2536~\text{\AA}, a Raman line for a sample is observed at 2612~\text{\AA}. Calculate the Raman shift in wave number.
The first rotational line of {}^{12}\text{C}^{16}\text{O} is observed at 3\cdot 84235~\text{cm}^{-1} and that of {}^{13}\text{C}^{16}\text{O} at 3\cdot 67337~\text{cm}^{-1}. Assuming the mass of {}^{16}\text{O} to be 15\cdot 9949~\text{u}, calculate that of {}^{13}\text{C}.
Draw the schematic diagram of a nuclear magnetic resonance (NMR) spectrometer. Discuss nuclear magnetic resonance imaging.
Write down the Franck-Condon principle and explain how it accounts for the intensities of spectral lines in vibrational-electronic spectra with suitable illustrations.
Why are Raman active vibrations and IR vibrations in \mathrm{CO}_2 molecule complementary to each other?
What is Franck-Condon principle? Discuss the intensity distribution in the vibrational electronic spectra of a diatomic molecule on the basis of this principle.
What is Lamb shift? Discuss its significance in determining the fine structure of \mathrm{H}_{\alpha} Balmer line in hydrogen atom.
What is Lamb shift? Why does the study of Lamb shift enjoy so much attention?
If the state of the hydrogen atom is 2p state, calculate the energy levels of the spin-orbit interaction Hamiltonian A \vec{L} \cdot \vec{S}, where A is a constant.
