(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}]
Explain the salient features of fluorescence and phosphorescence with the help of energy level diagram. Name a few applications of these phenomena in our daily life.
Write the electronic configurations for carbon (C), nitrogen (N) and oxygen (O) atoms, and then derive their ground states.
Why were silver atoms used in Stern-Gerlach experiment? Also, write the importance of this experiment.
Obtain the resonance condition of nuclear magnetic resonance spectroscopy. Write down at least three important applications.
If ^{11}\text{Na} atoms in their ground state are placed in a region having electromagnetic radiation of frequency \nu = 1\cdot 0 \times 10^{10}\text{ Hz}, calculate the required magnetic field B at which the electromagnetic radiation will be in resonance with the Zeeman splitting.
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) 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.
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}.
Describe in brief the Raman effect.
The force constant of the bond in CO molecule is 1900\text{ N m}^{-1}. Calculate the energy of the lowest vibrational level. The reduced mass of CO molecule is 1\cdot 14 \times 10^{-26}\text{ kg}. Given h = 6\cdot 63 \times 10^{-34}\text{ J s} and 1\text{ eV} = 1\cdot 6 \times 10^{-19}\text{ J}.
Discuss the rotational fine structure of electronic bands of molecule.
Explain the formation of molecular hydrogen in the interstellar medium.
In the vibrational Raman spectrum of HF, the Raman lines are observed at wavelengths 2670\text{ \AA} and 3430\text{ \AA}. Find the fundamental vibrational frequency of the molecule.
How does the Stern-Gerlach experiment explain the concept of electron spin and its angular momentum quantization?
Evaluate the Land'e g-factor for the ^3\mathrm{P}_1 level in the 2p 3s configuration of the ^6\mathrm{C} atom, and then calculate the splitting of the level in eV, when the atom is in an external magnetic field of 0.2 tesla.
What is vector model of the atom? On the basis of it, explain the L-S and j-j coupling under external magnetic field.
An atomic state is denoted by ^4\mathrm{D}_{5/2}. What should be the minimum number of electrons involved for this state? Give a possible electron configuration.
Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.