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}.
Explain the formation of molecular hydrogen in the interstellar medium.
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}.
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.
What is Lande's g factor ? Evaluate the Lande's g factor for the {}^3P_1 level in the 2p3s configuration of the {}^6\text{C} atom. Also calculate the splitting of the level when the atom is placed in an external magnetic field of 0\cdot 1\text{ tesla}.
What is Raman effect ? Explain Quantum theory of Raman effect and Rotational Structure of a Raman spectrum.
What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?
A beam of hydrogen atoms emitted from an oven at 400\text{ k} is sent through a Stern-Gerlach experiment having magnet of length 1\text{ m} and a gradient field of 10\text{ tesla/m}. Calculate the transverse deflection of an atom at the point where the beam leaves the magnet.
(i) Homonuclear diatomic molecules do not give any pure rotational or vibrational spectra, whereas they do give a rotational Raman spectra. Comment. (ii) The separation between the adjacent rotational Raman lines is 4B in hydrogen molecule, whereas in oxygen molecule it is 8B. Why?
Evaluate the Landé 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.
Often the intensity of rotational transition J = 0 \to J = 1 is not the most intense. Explain.
What is vector model of the atom? On the basis of it, explain the L-S and j-j coupling under external magnetic field.
Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.
If an atom is placed in a magnetic field of strength 0\cdot 1\text{ weber/m}^2, then calculate the rate of precession and torque on an electron with l=3 in the atom. Given that the magnetic moment of the electron makes an angle of 30^\circ with the magnetic field.
What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.
The rotational and centrifugal distortion constants of a diatomic molecule are 10\cdot 59\text{ cm}^{-1} and 5\cdot 3 \times 10^{-4}\text{ cm}^{-1}, respectively. Obtain an estimate each for the vibrational frequency and force constant of the molecule. [\text{Given } : \text{The reduced mass of the molecule is } 1\cdot 626 \times 10^{-27}\text{ kg}]
How does the Stern-Gerlach experiment explain the concept of electron spin and its angular momentum quantization?
Explain the mechanism of phosphorescence emission of radiation. Distinguish between fluorescence and phosphorescence.
The quantum numbers of the two optical electrons in a two-valence electron atom are n_1 = 6, \quad l_1 = 3, \quad s_1 = \frac{1}{2} n_2 = 5, \quad l_2 = 1, \quad s_2 = \frac{1}{2} Assuming j-j coupling, find the possible values of J.
Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.
