UPSC Physics Optional PYQs (CSE & IFoS)PYQs

How is Rydberg constant related to emission wavelength of hydrogen spectrum ?

What is Lamb shift in the fine structure of hydrogen spectrum ? Discuss its theory based upon second quantization.

(i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume that sodium has one free electron per atom and its density is 0\cdot 97\text{ gm/cm}^3. (ii) Draw the energy level diagram and mathematical expressions for the following : I. E_n of an electron confined in a one-dimensional box II. Linear harmonic oscillator Make a qualitative comparison of the above two cases.

Describe Electron Paramagnetic Resonance. Highlight its differences with NMR and discuss its applications.

Explain how the hydrogen spectrum is used for imaging the universe.

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}.

How do Stokes lines appear in Raman spectrum as per classical and quantum theory of Raman effect ?

Differentiate between L-S coupling and J-J coupling. What are the possible orientations of \vec{J} for the J = \frac{3}{2} and J = \frac{1}{2} states that correspond to l = 1 ?

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.

What is nuclear magnetic resonance ? Explain its working principle and use in magnetic resonance imaging systems.

What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach experiment ?

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 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.

An atomic state is denoted by {}^4D_{5/2}. Find the values of L, S and J. For this state, what should be the minimum number of electrons involved? Suggest a possible electronic configuration.

(i) Why does Stern-Gerlach experiment enjoy so much importance in atomic physics?

(ii) Draw the schematic diagram of this experiment and comment on the shapes of the magnet pole pieces.

(iii) Why was the atomic beam of silver used in this experiment?

Calculate the magnetic field strength required to observe the NMR spectrum of protons in benzene at 120\,\mathrm{MHz}. [Given the value of nuclear g-factor g_N for protons is 5.585]

Show that the Landé g-factor for pure orbital angular momentum and pure spin angular momentum are 1 and 2 respectively. Further, evaluate the g-factor for the state {}^3P_1.

Define Franck-Condon principle. How does it help in explaining the intensity distribution of vibrational-electronic spectra of diatomic molecules.

(i) Briefly explain the effect of anharmonicity on the vibrational spectra of diatomic molecules.

(ii) Calculate the average period of rotation of HCl molecule if it is in the J=3 state. The internuclear distance and the moment of inertia of HCl are 0.1274\,\mathrm{nm} and 0.0264\times10^{-45}\,\mathrm{kg\,m^2} respectively.