UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Discuss the main features of the vibrational and the rotational Raman spectra of diatomic molecules. How is it used to explain the structure of a molecule?

Distinguish between normal and anomalous Zeeman effects. Explain the Zeeman pattern of the resonance (D_1, D_2) lines of sodium.

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.

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.

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

(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?

(i) In a diatomic molecule when one constituent atom is replaced by one of its heavier isotopes, what change takes place in the rotational spectrum?

(ii) Calculate the change in rotational constant B when hydrogen is replaced by deuterium in the hydrogen molecule.

(iii) Draw the spectra of rigid and non-rigid rotors by using the schematic representation of the rotational energy levels and comment on it.

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.

(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.

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]

Explain the mechanism of phosphorescence emission of radiation. Distinguish between fluorescence and phosphorescence.

Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.

The fine-structure lines of CN band at 3883\cdot 4\text{ \AA} can be represented by the following equation : \nu = 25798 + 3\cdot 85m + 0\cdot 068m^2\text{ cm}^{-1} Calculate the separation between the null-line and the band-head, and state the direction of degradation of the band.

The normalized eigenfunction for the ground state of hydrogen atom is \Psi_{100} = \frac{1}{\sqrt{\pi}} \left( \frac{Z}{a_0} \right)^{3/2} e^{-Zr/a_0} Calculate the expectation value of the radius vector r of the electron in the ground state.

The components of the angular momenta \vec{J}_1 and \vec{J}_2 satisfy commutation rules. Show that the components of the sum \vec{J} = \vec{J}_1 + \vec{J}_2 also satisfy the commutation rules. Whether the difference \vec{J}_1 - \vec{J}_2 satisfies an angular momentum?

Obtain the normalized eigenvectors of \sigma_x and \sigma_y matrices.

Show that E_n=\langle V\rangle in the stationary states of the hydrogen atom.

Set up the Schrodinger's wave equation for one dimensional potential barrier and obtain the probability of tunnelling.

An electron in a one-dimensional infinite potential well, defined by V(x)=0 for -a\leq x\leq a and V(x)=\infty otherwise, goes from n=4 to n=2 level and emits photon of frequency 3.43\times10^{14}\,\mathrm{Hz}. Calculate the width of the well. (Assume Plank's constant h=6.626\times10^{-34}\,\mathrm{J.S.} and mass of electron m=9.11\times10^{-31}\,\mathrm{kg})

What is the spin wave function (for s=\frac{1}{2}) if the spin component in the direction of unit vector \eta has a value of \frac{1}{2}\hbar?