PYQ Bank

How many fissions take place per second in a 300\text{ MW} reactor? Assume that 200\text{ MeV} is the energy released per fission.

What is the importance of the study of deuteron? Discuss the problem of ground state of deuteron and elicit information about nuclear forces from this study.

Discuss the vibrational spectra of a diatomic molecule treating potential energy function as a representation of Hooke's law type of interaction.

Explain the concept of shared pair of electrons with antiparallel spins forming a covalent bond in \text{H}_2-like molecule with reference to total energy.

A substance shows a Raman line at 4567\text{ \AA} when exciting line 4358\text{ \AA} is used. Estimate the positions of Stokes and anti-Stokes lines for the same substance when exciting line 4047\text{ \AA} is used.

What do you understand by H-one (HI) interstellar clouds and their importance to understand the universe.

Why are Raman active vibrations and infrared vibrations in \mathrm{CO_2} molecule complementary to each other?

How are electrons distributed in the various sub-shells for n=3? Give the quantum numbers for the electrons in the second shell.

The term symbol for atomic states are quoted as {}^3P_2 and {}^2D_{5/2}. What are the values of L, S and J?

Discuss the fine structure of sodium D line. Draw D_1 and D_2 lines due to the transitions between {}^2P and {}^2S levels.

With proper selection rules, construct the energy level diagram and allowed transitions for ESR spectrum of hydrogen atom.

In a Raman spectrum of a linear triatomic molecule, the first three lines are 4.86, 8.14 and 11.36\ \mathrm{cm^{-1}}. Calculate the rotational constant, B and the moment of inertia of the molecule. (Given h = 6.626 \times 10^{-27}\ \mathrm{J\,s}, C = 3.0 \times 10^{10}\ \mathrm{cm/sec.})

Explain why the separation between vibrational levels is smaller in an excited electronic state than in the ground electronic state.

Show that the spherical harmonics Y_{lm}(\theta, \phi) are simultaneous eigenfunctions of L^2, L_z and L_z^2. What are their corresponding eigenvalues?

Develop and write down the expressions of L^2, L_z and L_z^2 in angular momentum operator algebra.

A particle is bound in a potential well given by V(x) = \begin{cases} \infty & \text{for } x \le 0 \\ cx & \text{for } x > 0 \end{cases} Estimate the ground state energy of the system from uncertainty principle.

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The particle in a box has a ground state wave function given as \psi(x) = \frac{1}{\sqrt{l}} \cos \frac{\pi x}{2l} The box width is 2l and the particle is confined within (-l, +l). Calculate the expectation value of x^2.

Write down Schr"{o}dinger equations for a particle of energy E < V_0, incident on a step potential height V_0. Solve them to find out the transmission and reflection coefficients in terms of k and k', where k = \sqrt{\frac{2mE}{\hbar^2}} and k' = \sqrt{\frac{2m(V_0 - E)}{\hbar^2}}. Show that in this case, there is a finite probability of finding the particle in a classically forbidden region.

The normalized wave function for the electron in the ground state of the hydrogen atom is given by \psi(r)=\dfrac{1}{\sqrt{\pi a_0^3}}e^{-r/a_0}, where a_0 is the radius of the first Bohr orbit. Calculate the probability of finding the electron within a distance r_0 of the proton in the ground state.