PYQ Bank

Obtain the ground-state wave function, depth of potential and range of nuclear force in deuteron and discuss. Also prove that no bound state exists for l \neq 0.

What is kinematics of nuclear reaction ? What is the Q-value and its significance ?

Describe the quark model. Obtain the quark composition of baryons and mesons.

Describe grand unification theories (GUT).

Discuss the four basic types of fundamental interactions in nature and compare them.

Write down the following decays in terms of quarks:

(i) \Omega^- \to \Lambda^0 + K^-

(ii) \Lambda^0 \to p + \pi^-

(iii) K^- \to \mu^- \bar{\nu}_\mu

Explain Russel Saunders coupling. Discuss the summation rules for orbital angular momentum, spin angular momentum and total angular momentum quantum numbers.

State the postulates of Bohr regarding his atom model. Obtain the expressions for the radius and electron-energy of the n^\text{th} orbit. Explain how Bohr's atom model successfully accounts for the hydrogen spectrum.

What is 'multiplicity' ? Give the term symbol for the following cases :

(i) S = \frac{1}{2} \qquad L = 2

(ii) S = 1 \qquad L = 1

If K, L and M energy levels of platinum are approximately 78, 12 and 3\ \mathrm{keV}, respectively, below the vacuum level, calculate the wavelengths of K_\alpha and K_\beta lines.

Obtain Zeeman splitting for sodium D-lines.

Find the magnetic moment of an atom in {}^3P_2 state, assuming that LS coupling holds for this case.

Use Hund's rules to find the ground-state quantum numbers, L and S of (i) Carbon and (ii) Oxygen atoms.

Derive the rotational-vibrational energy levels of a diatomic molecule. Give the analysis of spectral lines.

Distinguish between fluorescence and phosphorescence in electronically excited molecules.

The observed vibrational frequency of CO molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of the molecule?

The energy levels of a hydrogen atom are given by E_n = \left(\frac{-1}{n^2}\right)R_{\mathrm{yd}} where 1R_{\mathrm{yd}} = hcR. Show that R = 1.097 \times 10^7\ \mathrm{m^{-1}}.

Two successive lines in the rotational emission spectrum of HCl molecule appear at wave numbers 83.5\ \mathrm{cm^{-1}} and 104.1\ \mathrm{cm^{-1}}. Calculate the position of the next line appearing at the higher wave number.

Hydrogen molecule is diatomic. Obtain the rotational energy levels of this molecule. Write down the selection rules. Obtain the smallest energy required to excite the lowest rotational mode.

A particle trapped in an infinitely deep square well of width a has a wave function \psi=\left(\frac{2}{a}\right)^{1/2}\sin\left(\frac{\pi x}{a}\right). The walls are suddenly separated by infinite distance. Find the probability of the particle having momentum between p and p+dp.