Assuming that protons and neutrons possess equal masses, calculate how many times nuclear matter is denser than water if nuclear radius is given by 1\cdot 2 \times 10^{-15} A^{1/3}\text{ m}, where A is the mass number.

A sample of uranium emitting \alpha-particles of energy 4\cdot 18\text{ MeV} is placed near the ionization chamber. Assuming that only 10 particles per second enter the chamber, calculate the current produced. Given 1 ion pair requires 35\text{ eV}.

Calculate the mass of deuterium nucleus if the binding energy per nucleon is 1\text{ MeV}.

Which of the following reactions are possible ? (i) \quad \pi^+ + n^0 \rightarrow \Lambda^0 + K^+ (ii) \quad \pi^+ + n^0 \rightarrow K^0 + K^+ (iii) \quad \pi^+ + n \rightarrow \pi^- + p

(i) Describe the Quark model of hadrons, including the properties of quark. (ii) How does an up quark become a down quark ?

\rho^{0} and K^{0} mesons both decay mostly to \pi^{+} and \pi^{-}. Explain why the mean lifetime of \rho^{0} is shorter (\sim 10^{-23}\,\mathrm{s}) compared to the mean lifetime of K^{0} (\sim 10^{-10}\,\mathrm{s}).

In observing the Raman spectrum of a sample using 3637\,\mathring{\mathrm{A}} as the exciting line, one gets stoke line at 3980\,\mathring{\mathrm{A}}. Deduce the Raman shift in \mathrm{m}^{-1} units. Compute the wavelength in \mathring{\mathrm{A}} for corresponding stokes and anti-stokes lines if the exciting line is 6465\,\mathring{\mathrm{A}}.

Describe and explain different types of coupling in atoms. Deduce the various interaction energy terms for L – S coupling.

The first line in the pure rotational spectrum of HCl appears at 21\mathbin{\cdot}18\,\mathrm{cm}^{-1}. Calculate bond length of the molecule. Given atomic masses of H and Cl are 1.008 and 35.45\,\mathrm{amu}, respectively.

Explain spin-orbit coupling. Discuss the splitting of spectral lines of H-atom due to spin-orbit coupling.

The quantum numbers of two electrons in a two-valence electron atom are; n_1=8\quad l_1=4\quad s_1=\frac{1}{2} n_2=7\quad l_2=2\quad s_2=\frac{1}{2}

(i) Assuming L-S coupling, find the possible value of L and hence of J.

(ii) Assuming j-j coupling, find the possible values of J.

Explain ‘Lamb Shift’ and describe the experimental arrangement to observe it. What is its importance ?

The zero point energy of the ground state of \text{N}_2 is 1176\text{ cm}^{-1} and that of its lowest excited state is 727\text{ cm}^{-1}. The energy difference between the minima of the two potential energy curves is 50,206\text{ cm}^{-1}. What is the energy of the v' = 0 \rightarrow v'' = 0 transition and its corresponding wavelength in cm ?

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

Determine the possible terms of a one-electron atom corresponding to n = 3 and compute the angle between \vec{L} and \vec{S} vectors for the term ^{2}\text{D}_{5/2}.

State the Franck – Condon principle and give its wave-mechanical interpretation. How does it help in understanding the intensity distribution in the vibrational structure of the electronic transitions of a diatomic molecule ?

A beam of electrons enters a uniform magnetic field of flux density 1\cdot 2\text{ tesla}. Calculate the energy difference between electrons whose spins are parallel and antiparallel to the field.

Calculate the probability of finding a simple harmonic oscillator within the classical limits if the oscillator is in its normal state. Also show that if the oscillator is in its normal state, then the probability of finding the particle outside the classical limits is approximately 16\%.

Find the eigenvalues and eigenstates of the spin operator \vec{S} of an electron in the direction of unit vector \vec{n}. Assume that \vec{n} lies in the xz-plane using spin matrices.

A particle of rest mass m_0 has a kinetic energy K, show that its de Broglie wavelength is given by \lambda=\frac{hc}{\sqrt{\left[K\left(K+2m_0c^2\right)\right]}}. Hence calculate the wavelength of an electron of kinetic energy 2\mathrm{MeV}. What will be the value of \lambda if K << m_0c^2?