(i) What is nuclear binding energy and how does it vary with mass number of the nucleus ? (ii) Calculate the binding energy per nucleon of {}^{4}\text{He}. Given m (^{4}\text{He}) = 4\cdot 002602\text{ u}, m_p = 1\cdot 007825\text{ u} and m_n = 1\cdot 008665\text{ u}.
Delhi requires 3000\text{ MWh} of electric energy per day. It is to be supplied by a reactor which converts nuclear energy into electrical energy with an efficiency of 20\text{ percent}. If reactor uses nuclear fuel of \text{U}^{235}, calculate the mass of \text{U}^{235} needed for one day operation.
(i) Describe the Quark model of hadrons, including the properties of quark. (ii) How does an up quark become a down quark ?
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}.
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.
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.
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.
Describe and explain different types of coupling in atoms. Deduce the various interaction energy terms for L – S coupling.
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}.
(i) Derive the Schrodinger time-independent wave equation for matter waves. (ii) An electron is confined to move in a one-dimensional potential well of length 5\text{ \AA}. Find the quantized energy values for the three lowest energy states.
To illustrate the idea that the zero point energy gets larger by going from macroscopic to microscopic systems, calculate the zero point energy for a particle in an infinite potential well for the following three cases : (i) A 100\text{ g} ball confined on a 5\text{ m} long line. (ii) An oxygen atom confined to a 2 \times 10^{-10}\text{ m} lattice. (iii) An electron confined to a 10^{-10}\text{ m} atom.
A stream of electrons, each of energy E = 3\text{ eV}, is incident on a potential barrier of height V = 4\text{ eV}. The width of the barrier is 20\text{ \AA}. Calculate the percentage transmission of the beam through the barrier.
Use WKB method to estimate the energy levels of a one-dimensional harmonic oscillator.
Prove that [J^2, J_y] = 0.
Use the uncertainty principle to estimate (i) The ground state radius of the hydrogen atom, and (ii) The ground state energy of the hydrogen atom.
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.
