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) 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}.
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.
What are chain reactions? What do you mean by critical size of the core in which chain reaction takes place?
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}.
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.
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}.
Explain ‘Lamb Shift’ and describe the experimental arrangement to observe it. What is its importance ?
Explain spin-orbit coupling. Discuss the splitting of spectral lines of H-atom due to spin-orbit coupling.
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 ?
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.
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.
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 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.
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}}.
A particle is moving in a one-dimensional box of width 50\,\mathring{\mathrm{A}} and infinite height. Calculate the probability of finding the particle within an interval of 15\,\mathring{\mathrm{A}} at the centres of the box when it is in its state of least energy.
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\%.
A beam of 12\,\mathrm{eV} electron is incident on a potential barrier of height 25\,\mathrm{eV} and width 0.05\,\mathrm{nm}. Calculate the transmission coefficient.
