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Binding energy and rest mass energy of a two-nucleon bound state are denoted by B and Mc^2, respectively, where c is the speed of light. Calculate the minimum energy of a photon required to dissociate this bound state in terms of B and Mc^2.
Are the nucleons inside the nucleus governed by the laws of quantum physics? Justify your answer.
By considering the three-dimensional harmonic oscillator potential, explain the energy levels of nucleons inside the nucleus. Also, derive the zero-point energy of nucleons. Why did this assumption fail to explain the existence of nuclei with higher magic number?
What is the criticality of a self-sustained nuclear reactor? Write the basic processes affecting the nuclear chain reactions of a finite-size nuclear reactor. Also, write the critical size of reactors of different shapes in terms of geometrical buckling constant.
What do you understand by the \text{SU}(3) symmetry for the classification of baryons and mesons? Draw the octets for baryons and mesons along with their quarks and antiquarks.
What do you understand by the packing fraction 'f' and the binding energy 'E_b' of a nucleus? Draw the graphs for packing fraction f versus mass number (A) and binding energy fraction f_b \left(= \dfrac{E_b}{A}\right) versus mass number (A). Further, explain how the graphs of the variation of f and f_b with A have complementary approaches.
A nucleus of rest mass M is initially in an excited state whose energy is \Delta E above its ground state. The nucleus emits a \gamma-ray of energy h\nu and makes a transition to its ground state. Calculate the fractional change in energy for the nucleus.
What do you understand by \text{SU}(3) symmetry for the quark model? On the basis of it, explain that the baryons can have +2 charge but mesons cannot have the same.
What is the minimum energy required to break a {}_2^4\text{He} nucleus into free protons and neutrons? [ Given, m_{\text{H}} = 1\cdot 007825 \text{ amu}, m_n = 1\cdot 008665 \text{ amu}, m_e = 0\cdot 00055 \text{ amu} and m_{\text{He}} = 4\cdot 002603 \text{ amu} ]
By considering a suitable nuclear potential well for the deuteron ground state, show that it is a loosely bound nucleus.
The total binding energies of {}_8^{15}\text{O}, {}_8^{16}\text{O} and {}_8^{17}\text{O} are 111\cdot 96 \text{ MeV}, 127\cdot 62 \text{ MeV} and 131\cdot 76 \text{ MeV} respectively. Determine the energy gap between 1p_{1/2} and 1d_{5/2} neutron shells for the nuclide whose mass number is close to 16.
Calculate the minimum energy (E_\gamma) required for a gamma ray photon to disintegrate a deuteron of mass M and binding energy B into a neutron and a proton. (Assume B \ll Mc^2)
\rho^0 and \text{K}^0 mesons both decay mostly to \pi^+ and \pi^-. Why the mean lifetime of \rho^0 is 10^{-23} \text{ s}, whereas that of \text{K}^0 is 0\cdot 89 \times 10^{-10} \text{ s}?
(i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e Explain the various leptonic family members. What is leptonic number conservation? Based on this conservation law, tell whether the following reactions are possible or not : (i) \pi^- \rightarrow \mu^- + \bar{\nu}_\tau (ii) n \rightarrow p^+ + e^- + \bar{\nu}_e
State the basic assumption of single-particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of three-dimensional spherical harmonic oscillator?
Consider a uranium nucleus ({}_{92}\text{U}^{236}) breaking up spontaneously into two equal parts. Estimate the reduction of electrostatic energy of the nucleus considering uniform charge distribution. [ Assume that nuclear radius is 1\cdot 2 \times 10^{-13} A^{1/3} \text{ cm} ]
What were the difficulties faced by the initial theory of \beta-decay? How did Pauli eliminate the difficulties? What were the expected properties of the new particle proposed by Pauli?
For the ground state of deuteron, prove that the radius of nucleon is of the order of \sim 2\cdot 15 \times 10^{-13}\text{ cm}.