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 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.
Are the nucleons inside the nucleus governed by the laws of quantum physics? Justify your answer.
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.
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?
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.
If plutonium ({}^{239}_{94}\text{Pu}) is used as fuel in a fission reactor and is producing fragments barium ({}^{146}_{56}\text{Ba}) and strontium ({}^{91}_{38}\text{Sr}) by initiating the reaction by one neutron and producing three neutrons in the process, then calculate the number of fissions per second required in a 100\text{ MW} reactor. [Given : BE per nucleon (MeV) : 7\cdot 6 for {}^{239}\text{Pu}, 8\cdot 2 for {}^{146}\text{Ba} and 8\cdot 6 for {}^{91}\text{Sr}]
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.
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?
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}?
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.
By considering a suitable nuclear potential well for the deuteron ground state, show that it is a loosely bound nucleus.
(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
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} ]
Using the semi-empirical binding energy formula, establish the relation between atomic number and mass number for a most stable light nucleus. Also, explain which is the most stable nucleus among {}^{3}_{2}\text{He}, {}^{6}_{4}\text{Be} and {}^{6}_{3}\text{Li}. [Given : a_c = 0\cdot 71\text{ MeV}, a_n = 22\cdot 7\text{ MeV} and assume Z(Z-1) \approx Z^2]
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} ]
(i) Write semi-empirical mass formula. Calculate the atomic number (Z) of most stable nucleus for given mass number (A) using the above formula. (Use the value of fitted coefficients for Coulomb energy a_3 = 0\cdot 711\text{ MeV} and that for asymmetry energy a_4 = 23\cdot 702\text{ MeV}). (ii) Calculate the Q-value of the following nuclear reaction : {}_4\text{Be}^9 + {}_2\text{He}^4 = {}_6\text{C}^{12} + {}_0\text{n}^1 Given : the mass of neutral atoms of \text{Be}, \text{He} and \text{C} are 9\cdot 015060, 4\cdot 003874 and 12\cdot 003815\text{ amu}, respectively. The mass of neutron is 1\cdot 008986\text{ amu}.
Does the nucleus possess magnetic moment ? Justify your answer. Define nuclear magneton (\mu_{\text{N}}) and Bohr magneton (\mu_{\text{B}}). Calculate their values.
