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}]
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 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.
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)
By considering a suitable nuclear potential well for the deuteron ground state, show that it is a loosely bound nucleus.
Assume that the range of the interaction of nuclear force and of meson is 2 \times 10^{-15}\text{ m}. Estimate the mass of the meson.
(ii) From a study of the radial part of the Schrödinger equation of a deuteron for any angular momentum l, what do we conclude?
Apply the meson theory of nuclear forces to write the interaction between protons, neutrons, proton to neutron and neutron to proton.
A sample contains 4\text{ mg} of {}^{210}\text{Bi}. If the half-life of radioactive {}^{210}\text{Bi} is 5\text{ days} and the average energy of the \beta-particles emitted is 0\cdot 34\text{ MeV}, then at what rate does the sample emit energy?
A radionuclide (N_1) decays to a radioactive daughter (N_2) that subsequently decays to a third daughter (N_3). If at t = 0, the initial concentrations of N_1, N_2 and N_3 are N_1^0, 0 and 0 respectively, and the decay constants are \lambda_1 (from N_1 \rightarrow N_2) and \lambda_2 (from N_2 \rightarrow N_3), then derive the expression for N_2 at time t. Given that the daughter N_3 is stable.
In the case of deuterons, answer the following : (i) What percentage of the time do the nucleons of a deuteron spend within the range of the nuclear forces?
Write the decay reactions of the neutral pions (\pi^0) and the charged pions (\pi^+, \pi^-).
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?
What do you understand by the critical size of a nuclear reactor? Write down the common features of nuclear reactors used for the production of electricity.
Justify the fact that the electrons are emitted from nuclei in \beta-decay but they cannot be contained inside the nuclei.
Derive an expression for \alpha-disintegration energy for a nucleus in a radioactive decay process.
Why does a neutron star have a magnetic field if it is composed of neutrons?
The nature of curves of binding energy and packing fraction are complementary to each other. Explain.
On the basis of conservation laws, explain whether the following reactions are allowed or forbidden : (i) \pi^- + \text{p} \longrightarrow \Sigma^+ + \text{K}^- (ii) \text{K}^- + \text{p} \longrightarrow \Omega^- + \text{K}^+ + \text{K}^0 (iii) \Omega^- \longrightarrow \Xi^0 + \pi^- (iv) \pi^+ + \text{p} \longrightarrow \text{p} + \text{p} + \bar{\text{n}} (v) \Sigma^+ \longrightarrow \Lambda^0 + \text{K}^+
Explain Gell-Mann and Ne'eman SU(3) symmetry for the classification of elementary particles — baryons and mesons.
