(i) Explain how neutrino was discovered from the [[UNCLEAR]]-decay of radioactive nuclei. (ii) Show that for a cubic lattice, the difference between the successive h, k, l planes is given by d_{h,k,l} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}
Explain shell model of the nucleus. Give evidence for nuclear shell structure. What are the limitations of the shell model?
(i) Explain why a neutral particle such as neutron possesses a finite value of magnetic moment, and how it is determined. (ii) Write down the electronic configuration of {}^7\text{Li}, \, {}^{13}\text{C} \quad \text{and} \quad {}^{25}\text{Mg} in the ground state of the nuclear shell model.
Discuss the significance of Gellmann-Nishijima relation in strange particle production and decay. Give examples in support of your answer. Obtain quark quantum numbers using the modified relation for quarks.
Illustrate with any five examples that production of strange particles conserves strangeness, parity and isotopic spin while their decay violates all these quantities.
Describe important experimental facts that led Pauli to postulate the existence of neutrino particle.
Discuss briefly the concepts of fission barrier, excitation energy and activation energy on the basis of liquid drop model. Why {}^{235}_{92}\text{U} is fissionable by thermal neutrons while {}^{238}_{92}\text{U} is not ?
Describe briefly the various cycles for energy production in stars, relating them to the life history of a star. "Fusion reactors operate in the core of stars but have not become a reality on earth as yet." Comment on the statement.
Use conservation laws to find the nature of residual nucleus when 50.0\text{ MeV} proton beam strikes the beryllium ({}^{9}_{4}\text{Be}) target nucleus producing a beam of neutrons.
A nuclear reactor operates at a power level of 10^8\text{ W}. What will be the flux of neutrons required to maintain this power level ? Given that a free neutron has an average lifetime of 10^{-3}\text{ second} before its capture in a uranium nucleus and energy released per fission is 200\text{ MeV}.
Classify the Indian power reactors into BWR, PHWR and FBR varieties, explaining the acronyms, type of fuel used and location for each variety.
Which of the following reactions are allowed? What are the conservation laws violated by the rest ? Classify the particles (fermions / bosons. mesons / baryons, leptons/ hadrons) involved and the type of interactions in the case of the allowed ones. (i) \Sigma^0 \rightarrow \pi^+ + \pi^- (ii) \pi^- + p \rightarrow n + \pi^0 (iii) \pi^+ + p \rightarrow \pi^+ + p + \pi^- + \pi^0 (iv) \pi^0 \rightarrow \gamma + \gamma
Using the uncertainty principle, show that the electrons cannot exist inside the nucleus. How does then one account for the beta decay of a nucleus ?
How do you explain the continuous spectrum in beta decay of radioactive nuclei ?
A nuclear reactor has an output power of 1\text{ MW} with a thermal efficiency of 30\%. How much uranium per day is consumed to run this reactor, if the average energy released per fission of {}^{235}\text{U} is 200\text{ MeV}, and the uranium is enriched to 2\%\ {}^{235}\text{U} ?
Give Weiszacker formula for the binding energy of a nucleus. Explain the significance of each term. Derive an expression for the atomic number Z of the most stable nucleus for a given mass number A. Determine the atomic number Z of the stable nucleus having A = 64.
The following reaction do not take place : (i) n \rightarrow p + e^- + \nu (ii) p \rightarrow \pi^0 + e^+ + \nu Explain the reasons in terms of conservation laws.
The specific activity of a sample containing radioactive \text{Co}^{58} and non-radioactive \text{Co}^{59} was observed to be 2.2 \times 10^{12} disintegrations per second per gm. Half-life of \text{Co}^{58} is 71.3 days. Find the percentage of mass of radioactive element in the sample.
What is the basis of thermonuclear fusion? Estimate the order of temperatures required for promoting the fusion reaction of lighter nuclei. Calculate the Q-value of the proton-proton cycle. 4 {}_1^1 H \rightarrow {}_2^4 He + 2 {}_{+1}^0 e + Q.
In nature, we have basically four kinds of forces in the following order of increasing interaction strength: (i) Gravitational (ii) Weak (iii) electromagnetic (iv) Nuclear or strong Comment on their spatial dependence and give their strength in terms of dimensionless coupling constants.
