What is \beta-decay ? Give three examples of \beta-decay of nuclei. Explain how neutrino hypothesis helped in explaining conservation of energy-momentum and angular momentum. What is Kurie plot ? How can one use Kurie plot to set limits on mass of the neutrino ?
Explain lepton number conservation and why it is necessary to distinguish between different types of neutrinos ?
State the quantum numbers I_3, Y and S for the uds quarks and antiquarks. Which combination of these leads to the formation of (1) proton and (2) neutron ?
Give some characteristic properties of strange particles which distinguish them from non-strange ones. Write the Gell-Mann-Nishijima relation. How is it used for the classification of elementary particles?
A star converts all its hydrogen to helium, achieving 100% helium composition. It then converts the helium to carbon via the reaction {}^{4}_{2}\text{He} + \text{He} \rightarrow {}^{12}_{6}\text{C} + 7.27\text{ MeV} The mass of the star is 5 \times 10^{32}\text{ kg} and it generates energy at the rate of 5 \times 10^{30}\text{ W}. How long will it take to convert all helium to carbon at this rate ?
What are mirror nuclei ? How does the charge independence of nuclear force emerge from this concept?
Write down the Bethe-Weizsacker semi-empirical mass formula for a nucleus. Explain the significance of each term occurring in it. Discuss the stability of a nucleus against \beta-decay. What is the effect of pairing term on stability?
(i) Calculate the Q-value of the reaction {}^9_4\text{Be} (^4_2\text{He}, n) ^{12}_6\text{C} Given \text{Mass } (^9\text{Be}) = 9.012183\text{ u} \text{Mass } (^4\text{He}) = 4.002603\text{ u} \text{Mass } (^{12}\text{C}) = 12.000\text{ u} Write down the nucleonic configuration of {}^{7}\text{Li}, {}^{12}\text{C}, {}^{17}\text{O} and {}^{27}\text{Al} in the ground state of the nuclear shell model and hence calculate the corresponding ground state angular momenta and parities. How do the observed ground state angular momenta and parities agree with those predicted on the basis of the shell model ?
Based on physical calculations, explain why deuteron is stable.
(i) Exlain the quark structure of hadrons. Identify the field of quark of electro-weak and electro-strong interactions. Also verify the conservation of strangeness in the following reactions : 10 \pi^- + p \rightarrow \Lambda^\circ + K^\circ K^+ \rightarrow \pi^+ + \pi^+ + \pi^- (ii) Drawing necessary diagrams, explain diamond structure and CsCl structures. 10
What is the role of neutrino in the weak interaction of radioactive nuclides ? Explain the experimental detection of neutrino.
In the following reactions indicate with an explanation, whether they proceed by strong, electromagnetic or weak interaction or they are forbidden : \pi^+ \rightarrow \mu^+ + u_\mu p \rightarrow n + e^+ + u_e p + \pi^- \rightarrow K^+ + \Sigma^-
(i) Discuss in detail the classification of elementary particles. 10 (ii) On the basis of band theory, explain the classification of solids by considering their electrical properties. 10
Illustrate the Geiger-Nuttall law in a plot between the decay constant and energy of various nuclides for any radioactive series.
Name the various classifications of the gamma rays based on electric, magnetic and order. How does parity affect these radiations ?
Describe briefly the different types of physical processes with which gamma rays are absorbed by matter as they are emitted.
(i) What are the basic interactions in nature ? Give one example for each. Compare their relative strengths and ranges. (ii) What are the conservation laws for strong, electromagnetic and weak interactions ? (iii) Distinguish between particle and anti-particle. How was positron discovered ?
(i) Write the Weizacker mass formula and explain the significance of various terms. (ii) Determine the amount of {}_{84}^{210}\text{Po} necessary to provide a source of \alpha-particles of strength 5 \text{ mC}_i. The half-life of {}_{84}^{210}\text{Po} is 138 \text{ d}.
(i) Differentiate between K-capture and inverse \beta-decay. (ii) Explain what is internal conversion and how it differs from \beta-decay.
Calculate the spin and parities of the ground states of {}_2^4\text{He} and {}_{30}^{67}\text{Zn} nuclei.
