Write down the Bethe-Weizsäcker mass formula. Explain various terms of the formula.

(i) State the quantum numbers I_z, Y and S for the uds quarks and antiquarks. What combination of these leads to the formation of (a) proton and (b) neutron ?

(i) Which of the following reactions are allowed and forbidden under the conservation of strangeness, conservation of baryon number and conservation of charge ? \pi^+ + n \rightarrow \Lambda^\circ + K^+ \pi^+ + n \rightarrow K^\circ + K^+ \pi^- + p \rightarrow \Lambda^\circ + K^+ \pi^- + p \rightarrow \pi^\circ + \Lambda^\circ (ii) By drawing E vs. \vec{k} curve, distinguish between metal, insulator and semiconductor.

Describe in detail one experiment for the detection of neutrino.

What is the difference between neutrino and anti-neutrino ? How is helicity of neutrino determined ?

Explain how energy is released in stars.

Calculate the binding energy per nucleon for {}_2^4\text{He} and {}_8^{16}\text{O}.

If x and p_x are two conjugate variables, show that [[UNCLEAR]] duce 4 watts and the amount of energy that is released in the complete fissioning of 1\text{ kg} of {}^{235}\text{U}. (Assume energy released per fission of {}^{235}\text{U} is 200\text{ MeV}.)

List some of the important properties of deuteron and show that it is a loosely bound system and has only one bounded state.

Sketch carefully the binding energy per nucleon curve for stable nuclei. Explain its salient features. On the basis of this curve explain why fusion is possible only for low mass nuclei, whereas fission takes place in heavy nuclei.

Distinguish between a nuclear reaction and decay. Which conservation laws are obeyed in nuclear reactions ? Explain the significance of Q value. Calculate the Q value for the following nuclear reaction: ^2_1 H + ^2_1 H \rightarrow ^3_2 H + n.

(i) State the conservation law which is violated in each of the following processes: (1) n \rightarrow p + e^- + r (2) \pi^- + p \rightarrow K^+ + K^- (3) \pi^- + p \rightarrow \Sigma^+ + K^- (4) \Sigma^- \rightarrow K^- + p + \bar{p} (ii) Draw a bcc lattice. Determine its primitive lattice vectors and calculate the packing fraction.

Give two characteristics properties of strange par- tides which distinguish them from non-strange ones. Write the Gellmann-Nishijima relation and show how it is used for the classification of elementary particles.

Distinguish between particle and antiparticle. How antiparticles were discovered?

(i) What is the lowest non zero angular momentum for an elementary particle? Name at least three elementary particles having such an angular momentum. (ii) Write the spectral symbol of the term with S= 1/2, J = 5/2 and g = 6/7.

Explain shell model of the nucleus. Give evidence for nuclear shell structure. What are the limitations of the shell model?

Which conservation laws are obeyed in nuclear reactions? Explain the significance of Q value of a nuclear reaction.

(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.

]-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}}

Mention the conservation laws for strong, electromagnetic, and weak interactions.