CONCEPTUAL PROBLEMS

1. Neutron is considered the most effective bombarding particle in a nuclear reaction. Why?
2. A nucleus consists of positively charged protons and electrically neutral neutrons in a small volume. How can this be possible as the like charges repel each other?
3. All the nuclei have nearly the same density. Justify.
4. Why is neutron considered the most effective bombarding particle in a nuclear reaction?
5. According to properties of charges, like charges repel each other. Then, how do the protons in a nucleus stay together?
6. Why is the mass of a nucleus slightly less than the mass of constituent nucleons?
7. Define atomic mass unit (amu). Hence convert the mass of a neutron, (1840 me), into amu where me is the mass of ‘an electron’.
8. Diameter of Al²⁷ nucleus is D_Al. How can one express the diameter of Cu⁶⁴ in terms of D_Al? Explain.
9. By what factor must the mass number of a nucleus increase to double its volume? Explain.
10. What is the significance of binding energy per nucleon?
11. Define atomic mass unit and convert it into MeV.
12. Does a nucleus contain electrons? Explain.
13. ‘Nuclear charge determines the chemical elements.’ Justify.
14. What does the energy balance (Q-value) of a nuclear reaction signify? Explain.
15. Why are neutrons used to initiate fission reaction?
16. Why does a mountain of uranium not explode as a bomb?
17. Point out the difference between’ nuclear fission and fusion.
18. Explain the significance of Einstein’s mass energy equivalence relation.
19. Define mass defect and packing fraction of a nucleus.
20. Distinguish between isotopes and isobar?
21. Explain binding energy in terms of packing fraction.

THEORY BASED PROBLEMS

22. Define binding energy and binding energy per nucleon. How does binding energy per nucleon vary with mass number? What is its significance?
23. Differentiate between nuclear fission and fusion. Explain the production of energy in the Sun.
24. Discuss fission and fusion with an example of each. In which reaction is the energy released greater?
25. Define mass defect and binding energy of a nucleus. Draw a graph showing the variation of binding energy per nucleon and atomic number of the elements. Also interpret the graph.
26. Write down the representative nuclear fission and fusion reactions. Explain, how the energy release in the case of four protons fused into doubly ionized helium can be estimated?
27. Discuss four important properties of nuclei.
28. What are meant by mass defect and binding energy per nucleon? Draw a graph showing the relation between binding energy per nucleon and atomic number. Explain its significances.
29. Write down the schemes for nuclear fusion and nuclear fission. How can the release energy in any of these reactions estimated? What do you mean by Q – value of a nuclear reaction?
30. What is nuclear fission? How energy is released in nuclear fission reaction?
31. What is nuclear fission? Give an example of nuclear reaction.
32. State and explain Einstein’s mass energy relation with example.

NUMERICAL PROBLEMS

1. Calculate the binding energy per nucleon of ₂₆Fe⁵⁶. Atomic mass of ₂₆Fe⁵⁶ is 55.9349 u and that of ₁H¹ is 1.00783u. Mass of ₀n¹ = 1.00867u and 1u = 931 MeV. Ans: [latex]1.41\times 10^{-12}[/latex] J
2. Calculate the binding energy per nucleon of calcium nucleus (₂₀Ca⁴⁰).
   Given: mass of ₂₀Ca⁴⁰ = 39.962589 u
   Mass of neutron, m_n = 1.008665u
   Mass of proton, m_p = 1.007825u
   1u = 931 MeV.
3. A city requires 10⁷ watts of electrical power on the average. If this is to be supplied by a nuclear reactor of efficiency 20%. Using ₉₂U²³⁵ as the fuel source, calculate the amount of fuel required per day. (Energy released per fission ₉₂U²³⁵ = 200 MeV).Ans: 0.0527 kg
4. A nucleus of ₉₂U²³⁸ disintegrates according to
   ₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴
   Calculate:
   (i) the total energy released in the disintegration process.
   (ii)  the K.E. of the [latex]\alpha[/latex] – particle, the nucleus at rest before disintegration. (Mass of ₉₂U²³⁸ = [latex]3.859\times 10^{-25}[/latex] kg, mass of ₉₀Th²³⁴ = [latex]3.787\times 10^{-25}[/latex] kg, ₂He⁴ = [latex]6.648\times 10^{-27}[/latex] kg). Ans: 4.236 MeV, 4.16 MeV
5. The mass of ₁₇Cl³⁵ is 34.9800 amu. Calculate its binding energy and binding energy per nucleon. Mass of one proton = 1.007825 amu and mass of one neutron = 1.008665 amu. Ans: 287.66 MeV, 8.21 MeV/nucleon
6. The energy liberated in the fission of single uranium – 235 atom is [latex]3.2\times 10^{-11}[/latex] J. Calculate the power production corresponding to the fission of 1 gm of uranium per day. Assume Avogadro constant as [latex]6\times 10^{23}\ mol^{-1}[/latex].Ans: [latex]9.46\times 10^5[/latex] W
7. What will be the amount of energy released in the fusion of three alpha particles into a C¹² nucleus if mass of He⁴ and C¹² nuclei are respectively 4.00263 amu and 12 amu. Ans: 7.34 MeV
8. The mass of the nucleus of the isotope Lithium ₃Li⁷ is 7.014351 u. Find its binding energy and binding energy per nucleon. (Given mass of proton = 1.00727 u, mass of neutron = 1.008665 u).Ans: 39.3 MeV, 5.6 MeV/nucleon
9. ₂₈Ni⁶² may be described as the most strongly bound nucleus because it has the highest B.E. per nucleon. Its neutral atomic mass is 61.928349 amu. Find its mass defect, its total binding energy and binding energy per nucleon.
   Given, mass of neutron = 1.008665 amu
   Mass of proton = 1.007825 amu
   1 amu = 931.5 MeV. Ans: [latex]\Delta m[/latex] = 0.583561 amu, B.E. = 543.58 MeV, B.E./Nucleon = 8.76 MeV per nucleon
10. The energy released per fission of one U²³⁵ atom is 200 MeV. Calculate the energy released in Kwh, when one gram of uranium undergoes fission. Ans: 2.278 x 10⁴ kwh
11. Calculate the binding energy per nucleon for a helium nucleus. Given that mass of helium nucleus = 4.001509 amu, mass of proton = 1.007277 amu and mass of neutron = 1.008666 amu. Ans: 7.07 MeV per nucleon
12. The most common isotope of uranium ₉₂U²³⁸, has atomic mass 238.050783 u. Calculate the a) mass defect, b) binding energy, c) Binding energy per nucleon. (Mass of proton = 1.007825 u, mass of neutron = 1.008665 u).Ans: 1.934207 amu, 1800.75 MeV, 7.57 MeV/Nucleon
13. Estimate the binding energy per nucleon of ₃Li⁷. Mass of ₃Li⁷, a proton & a neutron are respectively 7.01435 amu, 1.00728 amu and 1.00867 amu.Ans: 5.6 MeV/Nucleon
14. Assuming that about 200 MeV energy is released per fission of ₉₂U²³⁵ nuclei. What would be the mass of U²³⁵ consumed per day in the fission of power 1 MW approximately.Ans: 1.05 gm
15. A nucleus of uranium – 238 disintegrates according to the reaction ₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴. Calculate: i) the total energy released in the disintegration ii) the K.E. of the alpha particle, the nucleus being at rest before disintegration. (Mass of ₉₂U²³⁸ = 238.12492 u, mass of ₉₀Th²³⁴ = 234.1165 u, mass of ₂He⁴ = 4.00387 u, 1u = 931 MeV).Ans: 4.236 MeV, 4.16 MeV
16. The energy liberated in the fission of a single uranium – 235 atom is [latex]3.2\times 10^{-11}[/latex] J. Calculate the power production corresponding to the fission of 1 kg of uranium per day. (Avogadro constant = [latex]6.0\times 10^{23}\ mole^{-1}[/latex]).Ans: [latex]9.47\times 10^8 [/latex] W
17. Calculate the Q – value of the reaction & mention the type of reaction (endo – thermic or exothermic). ₂He⁴ = 4.00377 amu, ₈O¹⁷ = 17.00450 amu
    ₇N¹⁴ = 14.00783 amu, ₁H¹ = 1.00814 amu. Ans: – 0.96824 MeV
18. Calculate the speed of particle of the mass of it is equal to 5 times its rest value. Ans: [latex]2.93\times 10^8[/latex] m/s