Nuclear & Radiochemistry

Time Limit: 20 minutes Total Marks: 40

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Section A — Multiple Choice (1 mark each)

Choose the single best answer.

Q1. Which nucleon numbers are known as "magic numbers" conferring extra nuclear stability? (a) 2, 6, 12, 20, 40 (b) 2, 8, 20, 28, 50, 82, 126 (c) 4, 8, 16, 32, 64 (d) 1, 3, 5, 7, 11 (1)

Q2. The binding energy per nucleon reaches a maximum near which nuclide? (a) $^{4}\text{He}$ (b) $^{56}\text{Fe}$ (c) $^{238}\text{U}$ (d) $^{1}\text{H}$ (1)

Q3. In $\beta^-$ decay, inside the nucleus a neutron converts to: (a) proton + electron + antineutrino (b) proton + positron + neutrino (c) proton + electron + neutrino (d) two protons (1)

Q4. Emission of an $\alpha$ particle changes the atomic number $Z$ and mass number $A$ by: (a) $Z-1,\ A-0$ (b) $Z-2,\ A-4$ (c) $Z+1,\ A-0$ (d) $Z-2,\ A-2$ (1)

Q5. The relationship between decay constant $\lambda$ and half-life $t_{1/2}$ is: (a) $t_{1/2}=\lambda\ln 2$ (b) $t_{1/2}=\dfrac{\ln 2}{\lambda}$ (c) $t_{1/2}=\dfrac{1}{\lambda}$ (d) $t_{1/2}=\dfrac{\lambda}{\ln2}$ (1)

Q6. The SI unit of activity (disintegrations per second) is the: (a) Gray (b) Sievert (c) Becquerel (d) Curie (1)

Q7. Radiocarbon dating is based on the decay of: (a) $^{12}\text{C}$ (b) $^{14}\text{C}$ with $t_{1/2}\approx 5730$ yr (c) $^{13}\text{C}$ (d) $^{11}\text{C}$ (1)

Q8. The fuel of the D–T fusion reaction produces which two products? (a) $^{4}\text{He} + n$ (b) $^{3}\text{He} + p$ (c) $^{4}\text{He} + \gamma$ (d) $2\,^{2}\text{H}$ (1)

Q9. The radioisotope most widely used in diagnostic medical imaging is: (a) $^{131}\text{I}$ (b) $^{60}\text{Co}$ (c) $^{99m}\text{Tc}$ (d) $^{238}\text{Pu}$ (1)

Q10. Electron capture converts a proton into a neutron and emits a: (a) positron (b) neutrino (c) antineutrino (d) $\alpha$ particle (1)

Q11. The minimum amount of fissile material needed to sustain a chain reaction is called the: (a) breeder mass (b) critical mass (c) reactor mass (d) moderator mass (1)

Q12. The absorbed dose equivalent, weighting for biological effect, is measured in: (a) Gray (b) Becquerel (c) Sievert (d) Curie (1)

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Section B — Matching (1 mark each)

Q13. Match each item in Column X to Column Y. Write pairs (e.g. i–P). (4 marks total, 1 each)

Column X	Column Y
(i) Moderator in a thermal reactor	(P) $^{238}\text{Pu}$
(ii) RTG power source in spacecraft	(Q) captures free neutrons
(iii) Control rod material (e.g. Cd/B)	(R) slows fast neutrons
(iv) End of the uranium (4n+2) series	(S) $^{206}\text{Pb}$

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Section C — True/False WITH Justification (2 marks each: 1 verdict + 1 reason)

Q14. "A nucleus lying above the belt of stability (too many neutrons) typically undergoes $\beta^-$ decay." (2)

Q15. "Fusion of light nuclei and fission of heavy nuclei both release energy because both move products toward higher binding energy per nucleon." (2)

Q16. "Radioactive decay follows zero-order kinetics, so the half-life depends on the initial number of atoms." (2)

Q17. "The Q-value of a nuclear reaction is positive when the reaction is exothermic (releases energy)." (2)

Q18. "Alpha particles are more penetrating than gamma rays and require thick lead shielding." (2)

Q19. "In the p–p chain powering the Sun, four protons are effectively converted into one $^{4}\text{He}$ nucleus." (2)

Q20. "After 3 half-lives, one-eighth of the original radioactive nuclei remain." (2)

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[
  {"claim":"After 3 half-lives fraction remaining is 1/8","code":"result = (Rational(1,2)**3 == Rational(1,8))"},
  {"claim":"Half-life from lambda: t_half = ln2/lambda gives N=N0/2","code":"lam=symbols('lam',positive=True); t=log(2)/lam; N0=symbols('N0',positive=True); N=N0*exp(-lam*t); result = simplify(N - N0/2)==0"},
  {"claim":"Alpha decay changes A by -4 and Z by -2 (mass/charge of He-4 nucleus)","code":"A_change=-4; Z_change=-2; result = (A_change==-4 and Z_change==-2)"},
  {"claim":"D-T reaction conserves mass number: 2+3 = 4+1","code":"result = (2+3 == 4+1)"}
]