Self-Assessment Quiz — Chapter 28

Test your understanding of the core concepts before moving on. Try to answer each question before checking the solutions at the end.

Q1. (Multiple Choice) Which fissile isotope has the smallest bare critical mass?

(a) ${}^{233}\text{U}$ (b) ${}^{235}\text{U}$ (c) ${}^{239}\text{Pu}$ (d) ${}^{240}\text{Pu}$

Q2. (True/False) The gun-type fission weapon design can be used with either ${}^{235}\text{U}$ or ${}^{239}\text{Pu}$.

Q3. (Short Answer) Why does the gun-type design fail for plutonium? Name the specific isotope responsible and the physical process that causes the problem.

Q4. (Multiple Choice) In an implosion weapon, the critical mass is reduced primarily by:

(a) Increasing the temperature of the fissile material (b) Compressing the fissile material to higher density (c) Mixing the fissile material with a moderator (d) Removing the neutron reflector

Q5. (Short Answer) State the approximate bare critical masses of ${}^{235}\text{U}$ and ${}^{239}\text{Pu}$ metal. How does a reflector/tamper affect these values?

Q6. (Multiple Choice) In the Teller-Ulam thermonuclear design, the fission primary compresses the fusion secondary by:

(a) Direct mechanical shock wave (b) Radiation (X-ray) coupling (c) Magnetic confinement (d) Gravitational compression

Q7. (True/False) The largest nuclear weapon ever tested had a yield of approximately 50 megatons.

Q8. (Short Answer) Explain why ${}^{235}\text{U}$ and ${}^{238}\text{U}$ cannot be separated by chemical methods. What physical property does enrichment exploit?

Q9. (Multiple Choice) The separation factor for a gas centrifuge enriching $\text{UF}_6$ is approximately:

(a) $\alpha \approx 1.004$ (b) $\alpha \approx 1.04$ (c) $\alpha \approx 1.20$ (d) $\alpha \approx 2.0$

Q10. (Short Answer) Define "separative work unit (SWU)" conceptually. Approximately how many SWU are required to produce 1 kg of weapons-grade uranium (90% ${}^{235}\text{U}$) from natural feed?

Q11. (Multiple Choice) The IAEA "significant quantity" of plutonium is:

(a) 1 kg (b) 8 kg (c) 25 kg (d) 75 kg

Q12. (True/False) Environmental sampling by IAEA inspectors can detect undeclared enrichment activities by analyzing individual micrometer-sized uranium particles.

Q13. (Short Answer) Name the three pillars of the Non-Proliferation Treaty (NPT).

Q14. (Multiple Choice) In nuclear forensics, the ${}^{240}\text{Pu}/{}^{239}\text{Pu}$ ratio in a plutonium sample primarily indicates:

(a) The age of the sample since chemical separation (b) The reactor type and burnup level (c) The enrichment level of the original uranium fuel (d) Whether the material has been irradiated by cosmic rays

Q15. (Short Answer) Explain how the ${}^{241}\text{Am}/{}^{241}\text{Pu}$ ratio serves as a "nuclear chronometer" for plutonium. What physical process makes this work?

Q16. (Multiple Choice) Which gamma-ray detector type provides the best energy resolution for isotope identification?

(a) NaI:Tl (b) LaBr$_3$:Ce (c) HPGe (d) Plastic scintillator

Q17. (True/False) A radiological dispersal device (dirty bomb) produces a nuclear chain reaction.

Q18. (Short Answer) Why is the dirty bomb described as a "weapon of mass disruption" rather than a "weapon of mass destruction"? What is its primary impact?

Solutions

Q1. (c) ${}^{239}\text{Pu}$, with a bare critical mass of approximately 10 kg, compared to $\sim 16\,\text{kg}$ for ${}^{233}\text{U}$ and $\sim 52\,\text{kg}$ for ${}^{235}\text{U}$. ${}^{240}\text{Pu}$ is not fissile with thermal neutrons and has a very large critical mass.

Q2. False. The gun-type design works only with ${}^{235}\text{U}$. The slow assembly time ($\sim 1\,\text{ms}$) is too long for plutonium — spontaneous fission of ${}^{240}\text{Pu}$ (always present in reactor-produced Pu) causes pre-initiation.

Q3. ${}^{240}\text{Pu}$ has a very high spontaneous fission rate ($\sim 10^3\,\text{s}^{-1}\,\text{g}^{-1}$). During the $\sim 1\,\text{ms}$ assembly time of a gun-type weapon, these spontaneous fission neutrons would initiate the chain reaction prematurely (pre-initiation), causing the assembly to blow apart before an efficient explosion develops.

Q4. (b) Compressing the fissile material to higher density. The critical mass scales as $M_c \propto 1/\rho^2$, so doubling the density reduces the critical mass by a factor of four.

Q5. Bare critical masses: ${}^{235}\text{U}$ $\approx 52\,\text{kg}$; ${}^{239}\text{Pu}$ $\approx 10\,\text{kg}$. A reflector/tamper (e.g., natural uranium or beryllium) reflects neutrons back into the assembly, reducing the critical mass by a factor of approximately 2–3, to roughly 15–20 kg for ${}^{235}\text{U}$ and 4–5 kg for ${}^{239}\text{Pu}$.

Q6. (b) Radiation (X-ray) coupling. The X-rays from the fission primary fill the radiation case and ablate the outer surface of the secondary, driving a converging implosion that compresses and heats the fusion fuel.

Q7. True. The Soviet "Tsar Bomba" (30 October 1961) had a yield of approximately 50 Mt, the largest nuclear explosion in history.

Q8. ${}^{235}\text{U}$ and ${}^{238}\text{U}$ have identical electron configurations (both are uranium), so they are chemically identical. Enrichment exploits the tiny mass difference ($\Delta m / m \approx 1.26\%$) using physical processes: centrifugation (differential sedimentation in a centrifugal field), gaseous diffusion (differential molecular speed), or electromagnetic separation (differential deflection in a magnetic field).

Q9. (c) $\alpha \approx 1.20$ for a modern gas centrifuge with peripheral speed $\sim 600\,\text{m/s}$. Gaseous diffusion has $\alpha \approx 1.004$.

Q10. The SWU quantifies the effort (separative work) needed to separate isotopes, accounting for both the enrichment achieved and the mass flows. Approximately 230 SWU are required to produce 1 kg of 90%-enriched uranium from natural feed with 0.3% tails.

Q11. (b) 8 kg. This is approximately one bare critical mass and represents the minimum amount from which a nuclear explosive device could plausibly be constructed.

Q12. True. Using techniques such as secondary ion mass spectrometry (SIMS), inspectors can measure the ${}^{235}\text{U}/{}^{238}\text{U}$ isotopic ratio of individual particles ($\sim 1\,\mu\text{m}$), distinguishing LEU from HEU with high precision. This technique was instrumental in detecting Iran's undeclared enrichment activities.

Q13. (1) Nonproliferation — non-nuclear-weapon states agree not to acquire nuclear weapons. (2) Disarmament — nuclear-weapon states commit to pursuing nuclear disarmament. (3) Peaceful use — all parties have the right to peaceful nuclear energy, subject to safeguards.

Q14. (b) The reactor type and burnup level. Low ${}^{240}\text{Pu}/{}^{239}\text{Pu}$ ($< 0.065$) indicates low burnup (weapons-grade). High ratios ($> 0.30$) indicate high burnup (reactor-grade). ${}^{240}\text{Pu}$ is produced by neutron capture on ${}^{239}\text{Pu}$, so its abundance increases with irradiation time.

Q15. ${}^{241}\text{Pu}$ decays to ${}^{241}\text{Am}$ by $\beta^-$ emission with a half-life of 14.33 years. When plutonium is chemically separated, all americium is removed. The ${}^{241}\text{Am}/{}^{241}\text{Pu}$ ratio then grows from zero as ${}^{241}\text{Pu}$ decays: $N_{\text{Am}}/N_{\text{Pu}} = e^{\lambda t} - 1$. Measuring this ratio gives the time since last separation — a nuclear chronometer analogous to radiocarbon dating.

Q16. (c) HPGe (high-purity germanium), with energy resolution $\sim 0.2\%$ at 662 keV ($\sim 1.3\,\text{keV}$ FWHM), far superior to NaI ($\sim 7\%$) or LaBr$_3$ ($\sim 3\%$).

Q17. False. An RDD uses conventional explosives to disperse radioactive material. No nuclear chain reaction occurs — the energy release is entirely chemical. It is a radiological weapon, not a nuclear weapon.

Q18. The dirty bomb's primary impact is economic and psychological: contamination of an urban area forces costly decontamination and evacuation, causes public fear, and disrupts economic activity. The actual radiation dose to individuals is generally modest (unlikely to cause acute radiation sickness unless they are very close to the explosion). The asymmetry between the physical risk and the perceived risk is what makes the RDD a disruption weapon rather than a destruction weapon.