Fissile vs fertile recognition: among the following nuclides, which one is fissile under thermal-neutron irradiation?

Introduction / Context:
Fissile materials can sustain a chain reaction with thermal (slow) neutrons. Fertile materials are not fissile as-is but can be converted to fissile nuclides via neutron capture and decay. Distinguishing between them is fundamental to reactor physics and fuel-cycle engineering.

Given Data / Assumptions:

• Thermal spectrum context.
• Candidate nuclides: U-238, Th-232, Pu-239.

Concept / Approach:
Pu-239 is fissile with thermal neutrons. U-238 and Th-232 are fertile: U-238 breeds to Pu-239; Th-232 breeds to U-233. Only Pu-239 in the list undergoes efficient thermal fission to release energy and extra neutrons for chain reaction.

Step-by-Step Solution:
Identify fissile candidate: Pu-239.Classify others as fertile under thermal conditions.Choose the fissile option accordingly.

Verification / Alternative check:
Standard fissile set includes U-233, U-235, Pu-239, Pu-241 (thermal). U-238 and Th-232 are excluded as directly fissile in thermal spectra.

Why Other Options Are Wrong:
U-238: fertile, needs conversion to Pu-239.Th-232: fertile, needs conversion to U-233.“None of these”: incorrect because Pu-239 is indeed fissile.

Common Pitfalls:
Assuming any actinide is fissile; forgetting the spectrum dependence of fission probabilities.

Final Answer:
Plutonium-239