Nuclear engineering terminology: “critical mass” is defined as the minimum mass of a fissile material required for what key condition in a chain-reacting system?

Introduction / Context:
Critical mass is a foundational concept in reactor physics and nuclear safety. It specifies the smallest amount of fissile material that, with a given geometry, composition, reflector, and moderator condition, can support a self-sustaining nuclear chain reaction. Recognizing this definition helps distinguish neutronic feasibility from economic or commercial considerations.

Given Data / Assumptions:

• Material is fissile (e.g., U-235, Pu-239).
• Geometry, density, and presence/absence of reflector/moderator are fixed.
• We are concerned with neutronic sustainment, not economics.

Concept / Approach:
The chain reaction is sustained when the effective multiplication factor k_eff equals 1. The critical mass is the minimum mass for which, under specified conditions, neutron production from fission balances neutron losses (absorption in non-fuel and leakage). Below this mass, k_eff < 1 and the reaction dies out (subcritical). Above this mass, k_eff > 1 unless controlled.

Step-by-Step Solution:

Verification / Alternative check:
Textbook relationships (e.g., six-factor formula) and diffusion theory show how size affects neutron leakage; increasing system size reduces surface-to-volume ratio, lowering leakage and enabling k_eff → 1.

Why Other Options Are Wrong:

• Commercial or economic power generation depends on plant engineering and costs, not simply on reaching criticality.
• “None of these” is false because one option is correct.
• Prompt-critical excursion is a transient safety condition, not the definition of critical mass.

Common Pitfalls:
Equating critical mass with power plant sizing; ignoring the roles of reflectors and moderators which substantially reduce the critical mass.

Final Answer:
Sustainment of chain reaction.