Which formula best defines the effective neutron multiplication factor keff?

Which formula best defines the effective neutron multiplication factor keff?

• A. The ratio of neutrons produced at the end of generation to the neutrons present at the start of generation.
• B. The ratio of neutrons produced to neutrons absorbed
• C. The ratio of neutrons produced to neutrons lost by leakage
• D. The ratio of neutrons absorbed to neutrons produced at end of generation

Answer: (B)

Neutron multiplication factor keff gauges whether the neutron population stays steady, grows, or dies away by comparing neutrons in successive generations. The proper way to define it is as the number of neutrons produced by fission in one generation divided by the number of neutrons lost from that generation. Losses come from two paths: absorption in materials and leakage out of the system. So keff = neutrons produced by fission / (neutrons absorbed + neutrons leaked). Why this matters: if keff is greater than 1, the population grows; if keff equals 1, the system is critical and steady; if keff is less than 1, it dies away. The ratio to only absorbed neutrons ignores leakage, which can be a significant loss mechanism in finite systems, so it does not fully define keff in general. In an idealized, leakage-free infinite medium, absorption-only could approximate the concept, but the complete definition must include leakage.

Neutron multiplication factor keff gauges whether the neutron population stays steady, grows, or dies away by comparing neutrons in successive generations. The proper way to define it is as the number of neutrons produced by fission in one generation divided by the number of neutrons lost from that generation. Losses come from two paths: absorption in materials and leakage out of the system. So keff = neutrons produced by fission / (neutrons absorbed + neutrons leaked).

Why this matters: if keff is greater than 1, the population grows; if keff equals 1, the system is critical and steady; if keff is less than 1, it dies away. The ratio to only absorbed neutrons ignores leakage, which can be a significant loss mechanism in finite systems, so it does not fully define keff in general. In an idealized, leakage-free infinite medium, absorption-only could approximate the concept, but the complete definition must include leakage.