If k_eff is less than 1, what happens to the neutron population over generations?

If k_eff is less than 1, what happens to the neutron population over generations?

• A. It grows exponentially.
• B. It remains constant.
• C. It declines with each generation.
• D. It oscillates randomly.

Answer: (C)

When k_eff is less than 1, the system is subcritical, so the neutron population shrinks each generation. The population follows N_{n+1} = k_eff × N_n, which means after n generations N_n = N_0 × (k_eff)^n. Since the multiplier (k_eff) is less than 1, this factor decreases with every generation, producing an exponential decline in neutrons over time. It won’t grow or stay constant under these conditions, and random oscillations aren’t part of the simple, constant-k_eff behavior.

When k_eff is less than 1, the system is subcritical, so the neutron population shrinks each generation. The population follows N_{n+1} = k_eff × N_n, which means after n generations N_n = N_0 × (k_eff)^n. Since the multiplier (k_eff) is less than 1, this factor decreases with every generation, producing an exponential decline in neutrons over time. It won’t grow or stay constant under these conditions, and random oscillations aren’t part of the simple, constant-k_eff behavior.