β equals what in the multi-group model?

• A. β equals the product of all β_i.
• B. β equals the maximum β_i.
• C. β equals the average β_i.
• D. β equals the sum of the β_i values for all groups.

Answer: (D)

In a multi-group model of delayed neutrons, the total delayed-neutron fraction is the sum of the fractions from each precursor group. Each group i has its own delayed fraction β_i, representing the portion of fission neutrons that are emitted delayed through that group's precursors. Since these sources are independent and simply accumulate, the overall delayed-neutron fraction is β = Σ_i β_i. That additive relation reflects how all delayed emissions combine to form the total delayed-neutron content.

Choosing a product, a maximum, or an average would not correctly represent how delayed neutrons arise from multiple independent precursor groups: a product mixes the contributions in a nonphysical way, a maximum ignores the contributions from all other groups, and an average would not equal the total fraction produced by all groups.