What is the governing equation for the change in fission product I with respect to time?

The correct answer represents the governing equation for the change in fission product I over time, incorporating both the production and decay processes involved. In this equation, the first term, γ_i Σ_f φ, corresponds to the rate at which the fission product I is generated. Here, γ_i denotes the yield of the fission product per fission event, Σ_f represents the macroscopic fission cross-section, and φ is the neutron flux. This term captures the production of fission products resulting from ongoing fission reactions.

The second term, -λ_i I, represents the decay of the fission product I, where λ_i is the decay constant associated with that specific fission product. This term signifies that as time progresses, the amount of fission product decreases due to radioactive decay.

By combining these two terms, the equation describes how the fission product population evolves over time as a balance between its creation from fission events and its loss from decay. This relationship is crucial in understanding the behavior of fission products within a nuclear reactor environment, which must be managed for safety and efficiency.

The other choices either reference different types of radioactive decay dynamics without the context of fission product generation or misalign the variables involved, which do not