What is the equation for the simultaneous variation of the precursor population?

The equation representing the simultaneous variation of the precursor population is formulated based on how reactor kinetics are modeled, particularly in the context of neutron population behavior in a nuclear reactor. In this scenario, the correct choice illustrates a balance between two key processes: the generation of precursors from neutron interactions and their decay over time.

The term ( \beta / \Lambda n ) describes the production rate of precursors due to neutron reactions, where ( \beta ) is the fraction of delayed neutrons, ( \Lambda ) is the generation time, and ( n ) is the neutron population. This term signifies that the precursor population grows as neutron activity increases.

Conversely, the term ( - \lambda c ) represents the decay of the precursor population, with ( c ) being the precursor concentration and ( \lambda ) the decay constant for the precursor species. This captures the diminishing number of precursors over time as they transform into other products.

Combining these two effects yields the overall equation: ( dc/dt = \beta / \Lambda n - \lambda c ). This effectively models the dynamic behavior of the precursor population, making it the correct answer in the context of nuclear reactor kinetics. The equation properly reflects the interplay of