Final answer:
The number of radioactive atoms accumulated after an irradiation time t, with production rate r and decay constant λ, is represented by N(t) = R/λ(1-e^-λt).
option b is the correct
Step-by-step explanation:
When a sample of atoms is irradiated by neutrons, the formation and decay of radioactive atoms can be described by the Bateman equations, a set of coupled differential equations. However, for the case described in the question, where radioactive atoms are produced at a constant rate r and decay with a decay constant λ, we can reach a simpler expression.
The radioactive decay follows first-order kinetics, and thus, the decay rate is given by the product of the decay constant λ and the number of radioactive nuclei N still present at a given time. As new radioactive atoms are continuously produced at a constant rate r, the overall number of radioactive atoms present is the sum of those being produced and those that haven't decayed yet.
Thus, to find the number of radioactive atoms accumulated after an irradiation time t, we need to solve the balance equation considering the production and decay processes. The equation that matches this physical situation is N(t)= R/λ(1-e^-λt), which implies that the number of radioactive atoms at time t increases until it reaches a steady-state where production and decay rates are equal.
Therefore, the correct equation representing the number of radioactive atoms N(t) after an irradiation time t is B. N(t)= R/λ(1-e^-λt).