Question

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0 , there are N₀ nuclei of the element.

(a) Calculate the number N of nuclei of A at time t

(b) If α=2 N₀ λ, calculate the number of nuclei of A after one half life of A, and also the limiting value of N as t → ∞.

Answer 1

(a) Let at time ‘t’, number of radioactive nuclei are N.

Net rate of formation of nuclei of A.

Solving this equation, we get