A P 32 radionuclide with half-life T = 14 . 3 days is produced in a reactor at a constant rate q = 2 . 7 × 10 9 nuclei per second. How soon after the beginning of production of that nuclide will its activity be equal to A = 1 . 0 × 10 9 dis . / s ?

Step-by-step solution

According to the problem, the radio nuclide is being produced at a constant rate as well as it decay with rate - d ⁡ N ⁡ d ⁡ t = λ N ⁡ . Hence net rate of accumulation of radio nuclide is given by   d ⁡ N ⁡ d ⁡ t = q ⁡ - λ N ⁡ … 1 or         ∫ 0 N ⁡ d ⁡ N ⁡ q ⁡ - λ N ⁡ = ∫ 0 t d ⁡ t or         - 1 λ log q ⁡ - &#955