A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially, 10 g of A and, 1 g of B is taken. The time (approximate ) after which they will have the same quantity remaining is

Step-by-step solution

N ⁡ = N ⁡ 0 1 2 t 1 2 ⇒ N ⁡ A ⁡ = 1 0 1 2 t 1 and N ⁡ B ⁡ = 1 1 2 t 2 Given ⇒ 1 0 1 2 t = 1 2 t 2   ⇒ 1 0 = 1 2 - t 2 ⇒ 1 0 = 2 t / 2 Taking log on both sides log 1 0 = t 2 log 1 0 2 ⇒ 1 = t 2 × 0 · 3 0 1 0 ⇒ t = 6 · 6 2 years