The half-life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

Step-by-step solution

N ⁡ N ⁡ 0 = 1 2 n where n is number of half-lives ∴ 1 1 6 = 1 2 n or 1 2 4 = 1 2 n   or n = 4 Let the age of rock be t years ∵ n = t T ⁡ 1 / 2 or t =   n T 1 / 2   =   4   ×   50   years   =   200   years