A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If the half-life of C 14 is 5730 years , then the age of the wooden piece placed in the museum is approximately [This question was awarded a bonus and proper correction was made to avoid that]

Step-by-step solution

We know that, The rate of decay at the time t is A = A 0 e - λt 2 = 2 0 · e - λt ∴   1 1 0 = e - λt ∴   e λt = 1 0 ⇒ ln e λt = ln 10 ⇒ λ t = ln 10 ∵   λ = ln 2 T 1 / 2 t = ln 10 ln 2 T 1 / 2 ∵   ln 10 = 2.303 and ln 2 = 0.693 t = 2.303 0.693 × 5730 = 3.32 × 5730 ≈ 19042   years