The half life for radioactive decay of `.^(14)C` is 5730 years. An archaeological artifact containing wood had only `80%` of the `.^(14)C` found in a living tree. Estimat the age of the sample.

Explanation

(a) The important factors on which the rate of chemical reaction depends are :
(i) nature of the reacting species.
(ii) concentration of the reacting species
(iii) temperature at which a reaction proceeds
(iv) surface area of the reactanst
(v) presence of a catalyst
(b) Radioactive decay follows first order kinetics.Let `[A]_(o)=100`
Decay constant (K) = `(0.693)/(t_(1//2))=(0.693)/(5730)`
`t=(2.303)/(K)log.([Ao])/([A])=(2.303)/(0.693//5730)log.(100)/(80)`
`=(2.303xx5730)/(0.693)xxlog1.25=(2.303xx5730)/(0.693)xx0.0969`
`=(1278.7108)/(0.693)=1845~~1845` years