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 living tree. Estimate the age of the sample.

Explanation

Radioactive decay follows first order kinetics
Decay constant (k) `=(0.693)/(t_(1//2))=(0.693)/(5730)"years"^(-1)`
Using the equation for first order kinetics and substituting the values, we get
`t=(2.303)/(k)"log"([A]_(0))/([A])=(2.303)/((0.693//5730" years"^(-1)))"log"(100)/(80)`
or `t=(2.303xx5730)/(0.693)xx0.0969"years"=1845` years
Thus, age of the sample = 1845 years.