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

`t_(1//2)=(0.693)/(k) rArr (0.693)/(5730)(yr)^(-1)=k`
`t=(2.303)/(k) log""(R_(0))/(R )`
`t=(2.303)/((0.693)/(5730))log""(100)/(80) =(2.303xx5730)/(0.693)xx0.0969` year
=1845 years.