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. Estimate the age of the sample.

Explanation

Here ,
`k = (0.693)/(t_((1)/(2))`
`= (0.693)/(5730) "years"^(-1)`
It is known that ,
`t = (2.303)/(k) "log" ([R]_(0))/([R])`
= `(2.303)/(0.693) "log"(100)/(80)`
= 1845 years (approximately)
Hence , the age of the sample is 1845 years .