The half life for radio active decay of `""^14C` is 5730 Y. An achaeological artefact contained wood had only 80% of the 14 C found in a living tree. Estimate age of the sample.

Explanation

Decay constant (k) = `0.693/(t_1//2) = (0.693/5730yr^(-1))`
Radio active dacays follow first order kinetics
`t=2.303 / k log""([A]_0)/([A])`
`k = 0.693/ 5730 yr^1[A]_0= 100%, [A] = 80%`
`:.t = ((2.303 xx 5730)/0.693) xx log"" 100/80`
`=((2.303 xx 5730 xx0.0969)/0.693)= 18 45` years.