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

Radioactive decay follows first order kinetics.
Given `t_(1//2)=5730y`
`thereforek=(0.693)/(t_(1//2))=(0.693)/(5730)=1.209xx10^(-4)y^(-1)`
Let , initial `[A]_(0)` and observed [A] concentration of C-14 , be 100 and 80 respectively.
`thereforet=(2.303)/(k)log.([A0]_(0))/([A])=(2.303)/(1.209xx10^(-4))log.(100)/(80)=1846y`