An archaeological artefact containing wood has only 80% of `""^(14) C` activity as found in living trees. If the half-life of `C^(14)` is 5730 years, then the age of the artefact may be

Options

A. 1845 years
B. 184.5 years
C. 1900 years
D. 190 years

Answer

A

Explanation

Radioactive decay follows first order kinetics. Let `[A]_0 = 100`
`:. [A] = 100 xx 80% = 80`
Decay constant (k) `= (0.693)/(t_(1//2)) = (0.693)/5730`
`t=(2.303)/klog""([A_0])/([A])`
`=(2.303)/((0.693)/(5730))log""100/80`
`=(2.303xx5730)/(0.693)xxlog 1.25`
`=(2.303xx5730)/(0.693)xx0.0969 = 1845` yrs