Sample of oak from an ancient site have a carbon-14 content equal to 85.0 % that in living matter.

Estimate the age of the wood knowing that t_1/2(¹⁴C) = 5730 years.

Question

Sample of oak from an ancient site have a carbon-14 content equal to 85.0 % that in living matter.

Estimate the age of the wood knowing that t_1/2(¹⁴C) = 5730 years.

| General Chemistry 2

Accepted Answer

Radioactive decay is a first-order process:

ln $(\frac{N}{N_{0}})$ = -kt and t_1/2 = $\frac{\ln 2}{k}$

⇒ ln

(\frac{N}{N_{0}})

= -

\frac{\ln 2 \times t}{t_{1 / 2}}

⇒ t = ln

(\frac{N_{0}}{N})

x

\frac{t_{1 / 2}}{\ln 2}

= ln (100/85) x

\frac{5730}{\ln 2}

= 1340 years

Radioactive decay - 2 | Chemical Kinetics: Rate Laws