Question

A mammoth skeleton has a carbon-14 decay rate of 0.49 disintegrations per minute per gram of carbon (0.49 dis/min gC ). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min gC and that carbon-14 has a half-life of 5730 yr)
Express your answer using two significant figures.

Answer 1

The answer is: \(\underline{2.8 \times 10^{4}}\) years ago. See solution below:

Decay constant \(\mathrm{k}=\ln (2) /\) half life

\(=0.000120968\) year \(^{-1}\)

\(\ln (C / C o)=-k t\)

where \(C\) is the disintegrations per minute per gram of carbon

at time \(\mathrm{t}\), and \(\mathrm{Co}\) is the initial disintegrations per minute

per gram of carbon.

\(\ln (0.49 / 15.3)=-0.000120968 \times t\)

Time \(t=2.8 \times 10^{4}\) years