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