Cosmic rays impinging on our atmosphere generate radioactive \({ }^{14}
\mathrm{C}\) from \({ }^{14} \mathrm{~N}\) nuclei. \(^{78}\) These \({ }^{14}
\mathrm{C}\) atoms soon team up with oxygen to form \(\mathrm{CO}_{2}\), so that
plants absorbing \(\mathrm{CO}_{2}\) from the air will have about one in a
trillion of their carbon atoms in this form. Animals eating these plants
\(^{79}\) will also have this fraction of carbon in their bodies, until they die
and stop cycling carbon into their bodies. At this point, the fraction of
carbon atoms in the form of \({ }^{14} \mathrm{C}\) in the body declines, with a
half life of 5,715 years. If you dig up a human skull, and discover that only
one-eighth of the usual one-trillionth of carbon atoms are \({ }^{14}
\mathrm{C}\), how old do you deem the skull to be?