Radiocarbon Dating/Examples
Examples of Radiocarbon Dating
Lascaux Caves
Charcoal from the remains of the fire found in the Lascaux caves was analysed.
It was determined that $85.5 \%$ of the amount of carbon-14 had decomposed since the wood was alive.
The Formula for Radiocarbon Dating is used:
- $t = -8060 \ln r$
where:
- $t$ denotes the age in years of the sample of wood which is to be determined
- $r$ denotes ratio of the quantity of carbon-14 remaining in the sample after time $t$ to the quantity of carbon-14 in the sample at the time of its death.
Thus:
| \(\ds t\) | \(=\) | \(\ds -8060 \times \map \ln {1 - 0.855}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -8060 \times \ln 0.145\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -8060 \times \paren {-1.9310}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 15 \, 573\) |
Hence it is determined that the fire in the cave, and hence the dwellers therein, dates from approximately $15 \, 500$ years ago.
$7000$ BCE
It was reported in the newspaper that a prehistoric village had been dated using radiocarbon dating.
The carbon-$14$ test had been used to measure the amount of radioactivity still present in the organic material found in the ruins.
It was determined that a settlement existed in that place as long ago as $\text {7000 BCE}$.
Given that:
- the estimated half-life of carbon-$14$ used was $5600$ years
- the newspaper report dated from about $1960$
the carbon-$14$ test must have shown that approximately $32 \%$ or $33 \%$ of carbon-$14$ was still present in the organic material at the time of discovery.