Definition:Radiometric Dating/Radiocarbon Dating
Definition
Radiocarbon dating is a specific application of radiometric dating which is used to determine how long a piece of organic matter has been dead.
Because of bombardment by cosmic rays, the ratio of (radioactive) carbon-14 to (stable) carbon-12 in the atmosphere of Earth is fairly constant.
This ratio is known.
The ratio of carbon-14 to carbon-12 in a living organism is the same as it is in Earth's atmosphere, by biological respiration.
However, when the organism dies, it no longer respires, and the carbon in its body stays where it was at the time of its death.
As time passes, the carbon-14 decays to nitrogen-14 via the process of beta decay.
The half-life of carbon-14 is known to be $5700 \pm 40$ years.
Also known as
This technique of radiocarbon dating is known as the carbon-14 test.
Examples
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.
Also see
Historical Note
The technique of radiocarbon dating was devised by Willard Frank Libby.
He was awarded the Nobel Prize in Chemistry in $1960$ for his work in dating archaeological objects.
He determined the half-life of carbon-14 to be approximately $5600$ years.
Hence he established that the measurable life age span using this test was from $1000$ to $30 \, 000$ years.
Sources
- 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $1$: How Differential Equations Originate
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions