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The Wairau Bar in Blenheim is one of the oldest archaeological sites in New Zealand.
Amongst the artefacts that have been found are ancient moa bones.
In 1960, Libby was awarded the Nobel Prize in chemistry for this work.
He demonstrated the accuracy of radiocarbon dating by accurately estimating the age of wood from a series of samples for which the age was known, including an ancient Egyptian royal barge dating from 1850 BCE.
Once an organism is decoupled from these cycles (i.e., death), then the carbon-14 decays until essentially gone.
The half-life of a radioactive isotope (usually denoted by \(t_\)) is a more familiar concept than \(k\) for radioactivity, so although Equation \(\ref\) is expressed in terms of \(k\), it is more usual to quote the value of \(t_\).
This discovery is in contrast to the carbon dating results for the Turin Shroud that was supposed to have wrapped Jesus’ body.
Libby estimated that the steady-state radioactivity concentration of exchangeable carbon-14 would be about 14 disintegrations per minute (dpm) per gram.
Carbon-14 is first formed when cosmic rays in the atmosphere allow for excess neutrons to be produced, which then react with Nitrogen to produce a constantly replenishing supply of carbon-14 to exchange with organisms.
Historical artefacts like moa bones can be dated using a technique that measures the activity of the radioisotope carbon-14 still present in the sample.
The currently accepted value for the half-life of will remain; a quarter will remain after 11,460 years; an eighth after 17,190 years; and so on.
The equation relating rate constant to half-life for first order kinetics is \[ k = \dfrac \label\] so the rate constant is then \[ k = \dfrac = 1.21 \times 10^ \text^ \label\] and Equation \(\ref\) can be rewritten as \[N_t= N_o e^ \label\] or \[t = \left(\dfrac \right) t_ = 8267 \ln \dfrac = 19035 \log_ \dfrac \;\;\; (\text) \label\] The sample is assumed to have originally had the same (rate of decay) of d/min.g (where d = disintegration).