# Radioactive isotopes used in carbon dating

Although it may be seen as outdated, many labs still use Libby's half-life in order to stay consistent in publications and calculations within the laboratory.From the discovery of Carbon-14 to radiocarbon dating of fossils, we can see what an essential role Carbon has played and continues to play in our lives today.From that point on, scientist have used these techniques to examine fossils, rocks, and ocean currents and determine age and event timing.Throughout the years measurement tools have become more technologically advanced allowing researchers to be more precise and we now use what is known as the Cambridge half-life of 5730 /- 40 years for Carbon-14.The carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the constant influx of cosmic rays interacting with molecules of nitrogen (NFigure 1: Diagram of the formation of carbon-14 (forward), the decay of carbon-14 (reverse).Carbon-14 is constantly be generated in the atmosphere and cycled through the carbon and nitrogen cycles.Carbon is found in different forms in the environment – mainly in the stable form of carbon-12 and the unstable form of carbon-14.   Using this finding Willard Libby and his team at the University of Chicago proposed that Carbon-14 was unstable and underwent a total of 14 disintegrations per minute per gram.

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).

Radiocarbon dating (usually referred to simply as carbon-14 dating) is a radiometric dating method.

It uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.