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.Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.
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.
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 \(t_\).
Although it may be seen as outdated, many labs still use Libby's half-life in order to stay consistent in publications and calculations within the laboratory.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.Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.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).They found a form, isotope, of Carbon that contained 8 neutrons and 6 protons.