*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Although it may be seen as outdated, many labs still use Libby's half-life in order to stay consistent in publications and calculations within the laboratory.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.