# Carbon dating equation

*10-Nov-2014 11:03*

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.

The carbon-14 atoms undergo beta-minus decay (electron emission) and produce a beta particle and a nitrogen-14 atom.

In this equation, the units of measure for N and No can be in grams, atoms, or moles.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.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). From this science, we are able to approximate the date at which the organism were living on Earth.