# Radioactive isotopes in carbon dating

*21-Nov-2017 07:34*

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.After a creature's death the isotope would slowly decay away over millennia at a fixed rate.Thus the less of it that remained in an object, in proportion to normal carbon, the older the object was.The radioactive isotope carbon-14 is created in the upper atmosphere when cosmic-ray particles from outer space strike nitrogen atoms and transform them into radioactive carbon.Some of the carbon-14 might find its way into living creatures.

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).

C) dating usually want to know about the radiometric[1] dating methods that are claimed to give millions and billions of years—carbon dating can only give thousands of years.