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As explained below, the radiocarbon date tells us when the organism was alive (not when the material was used).

This fact should always be remembered when using radiocarbon dates.

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).

This technique is not restricted to bones; it can also be used on cloth, wood and plant fibers. The short half-life of carbon-14 means its cannot be used to date extremely old fossils.

Carbon-14 dating has been used successfully on the Dead Sea Scrolls, Minoan ruins and tombs of the pharohs among other things. Levels of carbon-14 become difficult to measure and compare after about 50,000 years (between 8 and 9 half lives; where 1% of the original carbon-14 remains undecayed).

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).

When these neutrons collide with nitrogen-14 in the atmosphere carbon-14 can be created.

Carbon-14 is created from nitrogen-14 in the upper atmosphere of the earth.

Radiation from the sun collides with atoms in the atmosphere.

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 \(t_\).

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