# Carbon dating decay equation

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).In contrast, living material exhibit an activity of 14 d/min.g. This is why it is such a big concern when a nuclear submarine sinks... (By the way, you are mostly Carbon-12, which is not radioactive.Eventually, the salt water will eat through the steel and release the Plutonium (which, as you know, is quite lethal.) They usually talk about either trying to raise the sub or encase it in concrete where it rests. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek.)Scientists use Carbon-14 to make a guess at how old some things are -- things that used to be alive like people, animals, wood and natural cloths. Anyway, they make an estimate of how much Carbon-14 would have been in the thing when it died...Carbon 14 is a common form of carbon which decays over time.The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^.However, the principle of carbon-14 dating applies to other isotopes as well.Potassium-40 is another radioactive element naturally found in your body and has a half-life of 1.3 billion years.

It comes from cosmic rays that rain down on the earth (and us) from outer space.It uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.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). As soon as a living organism dies, it stops taking in new carbon.The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced.