Libby estimated that the steady-state radioactivity concentration of exchangeable carbon-14 would be about 14 disintegrations per minute (dpm) per gram.In 1960, Libby was awarded the Nobel Prize in chemistry for this work.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.

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.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).So in order to date most older fossils, scientists look for layers of igneous rock or volcanic ash above and below the fossil.Scientists date igneous rock using elements that are slow to decay, such as uranium and potassium.

### Search for radiometric dating activities: 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).

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