# Process of carbon 14 dating

### Process of carbon 14 dating - consolidating debt into mortgage

From this science, we are able to approximate the date at which the organism were living on Earth.

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).Carbon-14 is constantly be generated in the atmosphere and cycled through the carbon and nitrogen cycles.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 \(t_{1/2}\)) is a more familiar concept than \(k\) for radioactivity, so although Equation \(\ref{E3}\) is expressed in terms of \(k\), it is more usual to quote the value of \(t_{1/2}\).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 \[ k = \dfrac{\ln 2}{ t_{1/2} } \label{E4}\] so the rate constant is then \[ k = \dfrac{\ln 2}{5.73 \times 10^3} = 1.21 \times 10^{-4} \text{year}^{-1} \label{E5}\] and Equation \(\ref{E2}\) can be rewritten as \[N_t= N_o e^{-\ln 2 \;t/t_{1/2}} \label{E6}\] or \[t = \left(\dfrac{\ln \dfrac{N_o}{N_t}}{\ln 2} \right) t_{1/2} = 8267 \ln \dfrac{N_o}{N_t} = 19035 \log_{10} \dfrac{N_o}{N_t} \;\;\; (\text{in years}) \label{E7}\] 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.Thus, using Equation \(\ref{E3}\), \[\ln \dfrac{14}{11} = (1.21 \times 10^{-4}) t \nonumber\] Thus, \[t= \dfrac{\ln 1.272}{1.21 \times 10^{-4}} = 2 \times 10^3 \text{years} \nonumber\] From the measurement performed in 1947 the Dead Sea Scrolls were determined to be 2000 years old giving them a date of 53 BC, and confirming their authenticity.This discovery is in contrast to the carbon dating results for the Turin Shroud that was supposed to have wrapped Jesus’ body.Carbon dating has shown that the cloth was made between 12 AD.Thus, the Turin Shroud was made over a thousand years after the death of Jesus.

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