## Carbon Dating

Read this text, which explains how we can use carbon dating to determine the age of an object. Scientists use these calculations extensively in archaeology, anthropology, and paleontology. Since the half-life for C-14 is approximately 5,700 years, carbon dating is only useful for fossils that are younger than approximately 50,000 years old. For older fossils, scientists use isotopes with longer half-lives.

Since we can determine the amount of an isotopic element that remains after a specific period of time, we can conversely determine the time over which a specific sample has been decaying once we know the rate constant for that element. This is the basis of carbon dating. Carbon dating is a process whereby the age of a material that contains carbon can be determined by comparing the decay rate of that material with that of living material.

Carbon-14 has a half life (t1/2) of 5.73 x 103 years for its decay to nitrogen-14 by the loss of a β particle.

$^{14}_{6}\text{C}\rightarrow ^{14}_{7}\text{N}+^{0}_{-1}e$

Using Equation 1 from the previous section on half-life ($k=\frac{\ln[2]}{t_{1/2}}=\frac{0.693}{t_{1/2}}$),

$k=\frac{0.693}{5.73\times 10^{3}}=1.21\times 10^{-4}\text{ year}^{-1}$

In 1947 samples of the Dead Sea Scrolls were analyzed by carbon dating. It was found that the carbon-14 present had an activity of d/min.g (where d = disintegration); by contrast in living material the activity is 14 d/min.g.

Thus, using Equation 2 from the previous section on half-life (\ln\frac{C_{0}}{C_{t}}=kt),

$\ln\frac{14}{11}=(1.21\times 10^{-4})t$

Thus,

$t=\frac{\ln1.272}{1.21\times 10^{-4}}=2.0\times 10^{3}\text{ years}$

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 which was supposed to have wrapped Jesus’s body. Carbon dating has shown that the cloth was made between 1260 and 1390 AD. Thus, the Turin Shroud is clearly a fake having been made over a thousand years after its supposed manufacture.

Source: Andrew R. Barron, http://www.vias.org/genchem/nuclear_chem_31328_04_06.html