Radiocarbon dating differential equation

After plants die or are consumed by other organisms, the incorporation of all carbon isotopes, including 14C, stops.

Thereafter, the concentration (fraction) of 14C declines at a fixed exponential rate due to the radioactive decay of 14C. ) Comparing the remaining 14C fraction of a sample to that expected from atmospheric 14C allows us to estimate the age of the sample.

Plants fix atmospheric carbon during photosynthesis, so the level of C14 in living plants and animals equals the level of C14 in the atmosphere. Carbon-14 has a half-life of 5730 years and would have long ago vanished from Earth were it not for the unremitting cosmic ray impacts on nitrogen in the Earth's atmosphere, which create more of the isotope.

The neutrons resulting from the cosmic ray interactions participate in the following nuclear reaction on the atoms of nitrogen molecules (N The highest rate of carbon-14 production takes place at altitudes of 9 to 15 km (30,000 to 50,000 ft), and at high geomagnetic latitudes, but the carbon-14 spreads evenly throughout the atmosphere and reacts with oxygen to form carbon dioxide.

The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age.

Carbon dioxide also permeates the oceans, dissolving in the water.

For approximate analysis it is assumed that the cosmic ray flux is constant over long periods of time; thus carbon-14 is produced at a constant rate and the proportion of radioactive to non-radioactive carbon is constant: ca. In 1958 Hessel de Vries showed that the concentration of carbon-14 in the atmosphere varies with time and locality.

Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.


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