The Process of Carbon-14 Decay and Dating

Index

Index
Introduction
The Carbon Isotope Family
The Natural Production of Carbon-14
The Incorporation of Carbon-14 into Organisms
Radioactive Deacy of Carbon-14
Dating Using Carbon-14
References

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Introduction

Carbon-14 dating is a form of radiometric dating that utilizes the naturally occurring radioisotope carbon-14 to estimate the age of organic materials. The method was developed by Willard Libby and his team at the University of Chicago in 1949. Dr. Libby was awarded the Nobel Prize in chemistry for his work on this technique. The development of carbon-14 dating has become a crucial tool for archaeologists in that it can give accurate ages of organic (carbon-containing) materials that are up to 60,000 years old. Carbon-14 dating is possible due to the production and radioactive decay of carbon-14, a process that takes place both in the atmosphere and on Earth?s surface.

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The Carbon Isotope Family

On Earth, Carbon has two stable, nonradioactive isotopes (carbon-12 and carbon-13) and one unstable isotope (carbon-14). The numbers 12, 13, and 14 represent the atomic mass of the respective isotopes, a quantity that denotes the number of protons added to the number of neutrons an atom possesses. Atoms with different numbers of protons constitute different elements while atoms with the same number of protons but different numbers of neutrons are isotopes of one another. Therefore, carbon-12 is an atom with 6 protons and 6 neutrons, carbon-13 has 6 protons and 7 neutrons, and carbon-14 has 6 protons and 8 neutrons. Noted above, carbon-14 is the carbon isotope that is unstable and uncommon on Earth. In fact, accepted approximations to the ratio of carbon-14 to carbon-12 on or near Earth are generally around 1:1,000,000,000,000, or one part carbon-14 per trillion parts carbon-12. This low level of radioactive carbon is enough to measure in organisms that take in atmospheric carbon (such as plants), but if it is unstable on Earth, where does it come from?


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The Natural Production of Carbon-14

Carbon-14 is produced by a chain of reactions, the first of which is the ejection of a neutron when a cosmic ray hits some atom floating in the atmosphere. A cosmic ray is any energetic subatomic particle (a proton, atomic nuclei, or electron) that originates in outer space and enters Earth?s atmosphere. When the ray collides with an atmospheric atom, the energy transfer from the impact causes protons and neutrons to be ejected from the nucleus of the atom. The number of particles ejected depends on the specific energy of the incoming ray (Figure 1). The particle of specific interest to the creation of carbon-14 is the neutron. Free neutrons then traverse the atmosphere and if one happens to strike a nitrogen-14 atom, the atom takes in the neutron and ejects a proton (note that these neutrons also interact with the many other elements present in Earth?s atmosphere). The nitrogen atom, which started off with 7 protons and 7 electrons, ends with 6 protons and 8 neutrons. It has now become an atom of carbon-14. Carbon-14 atoms (along with the other carbon isotopes) interact with oxygen in the atmosphere to form the greenhouse gas carbon dioxide, or CO2.


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The Incorporation of Carbon-14 into Organisms

The next step of the process is the incorporation of atmospheric carbon-14containing CO2 into plant material during photosynthesis. The basic principal of photosynthesis that relates to carbon-14 involves the ?breathing in? of carbon dioxide by a plant followed by the chemical breakdown of CO2 for energy and the integration of the carbon-14 into the plant structure. The amount of carbon-14 absorbed by plants approximately matches the ratio of the isotope in the atmosphere of the two stable isotopes. When animals or human ingest plants, they take in this carbon-14. Thus, everything living thing is constantly exchanging carbon-14 with its ambient environment.


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Radioactive Deacy of Carbon-14

When the plants die or are consumed by another organism, such as humans or some animal, the unstable carbon-14 atoms begin to decay in a characteristic manner through the reaction:


where 146C is a carbon-14 atom, 147N1+ is the resultant nitrogen-14 atom (positively charged), e- is an electron, and ?e indicates some quantity of gamma radiation. Gamma radiation is energy that takes the form of an electromagnetic wave. Some examples of electromagnetic waves are visible light, microwaves, radio waves, and X-rays. These are all forms of electromagnetic radiation with different frequencies. Theoretical and empirical studies have shown that this reaction has a half-life of 5730 years. One half-life is the amount of time it takes for the original amount of carbon-14 to decay to half of its original value. It follows that the passing of a second half-life would halve the number of remaining carbon-14 atoms, resulting in the sample containing one quarter the number of carbon-14 atoms compared to the sample at the beginning of the decay process (1/2 x 1/2 = 1/4).


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Dating Using Carbon-14

After decaying for some period of time, the remains of an organic material whose date is in question have a measurable quantity of carbon-14 and a measurable quantity of positively charged nitrogen-14 atoms. Using a simple equation that takes into account the original amount of carbon-14, the present amount of carbon-14, the rate of the decay reaction (half-life of 5730 years), and a correction factor for the change of atmospheric CO2 over time (all of which are known), the sample can be dated within fairly strict confidence. The equation is as follows: N(t)= N_0*e^(-?t) Where N(t) is the total carbon-14 at dating, N0 is the original amount of carbon-14, ? is the decay constant [or 1/(rate of decay)], and t is the elapsed time. t is the variable that is solved for to attain an age of the material.

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References

1) Higham, Thomas. "The method." Radiocarbon WEB-info. 9 August 2002. http://www.c14dating.com/int.html

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Appendix

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