Radiocarbon Dating

The impact of high-energy primary and secondary cosmic rays on atoms and molecules of the upper layers of the earth's atmosphere (lower stratosphere and upper troposphere) results in many nuclear reactions in which a number of neutrons, protons, a-particles and other subatomic particles are produced (Figure K.1). A large portion of neutrons produced by cosmic rays are slowed down by collision with atoms in the atmosphere. The resulting thermal neutrons react with 14N atoms to form a 14C atom and a proton (hydrogen nucleus) through a nuclear reaction (Appendix G):

Cosmic ray data show that the production rate of 14C atoms averaged over the whole atmosphere is about 2 per g per cm2 of the earth's surface. In this way approximately 7.5 kg of 14C is produced and added to the world's carbon reservoir every year. The entire carbon reservoir contains close to 4 X 1015 kg of carbon. Most of the carbon is in the form of stable isotopic 12C (98.9%) and 13C (1.1%). After formation, 14C quickly combines with oxygen to form 14CO and later 14CO2. This carbon dioxide mixes throughout the atmosphere by air mass movements and turbulences. Once a radiocarbon 14CO2 molecule reaches the biosphere, it enters into the carbon exchange cycle. Living organisms are part of the equilibrium. plants build 14C into their cellular structures by the process of photosynthesis. Other organisms obtain it by ingestion of plant ma-

Radiocarbon Upper Atmosphere Image
Fig. K.1. Production of 14C and its movement in the earth's biosphere.

terial. The concentration ratio between radioactive isotope 14C and stable carbon isotopes (12C + 13C) is approximately 1:10~12. This concentration ratio stays approximately constant with time and represents the dynamic equilibrium established on a global scale between 14C loss by radioactive decay and cosmic ray production [K1].

Within a living organism the concentration of 14C is also constant and is continuously being replenished from the biosphere carbon exchange reservoir. When an organism dies, the 14C intake process stops, and a finite amount of the 14C fixed in the organism faces the slow process of radioactive decay.

14C is radioactive, and it decays back to 14N by emission of a beta particle (electron) and antineutrino:

The death of the organism sets a time zero (t = 0) on a "radiocarbon clock." The decrease of concentration of 14C in a dead organism follows the exponential radioactive decay law (Figure K.2). This law relates the number of radioactive atoms A left after time t to the initial number A0 of radioactive atoms (at t = 0):

Where l is a constant equal to the reciprocal value of the mean life t of the radioactive isotope. The mean life is related to the half-life of the radioactive isotope by the equation

Both half-lives and mean lives are specific constants for a given radionuclide. The Libby half-life T1/2 = 5568 years and Libby meanlife t = 8033 years are conventionally used in the calculations of radiocarbon age.

From 1949 till the late 1970s the only experimental method for measurement of 14C concentration in a given sample was based on the measurement of the radioactive decay rate, the same principle that was originally developed by Libby. The Geiger counter used by Libby was later replaced by gas proportional and liquid scintillation counters. Several other important improvements have been made to increase sensitivity, improve precision and accuracy of the measurements, and decrease sample size requirements. Despite all of these improvements, the conventional counting techniques face the problem of low specific activity of 14C (disintegrations rate per gram of radioisotope).

For example, the activity of recent carbon samples would be 13.6 dpm/gC (disintegration per minute per gram of carbon), for samples 5730 years old the activity would be about 6.8 dpm/gC, and a sample 50,000 years old would have activity of a mere 0.03 dpm/gC. These are very small numbers. In addition to weak signals from 14C, any of radioactivity detector records so-called counter background caused by cosmic radiation or trace radioactivity of surrounding material. This causes a major limitation in age determination of material older than 50,000 years even when modern scintillation counters are used.

Typical sample sizes needed for conventional gas and liquid scintillation counting are equivalent to about 5-10 grams of pure carbon [K5]. The sample needed for dating of material older than 50,000 years is even greater. The dating of older samples is very important for archaeological research but not so critical for fine-art research, which deals mostly with later periods of civilization. In art research a much more critical issue is the problem of minimum sample size. Over the past decades several attempts have been made to date small samples by conventional

Time (years)

Fig. K.2. Decay curve of 14C.

counting methods. The mini-gas counters that have been introduced are able to work with sample sizes as small as 100 mg of pure carbon. To achieve the same quality of counting statistics as we can achieve for samples of ordinary sizes, the reduction in sample size has to be compensated by approximately equivalent multiplication of counting time from the usual 24 or 48 hours to several weeks or months. In most of the cases the sample sizes needed for mini-gas counters exceed the amount of material that might be available from the art object or that museum curators or fine-art or antique collectors might agree to provide for such an analysis [K6].

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