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Variability in amount of carbon

 In addition to the variation in production and distribution of 14C over time and within portions of various carbon reservoirs, variations may result from situations where carbon not in equilibrium with the contemporary standard values is added or removed from any reservoir. Two instances are well documented since they occurred within the last century as a result of human intervention in the carbon cycle. The first, beginning in the middle of the nineteenth century, is known as the industrial or Suess effect. The combustion of fossil fuels added enough “dead” 14C to the atmosphere to result in the reduction by about 3% in biospheric 14C activity. In the more recent atomic bomb or Libby effect, relating to the detonation of thermonuclear devices in the atmosphere in the early 1950s, large amounts of artificial 14C were produced, almost doubling the amount of 14C in the terrestrial biosphere. When combined with the late-eighteenth-century De Vries excurses, the Suess effect makes it difficult to distinguish 14C concentrations within the last two centuries. This is one of the reasons why laboratories generally use 100 or 150 years as the minimum age which can be cited. It also explains why laboratories cannot use modern wood as a contemporary reference.

 Half-life of radiocarbon

 The fundamental constant which permits the conversion of a 14C/12C ratio into an age value is the half-life or decay constant of 14C. Initially in the development of the method, Libby and collaborators used the value 5720 ± 47 as the half-life figure, but soon adopted the weighted average of three independently obtained measurements. The average value was 5568 ± 30 and this became identified as the Libby half-life. In 1962, at the 5th Radiocarbon Dating Conference at Cambridge, it was decided that 5730 ± 40 probably represented a more accurate approximation of the actual half-life. It was agreed, however, that the Libby half-life would be used in the calculation of conventional 14C determinations. The stated reason was that any changes in the value would introduce unneeded confusion in the radiocarbon literature.

The issue of the correct half-life for 14C has lost a considerable amount of its significance because of the discovery and documentation of similiar variation and De Vries effects. The existence of dendrochronologically documented relationships between 14C age and calendar age, for samples up to about 10,000 years old, enables researchers to circumvent the problem of the actual 14C half-life and proceed to calibrate these 14C age values directly.

 Statistical and contextual uncertainties

 Most 14C determinations are expressed in the form: age value (in 14C years B.P.) ± statistical uncertainty. The age value is calculated by using the equation previously presented. The measurement uncertainty results from statistical considerations inherent in the random decay process characteristic of all radioactive isotopes. A date, for example, of 5600 ± 80 14C years B.P. reflects the fact that the count rate of the sample is about 50% of the modern reference standard (that is, it has decayed for a period of about one Libby half-life) and the age value is known to about 1% or 80 years. Statistical uncertainties in 14C work are usually cited in terms of one standard deviation errors. The expression 5600 ± 80 is a shorthand manner of stating that there are two chances out of three that the age equivalent of the counting rate for this sample will be contained within the range 5520 to 5680. An accurate statement of the results of a 14C determination must include a listing of the measurement uncertainty. In addition, some laboratories increase this value to take into consideration changes that affect counting conditions, such as drift of electronic equipment and changes in barometric pressure. Statistical errors are not cited only when the counting rate of a sample is statistically indistinguishable from the background counting rate for the counter being used. The result is expressed as a minimum or infinite value by stating that the age is “greater than” a limit imposed by the characteristics of the counting system being employed (for example, >40,000).

The processing and counting of a sample to determine its 14C age is a challenging analytical procedure. However, a technically correct value which has been carelessly collected may be scientifically worthless. Often the significance and importance of a 14C determination are only as good as the attention to detail which went into documenting the geological, historical, or archeological context of the sample. It is important to be aware of what a 14C date does and does not indicate. A 14C value provides a temporal index of when the sample was removed from its reservoir. For example, a 14C determination on a piece of charcoal or wood provides an age value for the tree rings which make up the sample. A 14C date taken on a piece of wood taken from a beam excavated from a ruined structure may indicate the time when the building was constructed if the sample was taken from the outside rings of the tree used as the source of the timber and if the timber itself did not happen to be reused from an earlier structure. Problems such as these often confront geologists and archeologists as they attempt to critically interpret the dating evidence provided by the 14C method.

  E. Bard et al., Radiocarbon calibration by means of mass spectrometric ²³⁰Th/²³⁴U and ¹⁴C ages of corals: An updated base including samples from Barbados, Mururoa and Tahiti, Radiocarbon, 40:1085–1092, 1998

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