Page 125 - Radiochemistry and nuclear chemistry

Radionuclides in Nature 111

5.8.1. Dating by the 14C method

It is reasonable to assume that the production of 14C in the atmosphere has been constant
for at least a million years, which means that equilibrium exists between the rates of
formation and decay of the 14C in the atmosphere. Moreover, the half-life of 14C is
sufficient to allow equilibrium between the 14C in the atmosphere, the oceans (including
precipitations to ocean bottoms), and exchangeable carbon in natural materials. Thus from
measurement of the specific radioactivity of carbon, it should be possible to determine when
the sample became isolated from its natural environmental compartment.
The discovery that all living organic material has a certain specific radioactivity due to
14C led W. Libby to a new method for determination of the age of biological material. This
method, which has been of great importance in dating archeological, geological, etc
materials, is based on the assumption (i) that cosmogenic 14C has been producexl at a
constant rate, (ii) that the amount of anthropologic 14C is negligible compared to the
cosmogenic, (iii) that after the organism incorporating the biological material died, no
exchange occurs between the carbon atoms of the material and those of the surroundings.
In such material the number of 14C atoms decreases with time according to the half-life of
14C. The equation is (for notation, see w 4.13)

14C (Bq/g) = 14C o r (5.3a)

01"

t (y) = (log 14C o - log 14C) 5568/0.301 (5.3b)

where 14C o is the initial 14C activity of a standard (14C o ~-. 14 dpm/g, c.f. w 5.1.3) at time
of death of the plant, etc (t = 0). The reference time for 14C ages is AD 1950, which is
indicated with the letters bp or BP (for "before present"). The half-life of 5568 y is a
standard reference value introduced by Libby. For example, if the specific activity of a
sample is measured to be 0.1 dpm/g, then (5.3b) gives a value of 39 700 years as the time
since the material ceased to exchange its carbon. Only with extreme care and very
sophisticated equipment can a specimen this old be determined with reliability, but shorter
times can be measured more accurately since the specific activities are larger. 14C ages are
used for dating specimen of 300 to 50 000 y, with an uncertainty of 10 - 100 y. 14C-
determinations were originally made by transferring the carbon into carbon dioxide, which
was measured in an internal GM-counter (Ch. 8). Later, transformation into methane was
preferred, and the CH 4 counted in an internal proportional counter. The most sensitive
technique today is to introduce the sample into the ion source of a tandem-van-der-Graaff
accelerator and "count" the amount of 14C-ions relative to 12C-ions by mass-spectrometry.
There are many cautions that must be observed in the use of carbon dating. In addition
to those mentioned above, there is the possibility of isotopic effects in metabolic processes.
These could cause 14C to be slightly depleted relative to 12C due to chemical reactions in
the biological material. To take this into account to get the correct "solar age" instead of
a slightly misleading "14C age ~, the isotopic depletion can be determined from deviations
in the 12C/13C ratio. A "~13C correction" is introduced according to