Radiocarbon dating, or
carbon
dating, is a
radiometric
dating method that uses the naturally occurring
radioisotope carbon14
(
^{14}C) to determine the age of
carbonaceous materials up to about 58,000 to
62,000 years. Raw, i.e. uncalibrated, radiocarbon ages are usually
reported in
radiocarbon years "
Before Present" (BP), "Present" being defined
as
AD 1950. Such raw ages can be calibrated to
give calendar dates.
One of the most frequent uses of radiocarbon dating is to estimate
the age of organic remains from archaeological sites. When plants
fix atmospheric
carbon dioxide ( )
into organic material during
photosynthesis they incorporate a quantity of
^{14}C that approximately matches the level of this isotope
in the atmosphere (a small difference occurs because of
isotope fractionation, but this is
corrected after laboratory analysis). After plants die or they are
consumed by other organisms (for example, by humans or other
animals) the
^{14}C fraction of this organic material
declines at a fixed
exponential
rate due to the
radioactive decay of
^{14}C. Comparing the remaining
^{14}C fraction of
a sample to that expected from atmospheric
^{14}C allows
the age of the sample to be estimated.
The
technique of radiocarbon dating was developed by Willard Libby and his colleagues at the
University of
Chicago in 1949. Emilio
Segrè asserted in his autobiography that
Enrico Fermi suggested the concept to Libby in
a seminar at Chicago that year. Libby estimated that the steady
state radioactivity concentration of exchangeable carbon14 would
be about 14 disintegrations per minute (dpm) per gram. In 1960, he
was awarded the
Nobel Prize in
chemistry for this work. He first demonstrated the accuracy of
radiocarbon dating by accurately estimating the age of wood from an
ancient Egyptian royal barge for which
the age was known from historical documents.
Basic physics
Carbon has two stable, nonradioactive
isotopes:
carbon12
(
^{12}C), and
carbon13
(
^{13}C). In addition, there are trace amounts of the
unstable isotope
carbon14
(
^{14}C) on
Earth. Carbon14 has a
halflife of 5730 years, meaning that the
amount of carbon14 in a sample is halved over the course of 5730
years due to
radioactive decay.
Carbon14 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
_{2}) in the atmosphere:
 n + \mathrm{^{14}_{7}N^{1+}} \rightarrow \mathrm{^{14}_{6}C} +
p
The highest rate of carbon14 production takes place at altitudes
of 9 to 15 km (30,000 to 50,000 ft), and at high
geomagnetic latitudes, but the carbon14 spreads
evenly throughout the atmosphere and reacts with
oxygen to form
carbon
dioxide. 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 carbon14 is produced at a constant rate
and the proportion of radioactive to nonradioactive carbon is
constant: ca. 1
part per trillion
(600 billion atoms/mole). In 1958
Hessel
de Vries showed that the concentration of carbon14 in the
atmosphere varies with time and locality. For the most accurate
work, these variations are compensated by means of
calibration curves. When these curves are
used, their accuracy and shape are the factors that determine the
accuracy and age obtained for a given sample.
Plants take up atmospheric carbon dioxide by
photosynthesis, and are ingested by animals,
so every living thing is constantly exchanging carbon14 with its
environment as long as it lives. Once it dies, however, this
exchange stops, and the amount of carbon14 gradually decreases
through radioactive
beta decay with a
halflife of 5,730±40 years.
 \mathrm{~^{14}_{6}C}\rightarrow\mathrm{~^{14}_{7}N^{1+}}+ e^{}
+ \bar{\nu}_e
Carbon14 was discovered on February 27,
1940, by Martin Kamen and Sam Ruben at the University of California
Radiation Laboratory at Berkeley.
Computation of ages and dates
The radioactive decay of carbon14 follows an
exponential decay.A quantity is said to be
subject to exponential decay if it decreases at a rate proportional
to its value. Symbolically, this can be expressed as the following
differential equation, where
N is the quantity and λ is a positive number called the
decay constant:
 \frac{dN}{dt} = \lambda N.
The solution to this equation is:
 N = N_0e^{\lambda t}\,,
where, for a given sample of carbonaceous matter:
 N_0 = number of radiocarbon atoms at t = 0, i.e. the origin of
the disintegration time,
 N = number of radiocarbon atoms remaining after radioactive
decay during the time t,
 {\lambda} = radiocarbon decay or disintegration
constant.
Two related
times can be defined:
 * mean or averagelife: mean or average time each radiocarbon
atom spends in a given sample until it decays.
 * halflife: time lapsed for half the number of radiocarbon
atoms in a given sample, to decay,
It can be shown that:
 t_{avg} \, = \frac{1}{\lambda} = radiocarbon mean or
averagelife = 8033 years (Libby value)
 t_\frac{1}{2} \, = t_{avg} \cdot \ln 2 = radiocarbon halflife
= 5568 years (Libby value)
Notice that
dates are customarily given in
years
BP which implies
t(BP) = t because the
time arrow for dates runs in reverse direction from the time arrow
for the corresponding ages. From these considerations and the above
equation, it results:
For a raw radiocarbon date:
 t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}
and for a raw radiocarbon age:
 t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}
After replacing values, the raw radiocarbon age becomes any of the
following equivalent formulae:
using logs base
e and the average life:
 t(BP) = t_{avg}\cdot \ln{\frac{N}{N_0}}
and
using logs base
2 and the halflife:
 t(BP) = t_\frac{1}{2}\cdot \log_2 \frac{N}{N_0}
Wiggle matching uses the nonlinear
relationship between the
^{14}C age and calendar age to
match the shape of a series of closely sequentially spaced
^{14}C dates with the
^{14}C calibration
curve.
Measurements and scales
Measurements are traditionally made by counting the
radioactive decay of individual carbon
atoms by gas
proportional counting or by
liquid scintillation counting.
For samples of sufficient size (several grams of carbon) this
method is still widely used in the 2000s. Among others, all the
tree ring samples used for the calibration curves (see below) were
determined by these counting techniques. Such decay counting,
however, is relatively insensitive and subject to large statistical
uncertainties for small samples. When there is little carbon14 to
begin with, the long radiocarbon
halflife
means that very few of the carbon14 atoms will decay during the
time allotted for their detection, resulting in few disintegrations
per minute.
The sensitivity of the method has been greatly increased by the use
of
Accelerator Mass
Spectrometry (AMS). With this technique
^{14}C atoms
can be detected and counted directly
vs only detecting
those atoms that decay during the time interval allotted for an
analysis. AMS allows dating samples containing only a few
milligrams of carbon.
Raw radiocarbon ages (i.e., those not calibrated) are usually
reported in "years
Before Present"
(BP). This is the number of radiocarbon years before 1950, based on
a nominal (and assumed constant  see "
calibration" below) level of
carbon14 in the atmosphere equal to the 1950 level. These raw
dates are also based on a slightlyoff historic value for the
radiocarbon halflife. Such value is used for consistency with
earlier published dates (see "
Radiocarbon
halflife" below). See the section on
computation for the basis of
the calculations.
Radiocarbon dating laboratories generally report an uncertainty for
each date. For example, 3000±30BP indicates a
standard deviation of 30 radiocarbon
years. Traditionally this included only the statistical counting
uncertainty. However, some laboratories supplied an "error
multiplier" that could be multiplied by the uncertainty to account
for other sources of error in the measuring process. More recently,
the laboratories try to quote the overall uncertainty, which is
determined from control samples of known age and verified by
international intercomparison exercises. In 2008, a typical
uncertainty better than ±40 radiocarbon years can be expected for
samples younger than 10,000 years. This, however, is only a small
part of the uncertainty of the final age determination (see section
Calibration
below).
, the limiting age for a 1 milligram sample of graphite is about ten halflives, approximately 60,000 years. This age is derived from that of the calibration blanks used in an analysis, whose ^{14}C content is assumed to be the result of contamination during processing (as a result of this, some facilities will not report an age greater than 60,000 years for any sample).
A variety of sample processing and instrumentbased constraints
have been postulated to explain the upper agelimit. To examine
instrumentbased background activities in the AMS instrument of the
W. M. Keck Carbon Cycle Accelerator Mass Spectrometry Laboratory of
the University of California, a set of natural diamonds were dated.
Natural diamond samples from different sources within rock
formations with standard geological ages in excess of 100 my
yielded
^{14}C apparent ages 64,920±430 BP to 80,000±1100 BP
as reported in 2007.
Calibration
The need for calibration
Calibration curve for the radiocarbon
dating scale.
Data sources: Stuiver et al. (1998).
Samples with a real date more recent than AD 1950 are dated
and/or tracked using the N & SHemisphere graphs.
A raw BP date cannot be used directly as a calendar date, because
the level of atmospheric
^{14}C has not been strictly
constant during the span of time that can be radiocarbon dated. The
level is affected by variations in the
cosmic
ray intensity which is in turn affected by variations in the
earth's
magnetosphere. In addition,
there are substantial reservoirs of carbon in organic matter, the
ocean, ocean sediments (see
methane
hydrate), and
sedimentary
rocks. Changes in the Earth's
climate
can affect the carbon flows between these reservoirs and the
atmosphere, leading to changes in the atmosphere's
^{14}C
fraction.
Aside from these changes due to natural processes, the level has
also been affected by human activities. From the beginning of the
industrial revolution in the
18th century to the 1950s, the fractional level of
^{14}C
decreased because of the admixture of large quantities of
CO
_{2} into the atmosphere, due to the excavated oil
reserves and combustion production of
fossil
fuel. This decline is known as the
Suess effect, and also affects the
^{13}C isotope. However, atmospheric
^{14}C was
almost doubled for a short period during the 1950s and 1960s due to
atmospheric
atomic bomb tests.
As a consequence, the radiocarbon method shows limitations on
dating of materials that are younger than the industrial era. Due
to these fluctuations, greater carbon14 content cannot be taken to
mean a lesser age. It is expected that in the future the
radiocarbon method will become less effective. A calibration curve
must sometimes be combined with contextual analysis, because there
is not always a direct relationship between age and carbon14
content.
Calibration methods
The raw radiocarbon dates, in BP years, are calibrated to give
calendar dates. Standard
calibration
curves are available, based on comparison of radiocarbon dates
of samples that can be dated independently by other methods such as
examination of tree growth rings (
dendrochronology), deep ocean
sediment cores, lake sediment
varves,
coral samples, and
speleothems (cave deposits).
The calibration curves can vary significantly from a straight line,
so comparison of uncalibrated radiocarbon dates (e.g., plotting
them on a graph or subtracting dates to give elapsed time) is
likely to give misleading results. There are also significant
plateaus in the curves, such as the one from 11,000 to 10,000
radiocarbon years BP, which is believed to be associated with
changing ocean circulation during the
Younger Dryas period. Over the historical
period from 0 to 10,000 years BP, the average width of the
uncertainty of calibrated dates was found to be 335 years, although
in wellbehaved regions of the calibration curve the width
decreased to about 113 years while in illbehaved regions it
increased to a maximum of 801 years. Significantly, in the
illbehaved regions of the calibration curve, increasing the
precision of the measurements does not have a significant effect on
increasing the accuracy of the dates.
The 2004 version of the calibration curve extends back quite
accurately to 26,000 years BP. Any errors in the calibration curve
do not contribute more than ±16 years to the measurement error
during the historic and late prehistoric periods (0  6,000 yrs BP)
and no more than ±163 years over the entire 26,000 years of the
curve, although its shape can reduce the accuracy as mentioned
above.
History
Carbon dating was developed by a team led by
Willard Libby. He worked out a carbon14
halflife of 5568±30 years, the Libby halflife. Later a more
accurate figure of 5730±40 years was determined, which is known as
the Cambridge halflife. This is, however, not relevant for
radiocarbon dating. If calibration is applied, the halflife
cancels out, as long as the same value is used throughout the
calculations. Laboratories continue to use the Libby figure to
avoid inconsistencies with previous publications.
Carbon exchange reservoir
Libby's original exchange reservoir hypothesis assumes that the
exchange reservoir is constant all over the world. The calibration
method also assumes that the temporal variation in
^{14}C
level is global, such that a small number of samples from a
specific year are sufficient for calibration. However, since
Libby's early work was published (1950 to 1958), latitudinal and
continental variations in the carbon exchange reservoir have been
observed by
Hessel de Vries (1958;
as reviewed by Lerman
et al., 1959, 1960). Subsequently,
methods have been developed that allow the correction of these
socalled
reservoir effects, including:
 When CO_{2} is transferred from the atmosphere to the
oceans, it initially shares the ^{14}C concentration of the
atmosphere. However, turnaround times of CO_{2} in the
ocean are similar to the halflife of ^{14}C (making
^{14}C also a dating tool for ocean water). Marine
organisms feed on this "old" carbon, and thus their radiocarbon age
reflects the time of CO_{2} uptake by the ocean rather than
the time of death of the organism. This marine reservoir effect is
partly handled by a special marine calibration curve, but local
deviation of several 100 years exist.
 Erosion and immersion of carbonate rocks (which are generally
older than 80,000 years and so shouldn't contain measurable
^{14}C) causes an increase in ^{12}C and
^{13}C in the exchange reservoir, which depends on local
weather conditions and can vary the ratio of carbon that living
organisms incorporate. This is believed negligible for the
atmosphere and atmospherederived carbon since most erosion will
flow into the sea. The atmospheric ^{14}C concentration may
differ substantially from the concentration in local water
reservoirs. Eroded from CaCO_{3} or organic deposits, old
carbon may be assimilated easily and provide diluted ^{14}C
carbon into trophic chains. So the method is less reliable for such
materials as well as for samples derived from animals with such
plants in their food chain.
 Volcanic eruptions eject large amount of carbon into the air,
causing an increase in ^{12}C and ^{13}C in the
exchange reservoir and can vary the exchange ratio locally. This
explains the often irregular dating achieved in volcanic
areas.
 The earth is not affected evenly by cosmic radiation, the
magnitude of the radiation depends on land altitude and earth's
magnetic field strength at any given location, causing minor
variation in the local ^{14}C production. This is accounted
for by having calibration curves for different locations of the
globe. However this could not always be performed, as tree rings
for calibration were only recoverable from certain locations in
1958. The rebuttals by Münnich et al. and by Barker both
maintain that while variations of carbon14 exist, they are about
an order of magnitude smaller than those implied by Crowe's
calculations.
These effects were first confirmed when samples of wood from around
the world, which all had the same age (based on tree ring
analysis), showed deviations from the
dendrochronological age. Calibration
techniques based on treering samples have contributed to increase
the accuracy since 1962, when they were accurate to 700 years
at worst.
Speleothem studies extend ^{14}C calibration
Relatively recent (2001) evidence has allowed scientists to refine
the knowledge of one of the underlying assumptions.
A peak in the amount
of carbon14 was discovered by scientists studying speleothems in caves in the
Bahamas. Stalagmites are
calcium carbonate deposits left
behind when seepage water, containing dissolved
carbon dioxide, evaporates. Carbon14 levels
were found to be twice as high as modern levels. These discoveries
improved the calibration for the radiocarbon technique and extended
its usefulness to 45,000 years into the past.
Examples
See also
References

http://www.mnsu.edu/emuseum/information/biography/klmno/libby_willard.html

http://www.thefreelibrary.com/Coral+corrects+carbon+dating+problemsa09093001
 These results were obtained from a Monte Carlo
analysis calibrating simulated measurements of varying precision
using the 1993 version of the calibration curve. The width of the
uncertainty represents a 2σ uncertainty (that is, a likelihood of
95% that the date appears between these limits).
 A web interface is here.
Further reading
 de Vries, H. L. (1958). "Variation in Concentration of
Radiocarbon with Time and Location on Earth", Proceedings
Koninlijke Nederlandse Akademie Wetenschappen B, 61: 94102;
and in Researches in Geochemistry, P. H. Abelson (Ed.) (1959)
Wiley, New York, p. 180.
 Gove, H. E. (1999) From Hiroshima to the Iceman. The
Development and Applications of Accelerator Mass Spectrometry.
Bristol: Institute of Physics Publishing.
 ; Lerman, J. C., Mook, W. G., and Vogel, J. C. (1970) Proc.
12th Nobel Symp.
 Weart, S. (2004) The
Discovery of Global Warming  Uses of Radiocarbon
Dating.
 Willis, E.H. (1996) Radiocarbon dating in Cambridge: some personal
recollections. A Worm's Eye View of the Early Days.
External links