${\displaystyle {}^{1}\!X}$

${\displaystyle {\frac {d{}^{40}\!K}{dt}}=-\lambda {}^{40}\!K.}$

Articles on

• Carbon-14.
• Cosmogenic isotopes
• Environmental isotopes

• Shroud of Turin
• Santorini
• Vinland map
• Skeleton Lake
• Kennewick Man

The method and its results are rejected by creation science and Young Earth creationism for religious reasons.

• NOAA [1]
• Gerhard Morgenroth: "Radiokarbon-Datierung: Xerxes' falsche Tochter", Physik in unserer Zeit 34 (1), S. 40 - 43 (2003), ISSN 0031-9252 Abstract
• Definitions and use of the radioactive decay constant and other constants characterizing radioactive decay
• Discussion of half-life and average-life in measurements of radioactive decay
• Radiocarbon - The main international journal of record for research articles and date lists relevant to 14C
• Harry E. Gove: From Hiroshima to the Iceman. The Development and Applications of Accelerator Mass Spectrometry. Bristol: Institute of Physics Publishing, 1999
• Roman Laussermayer: Meta-Physik der Radiokarbon-Datierung des Turiner Grabtuches. VWF Verlag für Wissenschaft und Forschung, Berlin, 2000, ISBN 3-89700-263-9.
• J. R. Arnold and W. F. Libby, Age Determinations by Radiocarbon Content: Checks with Samples of Known Age (Science (1949), Vol. 110)
• Michael Friedrich, Sabine Remmele, Bernd Kromer, Jutta Hofmann, Marco Spurk, Klaus Felix Kaiser, Christian Orcel, Manfred Küppers: The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—a Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions. Radiocarbon 46/3, S. 1111-1122 (2004).
• Libby, W. F., Radiocarbon Dating, 2nd ed. (Univ. of Chicago Press, Chicago, Ill.,. 175 pp., 1955).
• Radiocarbon dating in Cambridge: some personal recollections. A Worm's Eye View of the Early Days, by E. H. Willis [2]
• de Vries, Hessel (1916-1959), by J. J. M. Engels [3]
• The Discovery of Global Warming, by Spencer Weart [4]

• C14dating.com - General information on Radiocarbon dating
• CalPal - Cologne Radiocarbon Calibration & Paleoclimate Research Package with online manual.
• CalPal - Online Radiocarbon Calibration
• OxCal program for calibration
• Layman's explanation of how calibration curves are made
• Further basic information on radiocarbon dating (PDF)
• Calibration curves comparison (PDF)

The radioactive decay of carbon-14 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:

${\displaystyle {\frac {d⁴⁰Ar}{dt}}=-\lambda N.}$

The solution to this equation is:

${\displaystyle N=Ce^{-\lambda t}\,}$,

where ${\displaystyle C}$ is the initial value of ${\displaystyle N}$.

For the particular case of radiocarbon decay, this equation is written:

${\displaystyle N=N_{0}e^{-\lambda t}\,}$,

where, for a given sample of carbonaceous matter:

${\displaystyle N_{0}}$ = number of radiocarbon atoms at ${\displaystyle t=0}$, i.e. the origin of the disintegration time,

${\displaystyle N}$ = number of radiocarbon atoms remaining after radioactive decay during the time ${\displaystyle t}$,

${\displaystyle {\lambda }=}$radiocarbon decay or disintegration constant.

Two related times can be defined:

• half-life: time lapsed for half the number of radiocarbon atoms in a given sample, to decay,
• mean- or average-life: mean or average time each radiocarbon atom spends in a given sample until it decays.

It can be shown that:

${\displaystyle t_{1/2}}$ = ${\displaystyle {\frac {\ln 2}{\lambda }}}$ = radiocarbon half-life = 5568 years (Libby value)

${\displaystyle t_{avg}}$ = ${\displaystyle {\frac {1}{\lambda }}}$ = radiocarbon mean- or average-life = 8033 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:

${\displaystyle t(BP)={\frac {1}{\lambda }}{\ln {\frac {N}{N_{0}}}}}$

and for a raw radiocarbon age:

${\displaystyle t=-{\frac {1}{\lambda }}{\ln {\frac {N}{N_{0}}}}}$

Category:Radiometric dating Category:Radioactivity