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[edit] formulae

{}^1\!X


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

[edit] See also

Articles on

[edit] Examples of carbon dating and historical disputes

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

[edit] References

[edit] External links


[edit] Note: Computations of ages and dates

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:

\frac{d<sup>40</sup>Ar}{dt} = -\lambda N.

The solution to this equation is:

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

where C is the initial value of N.

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

N = N_0e^{-\lambda t}\,,

where, for a given sample of carbonaceous matter:

N0 = 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,
λ = 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:

t1 / 2 = \frac{\ln 2}{\lambda} = radiocarbon half-life = 5568 years (Libby value)
tavg = \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:

t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}

and for a raw radiocarbon age:

t = -\frac{1}{\lambda} {\ln \frac{N}{N_0}}






Category:Radiometric dating Category:Radioactivity