User:Rickert/Sandbox

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


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

Examples of carbon dating and historical disputes

 * 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.

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:


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

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:
 * $$N_0$$ = 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:
 * 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:


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


 * $$t_{avg}$$ = $$ \frac{1}{\lambda} $$ = 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

Kulstof 14-datering Radiokohlenstoffdatierung Datation au carbone 14 Carbonio 14 תיארוך פחמן 14 C14-datering 放射性炭素年代測定 Karbondatering Datowanie radiowęglowe Радиоуглеродный анализ Uhlíková metóda C14 C14-metoden Radyokarbon metodu Радіовуглецеве датування 放射性碳定年法