Radiocarbon Dating

Radiocarbon dating is a technique used to find the age of historic and archaeological ORGANIC samples -- things like old wood samples, or animal and human fossils -- by exploiting the known, steady decay of the radioactive carbon isotope 14C.

14C is continually being formed, even today, in the upper atmosphere, where cosmic-ray neutrons bombard ordinary atmospheric nitrogen-14: $14$-$7$-$N + 1$-$0$-$n \rightarrow 14$-$6$-$C + 1$-$1$-$H$. This newly formed 14C combines with atmospheric oxygen to form 14-CO2, which then mixes thoroughly with the far more abundant ordinary 12-CO2 already present in the air. Plants take up this mixed CO2 during photosynthesis, and animals in turn acquire it by eating plants (and each other), so 14C becomes a genuine, ongoing part of the carbon in both plant and animal bodies. As long as an organism is alive and still actively exchanging carbon with its environment (via photosynthesis or feeding), the ratio $^{14}C/^{12}C$ within its body stays essentially CONSTANT, matching the ratio in the atmosphere.

Once the organism dies, that exchange stops -- no more photosynthesis, no more feeding -- so the ^{14}C/^{12}C} ratio in its remains is no longer replenished, and it falls over time purely because the 14C already present continues to decay by beta emission, $14$-$6$-$C \rightarrow 14$-$7$-$N + \,^{0}_{-1}e$, with a half-life of 5730 years, giving a decay constant $\lambda = \frac{0.693}{5730\,\text{y}} \approx 1.21 \times 10^{-4}\ \text{y}^{-1}$. …