How Great Is the 14C Activity in Living Tissue?

To find the activity $R$ using the equation $R=\frac{0\text{.}\text{693}N}{t_{1/2}}$, we must know $N$ and $t_{1/2}$. The half-life of ${}^{\text{14}}\text{C}$ can be found in Appendix B, and was stated above as 5730 y. To find $N$, we first find the number of ${}^{\text{12}}\text{C}$ nuclei in 1.00 kg of carbon using the concept of a mole. As indicated, we then multiply by $1\text{.}3\times {\text{10}}^{-\text{12}}$ (the abundance of ${}^{\text{14}}\text{C}$ in a carbon sample from a living organism) to get the number of ${}^{\text{14}}\text{C}$ nuclei in a living organism.

One mole of carbon has a mass of 12.0 g, since it is nearly pure ${}^{\text{12}}\text{C}$. (A mole has a mass in grams equal in magnitude to $A$ found in the periodic table.) Thus the number of carbon nuclei in a kilogram is

So the number of ${}^{\text{14}}\text{C}$ nuclei in 1 kg of carbon is

Now the activity $R$ is found using the equation $R=\frac{0\text{.}\text{693}N}{t_{1/2}}$.

Entering known values gives

or $7\text{.}\text{89}\times {\text{10}}^9$ decays per year. To convert this to the unit Bq, we simply convert years to seconds. Thus,

or 250 decays per second. To express $R$ in curies, we use the definition of a curie,

Thus,

Our own bodies contain kilograms of carbon, and it is intriguing to think there are hundreds of ${}^{\text{14}}\text{C}$ decays per second taking place in us. Carbon-14 and other naturally occurring radioactive substances in our bodies contribute to the background radiation we receive. The small number of decays per second found for a kilogram of carbon in this example gives you some idea of how difficult it is to detect ${}^{\text{14}}\text{C}$ in a small sample of material. If there are 250 decays per second in a kilogram, then there are 0.25 decays per second in a gram of carbon in living tissue. To observe this, you must be able to distinguish decays from other forms of radiation, in order to reduce background noise. This becomes more difficult with an old tissue sample, since it contains less ${}^{\text{14}}\text{C}$, and for samples more than 50 thousand years old, it is impossible.