We will be discussing Radionuclide dating this week in class. This is how we can know how old certain types of fossils, bones, rocks, etc are – especially when they are so old that no one was around to see them and write down the date. In fact, this type of dating can even help us determine how old some things are from a time before there was any humans around at all. This video, from scientific american, does an excellent job at introducing the concept using carbon dating as an example.
The general idea is that there are two common types of Carbon, Carbon-12 is the non-radioactive form and Carbon-14 is a radioactive form of the same element. The only difference between the two is that C-14 breaks down by radioactive decay at a certain rate. Once it decays, C-14 will be transformed into Nitrogen.
There is a steady ratio of C-12 / C-14 in the atmosphere that gets incorporated into plants during photosynthesis, and eventually makes its way into all organisms through the food chain. Therefore, this ratio of Carbon will also exist in all living beings and will remain at this steady state until the last time this organism ingests a Carbon food source (just before it dies). From that point on, the Radioactive Carbon will decay, while C-12 remains steady.
The rate of radioactive decay is called the ‘half-life’, which is the time it takes for half the radioactive material to decay. This means we can watch the ratio of the two elements over time, and by determining how many halves have decayed, we know how long it has been since the organism died.
Below, I’ve made a graph similar to the one in the video to show how this looks (Click for Enlarged Image):

A Geiger Counter illustrates the reduction of radioactivity over several half-lives. A. Detail of the Geiger Counter. Higher counts (9 o’clock) indicate more radioactive material. B. Graph of radioactive material decaying vs non-decaying material.