Radiocarbon Dating

I found many of the technological methods Archaeologists use throughout the duration of their explorations to be fascinating (I’m a Physics major, so I’m pretty geeky like that…). I contemplated using this opportunity to take one of these rather involved pieces of technology (such as LIDAR) and go into depth as to how it works exactly, but I figured that would put anyone unfortunate enough to stumble upon the blog post to sleep. Instead, I’d like to talk about probably one of the most well known tools in archaeology, radiocarbon dating.


As mentioned in class, it all starts with the nucleus of a carbon atom, and more particularly, some sort of isotope. What is an isotope? An isotope is a variant of an element (elements are characterized by the number of protons they have in their nuclei) that has a different number of neutrons from the number of protons in the nucleus. There are three naturally occurring isotopes of carbon: carbon-12 (the carbon we all know and love), carbon-13, and carbon-14. The dashes after the carbon indicate the total number of protons and neutrons in the nucleus; for carbon, there are always 6 protons in the nucleus so you can do the math to find the number of neutrons. Carbon-12 and carbon-13 are both stable isotopes, while carbon-14 is unstable and decays. When I say “decay” I mean that it lets go of some of the matter inside of it, and this happens because it is energetically “favorable” to do so, i.e. the nucleus wants to be in the lowest state of energy and undergoing beta decay (lets off an electron) allows it to do that. This part is rather complicated: but in short, a neutron is actually comprised of a proton, an electron and another particle called an electron anti-neutrino (not important in our case). Any who, the neutron lets off an electron, which means that the extra neutron in the carbon atom turns into a proton, which now gives the element 7 protons, making it a nitrogen atom! If you don’t quite get this part, that’s ok, just FYI.


Cool, now that we know about the decay of carbon-14, how do we use it? First off, we know that the half life of carbon-14 is 5730 years (plus or minus 40 years). This means if I took a big chunk of radioactive carbon-14 (probably not a good idea), half of it would be gone in about 5730 years (way after I’m dead). We also know that while someone is living, he/she/it is ingesting carbon-14 naturally, and when dead, no longer ingests that carbon-14. Here starts the decay process. So, one can naturally deduce that you could probably tell how old something is by taking the ratio of carbon-14 to regular carbon-12 (carbon-13 only accounts for 1% of naturally occurring carbon, so we can neglect it).


This process only allows us to date things in a specific time frame, accurately however. Why is this? It involves one function: the exponential function. The rate of any radioactive decay is proportional to e^(-kt) where k is the decay constant, and t is time. If we plot this on a graph as a function of t, you’ll notice a couple things: 1. The slope of the graph is steep at t=0 and2. The slope of the graph really flat for large t. what can we say about that? Think about if we’re trying to measure the ratio of the carbon-14 to carbon-12 for small t (where the graph is steep). We can see that there is a very wide range of carbon values during a very small amount of time: this makes measuring the exact chronology of living events almost impossible if there are any measurement errors! Now let’s take some very large t, where the curve is very flat: now we have the opposite problem. If there’s any small error in the calculation, this could mean the difference between 50,000 and 200,000 years, which is of no help.


I hope you’ve enjoyed this slightly more in depth look at radio carbon dating. There are a lot of other factors and a ton of research that goes into this subject as well, so research on your own if you’d like!