# Science of carbon dating

Organisms at the base of the food chain that photosynthesize – for example, plants and algae – use the carbon in Earth’s atmosphere.

They have the same ratio of carbon-14 to carbon-12 as the atmosphere, and this same ratio is then carried up the food chain all the way to apex predators, like sharks.

It decays with a half life of 5700 years into nitrogen 14 and electron and an electron antineutreno. So for that reason, every living thing that is interacting with its environment is expected to have this natural abundance of carbon 14. But when something dies, now it's not interacting with the environment anymore. We know that the amount at time t is equal to the initial amount times one half to the time over the half life, alright?

Know that not all of the carbon-14 atoms decay at the same time, but the half-life describes how long it takes for half of them to decay.So that's taking into account all the decays and all that stuff, this is a natural abundance. And that means that as time goes on, the carbon 14 abundance will decrease. So the amount that we've got at our time now is 0.5 times 10 to the -12.So that means the carbon 14 abundance can tell us how long something's been dead. So let's see how we can use this to do a problem. It's bound to have a carbon 14 ratio that's only 0.5 times 10 to the -12. The initial amount when he died must have been 1.3 because he was interacting with its environment. Alright, so that means that t is going to be, I'm just going to solve this equation real quickly, it's going to be 5700 years times the natural log of 0.5 over 1.3 divided by the natural log of one half.And if you type that in your calculator you'll find that this specimen is 700, oh sorry, 7860 years dead. So that's the way that we can do these calculations. Let's do it a different, let's do a different one.It's always the same thing and if you're having trouble in going from this step to this step, make sure you know how to do that. We take the natural log of both sides and then we solve for t. Let's say that a specimen has been dead for 10,000 years and I want to know its carbon 14 ratio.

Radiocarbon dating uses isotopes of the element carbon. Cosmic rays – high energy particles from beyond the solar system – bombard Earth’s upper atmosphere continually, in the process creating the unstable carbon-14. Because it’s unstable, carbon-14 will eventually decay back to carbon-12 isotopes.