# Mathematics of carbon dating

*15-Sep-2019 16:40*

So this is just an ordinary beta decay process and this carbon fourteen's half life is way way way too short for any carbon to just kind of exist naturally in the atmosphere, you'd think, not quite right. So that mean that 1.3 times 10 to the -12 carbon 14 atoms, exist for each and every carbon 12 atom in nature. So you'd think that if you got this 1.3 times 10 to the -12 carbon 14 atoms for each carbon 12 atom at some time, well then 5700 years later, half of the carbon 14 will have decayed. But in fact what happens is, cosmic rays from the sun interact with the upper atmosphere and they actually create carbon 14, at this rate so that in equilibrium, 1.3 times 10 to the -12 carbon 14 atoms will exist for every carbon 12 atom. It's no longer replenishing its carbon 14 supply. This is our standard radioactive decay formula, always works.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 we'll say alright, the amount at 10,000 is equal to the initial amount that I started with 1.3 times 10 to the -12 times a half to the 10,000 divided by 5700. And when you do so, you'll end up with 0.385 times 10 to the -12. Now one thing that it's important to keep in mind about carbon dating is that this is a really small number. The abundance, the natural abundance is already very small. You can usually date something that's under about 40 or 50,000 years old using this technique.

Well, we're going to use exactly the same equation.

I do not have the decay constant but, by using the half-life information, I can find it.