Carbon dating and chemistry a simple mandating portugal
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?
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.
But nevertheless, this ratio can be determined, for carbon-14 is a radioactive isotope and manifests itself by its radiation.
It is converted into nitrogen by the emission of an electron which can be detected by a sensitive apparatus.
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.
After another 5,600 years, there is still one quarter left, and after an equally long period of time one eighth, etc.Carbon-14 is thus said to have a half-life of 5,600 years.