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And it has seven protons, and it also has seven neutrons. So the different versions of a given element, those are each called isotopes. So anyway, we have our atmosphere, and then coming from our sun, we have what's commonly called cosmic rays, but they're actually not rays. You can view them as just single protons, which is the same thing as a hydrogen nucleus. But every now and then one of those neutrons will bump into one of the nitrogen-14's in just the right way so that it bumps off one of the protons in the nitrogen and essentially replaces that proton with itself. But this number 14 doesn't go down to 13 because it replaces it with itself. And now since it only has six protons, this is no longer nitrogen, by definition. And that proton that was bumped off just kind of gets emitted. But this process-- and once again, it's not a typical process, but it happens every now and then-- this is how carbon-14 forms. You can essentially view it as a nitrogen-14 where one of the protons is replaced with a neutron. It makes its way into oceans-- it's already in the air, but it completely mixes through the whole atmosphere-- and the air. And plants are really just made out of that fixed carbon, that carbon that was taken in gaseous form and put into, I guess you could say, into kind of a solid form, put it into a living form. It gets put into plants, and then it gets put into the things that eat the plants. Well, the interesting thing is the only time you can take in this carbon-14 is while you're alive, while you're eating new things.

And we talk about the word isotope in the chemistry playlist. But this number up here can change depending on the number of neutrons you have. And every now and then-- and let's just be clear-- this isn't like a typical reaction. So instead of seven protons we now have six protons. And a proton that's just flying around, you could call that hydrogen 1. If it doesn't gain an electron, it's just a hydrogen ion, a positive ion, either way, or a hydrogen nucleus. And so this carbon-14, it's constantly being formed. I've just explained a mechanism where some of our body, even though carbon-12 is the most common isotope, some of our body, while we're living, gets made up of this carbon-14 thing.

The amount of carbon-14 in the air has stayed the same for thousands of years.

And carbon-14 is constantly doing this decay thing. So over the course of 5,730 years, roughly half of them will have decayed. Well, if you know that all living things have a certain proportion of carbon-14 in their tissue, as kind of part of what makes them up, and then if you were to find some bone-- let's just say find some bone right here that you dig it up on some type of archaeology dig.

But what's interesting is as soon as you die and you're not ingesting anymore plants, or breathing from the atmosphere if you are a plant, or fixing from the atmosphere. Once a plant dies, it's no longer taking in carbon dioxide from the atmosphere and turning it into new tissue. And this carbon-14 does this decay at a specific rate. And you say, hey, that bone has one half the carbon-14 of all the living things that you see right now.

So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon-12. And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue.

But what's interesting is that a small fraction of carbon-14 forms, and then this carbon-14 can then also combine with oxygen to form carbon dioxide.

For example, in 1991, two hikers discovered a mummified man, preserved for centuries in the ice on an alpine mountain.

Later called Ötzi the Iceman, small samples from his body were carbon dated by scientists.

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 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.