# Half life carbon dating example

I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting. And it does that by releasing an electron, which is also call a beta particle. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? So that after 5,740 years, the half-life of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. But we'll always have an infinitesimal amount of carbon. Let's say I'm just staring at one carbon atom. You know, I've got its nucleus, with its c-14. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. After two years, how much are we going to have left? And then after two more years, I'll only have half of that left again.

And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic. So one of the neutrons must have turned into a proton and that is what happened. And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen. And over 5,740 years, you determine that there's a 50% chance that any one of these carbon atoms will turn into a nitrogen atom. And we could keep going further into the future, and after every half-life, 5,740 years, we will have half of the carbon that we started. Now, if you look at it over a huge number of atoms. But after two more years, how many are we going to have? So this is t equals 3 I'm sorry, this is t equals 4 years.

Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.

The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay.

C-14 is produced in the upper atmosphere when nitrogen-14 (N-14) is altered through the effects of cosmic radiation bombardment (a proton is displaced by a neutron effectively changing the nitrogen atom into a carbon isotope).

The new isotope is called "radiocarbon" because it is radioactive, though it is not dangerous.

In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years.

But the question is, when does an atom or nucleus decide to decay? So it could either be beta decay, which would release electrons from the neutrons and turn them into protons. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. That's 6.02 times 10 to the 23rd carbon-12 atoms. This is more than we can, than my head can really grasp around how large of a number this is.

And maybe not carbon-12, maybe we're talking about carbon-14 or something. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay. And the atomic number defines the carbon, because it has six protons. If they say that it's half-life is 5,740 years, that means that if on day one we start off with 10 grams of pure carbon-14, after 5,740 years, half of this will have turned into nitrogen-14, by beta decay. What happens over that 5,740 years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon-14. So now we have seven and a half grams of nitrogen-14. This exact atom, you just know that it had a 50% chance of turning into a nitrogen.

So with that said, let's go back to the question of how do we know if one of these guys are going to decay in some way. That, you know, maybe this guy will decay this second. Remember, isotopes, if there's carbon, can come in 12, with an atomic mass number of 12, or with 14, or I mean, there's different isotopes of different elements. So the carbon-14 version, or this isotope of carbon, let's say we start with 10 grams. Well we said that during a half-life, 5,740 years in the case of carbon-14-- all different elements have a different half-life, if they're radioactive-- over 5,740 years there's a 50%-- and if I just look at any one atom-- there's a 50% chance it'll decay. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here. So we'll have even more conversion into nitrogen-14. So now we're only left with 2.5 grams of c-14. Well we have another two and a half went to nitrogen. So after one half-life, if you're just looking at one atom after 5,740 years, you don't know whether this turned into a nitrogen or not.

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.

The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.

So what we do is we come up with terms that help us get our head around this. So I wrote a decay reaction right here, where you have carbon-14. So now you have, after one half-life-- So let's ignore this. I don't know which half, but half of them will turn into it. And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left.