Libby and coworkers, and it has provided a way to determine the ages of different materials in archeology, geology, geophysics, and other branches of science.
Some examples of the types of material that radiocarbon can determine the ages of are wood, charcoal, marine and freshwater shell, bone and antler, and peat and organic-bearing sediments.
The carbon-14 atoms combine with oxygen to form carbon dioxide, which plants absorb naturally and incorporate into plant fibers by photosynthesis.
Animals and people take in carbon-14 by eating the plants.
In order to date the artifact, the amount of Carbon-14 is compared to the amount of Carbon-12 (the stable form of carbon) to determine how much radiocarbon has decayed.
The ratio of carbon-12 to carbon-14 is the same in all living things.
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.
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.
By measuring the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of the artifact.
SAL: In the last video we saw all sorts of different types of isotopes of atoms experiencing radioactive decay and turning into other atoms or releasing different types of particles.
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.
At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay. If I wait carbon-14's half-life-- this is a specific isotope of carbon. So when you have the same element with varying number of neutrons, that's an isotope. Let's think about what happens after another half-life. And by the law of large numbers, half of them will have converted into nitrogen-14. This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon-14.
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.