This is called the half-lifeā€”the amount of time required for one-half of a given number of atoms to disintegrate. The plot of the number of tiles as a function of the number of turns looks like this: Again, I made radioactive spheres disappear when they decayed.This is fine, because when carbon-14 decays, it produces nitrogen-14. But you could imagine that if you knew that the sample started with 20 percent blue spheres and you knew their half-life, then you could determine the age by examining one frame from the animation.

carbon dating decay curve-20carbon dating decay curve-8

Potassium-40 is another radioactive element naturally found in your body and has a half-life of 1.3 billion years.

Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).

And this is just when you're doing it with a discreet you know, when you're right at the half-life point.

We know that radiation is more than just the spooky, silent threat that we see in movies.

Now you could say, OK, what's the probability of any given molecule reacting in one second? But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So I have a description, and we're going to hopefully get an intuition of what half-life means. And how does this half know that it must stay as carbon? So if you go back after a half-life, half of the atoms will now be nitrogen. Then all of a sudden you can use the law of large numbers and say, OK, on average, if each of those atoms must have had a 50% chance, and if I have gazillions of them, half of them will have turned into nitrogen. How much time, you know, x is decaying the whole time, how much time has passed?

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. It'll probably still be carbon, but there's some probability that after one second it will have already turned into nitrogen-14. 1/2 to the 3rd power, because every time you have 1/2 of the original sample-- that's the number of half-lives-- after three half-lives you'll have 1/8 of your original sample. In the next video we're going to explore what if I asked you a question, how many of the particles, or how many grams will you have in exactly 10 days? 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. When an element undergoes radioactive decay, it creates radiation and turns into some other element.