# Types of radioactive decay dating

Trying to figure out the other product from our nuclear equation, I know nucleons are conserved, so if I have 238 nucleons on the left, I need 238 nucleons on the right.Well, I have four from my alpha particle, so I need 234 more.

The important thing is to be able to look at a nuclear equation, recognize it as beta decay, and be able to write everything in your nuclear equation. It's going to give off a gamma ray, so let's go ahead and draw in our gamma ray here, so zero and zero. 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. On the left, I know I have 92 protons, so 92 positive charges on the left. We already have two positive charges from our alpha particle, and so we need 90 more. So this is just a visual representation of what's going on here, in our nuclear equation. So in beta decay, an electron is ejected from the nucleus.We saw in the previous video that you represent an electron, since it has a negative one charge, you put a negative one down here, it's not a proton, nor is it a neutron, so we put a zero here.Let's say I have a bunch of, let's say these are all atoms. And let's say we're talking about the type of decay where an atom turns into another atom. Or maybe positron emission turning protons into neutrons. And we've talked about moles and, you know, one gram of carbon-12-- I'm sorry, 12 grams-- 12 grams of carbon-12 has one mole of carbon-12 in it.

So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, and it has a half-life of two years.

- [Voiceover] Let's look at three types of radioactive decay, and we'll start with alpha decay.

In alpha decay, an alpha particle is ejected from an unstable nucleus, so here's our unstable nucleus, uranium-238.

So we're going to make protactinium here, so Pa. Well, 234 minus 90, 234 minus 90 gives us the number of neutrons. On the right, we have 91 protons, how many neutrons do we have? When we think about what else is made, we know that nucleons are conserved, so we have one nucleon on the left, one nucleon on the right. In terms of charge, if we have zero charge on the left, plus one on the right, we need negative one right here. You're also going to make an anti-neutrino, and that's just really not part of this video, so we'll just ignore it for now.

This of course represents the electron, so this is the electron that's ejected from the nucleus. So a neutron has turned into a proton, and we're also getting a beta particle ejected from the nucleus.

What's going to happen after one billion years? And then you didn't build your time machine well.