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# Nuclear stability and nuclear equations

## Video transcript

- [Voiceover] In the last video, we talked about the helium nucleus, which contains two protons and two neutrons. Protons and neutrons in the nucleus are called nucleons, and so I'll use that term a few times in this video. Here's a picture of the nucleus, with two protons and two neutrons, and we know it's stable, even though we know like charges repel. And so these two protons are repelling each other, and that's the electrostatic force. So let me go ahead and write that here. The electrostatic force says like charges repel. We know that this nucleus is stable, so there must be something else holding the nucleus together, which we call the strong force. So the nuclear strong force is stronger than the electrostatic force. The strong force acts only over short distances though, but it does act between all nucleons. For example, a proton-proton interaction is the same as a proton-neutron interaction, which is the same as a neutron-neutron interaction. You can get into much more detail about the strong force. That's not really the point of this video. The point is that this nucleus is stable. And let's think about why. We have equal numbers of protons and neutrons, and so that's interesting. So let's think about the atomic number, which tells us the number of protons, which we represent by Z. And the number of neutrons we could say is capital N. So if we're concerned with the ratio, the ratio of neutrons to protons, so the N to Z ratio. In this example, we have two protons and two neutrons. So two neutrons over two protons is equal to one. We have N to Z ratio of one. It turns out that nuclei that have small numbers of protons, so if we're talking about Z is less than 20, they have stable nuclei when the N to Z ratio is equal to one. So when N over Z is equal to one, you can say you have a stable nucleus, so equal numbers of protons and neutrons turns out to be stable. So for this example, the helium-four nucleus is stable. Thinking about that, let's look at carbon-14 next. We have carbon-14, so let's get a little space right down here. So carbon-14 atomic number of six. Therefore, carbon has six protons in the nucleus. So there are six protons. Number of neutrons will be 14 minus six, so eight neutrons. So what's the neutron to proton ratio? So what's the N to Z ratio here? Well the N to Z ratio would be eight neutrons and six protons, and obviously that number is greater than one, so we have an unstable nucleus. The carbon-14 nucleus is unstable, it's radioactive, it's going to undergo spontaneous decay. It's going to try to get a better neutron to proton ratio. So let's look at the nuclear equation which represents the spontaneous decay of carbon-14. So here is our nuclear equation. And when you're writing nuclear equations, you're representing only the nuclei here, so for example, on the left side of my nuclear equation, I have carbon-14, we're talking about only the nucleus, so we're talking about six protons and eight neutrons in the nucleus. And so let's look and see what happens here. So carbon-14, the nucleus, the carbon-14 nucleus is actually going to give off an electron, and so that's pretty weird, and we'll talk about more why in the next video. It's a conversion that's governed by the weak nuclear force. But we know that an electron has a negative one charge, and so that's what we're talking about here. Here for carbon, we have six protons, let me go and write that, six protons here. An electron has a negative one charge, let's write a negative one charge here for the electron. The carbon-14 nucleus is turning into the nucleus for nitrogen here. Let's look at what we have. Our atomic number is seven, so we have seven protons, let's go ahead and write that here. Seven protons, and 14 minus 7 gives us seven neutrons. So we look at the mass number here, so 14 minus seven gives us seven neutrons. And so that ratio, the ratio of neutrons to protons is seven over seven, which is equal to one. That implies that we have a stable nucleus here. That's the reason why carbon-14 undergoes radioactive decay. Let's look at more details about a nuclear equation, because that's really what I'm most concerned about here in this video. The number of nucleons is conserved. Let's use a different color here. We have 14 nucleons on the left. We have six protons and eight neutrons. And on the right, we also have 14 nucleons, seven protons and seven neutrons, so obviously an electron is not a proton or a neutron. Nucleons are conserved, so we have 14 on the left, and we have zero plus 14 on the right. Also charge is conserved, and so that's what we see down here. We have six positive charges on the left side. On the right side, we have one negative charge and seven positive charges, so negative one and seven give us plus six, so we have plus six. So nucleons are conserved and charge is conserved in a nuclear equation. And notice what happened here. We changed the identity. We went from carbon to nitrogen, because we changed the number of protons. We went from six protons to seven protons, and so that's the idea of transmutations, of changing one element into another element. For nuclei with small numbers of protons, the N to Z ratio, the ideal one is one to one. For nuclei with more protons, it turns out the ratio changes, so let's look at that. As you increase the number of protons, the ratio changes for a stable nucleus. The N to Z ratio turns out to be 1.5, so as you increase in Z, so as you go above Z is equal to 20. As you get more and more protons, you need more neutrons. You need more neutrons, and let's think about why. If I have a bigger nucleus here, so this is a very poor representation of a nucleus. I think about two protons, let me use, I'll use magenta here. So I'll have two protons really close to each other. We know that there is a weak electrostatic repulsion here, and there's a strong nuclear force. There's a strong nuclear force between those protons. The strong nuclear force wins, but this is only when you're talking about short distances. Remember the strong force acts only over short distances. So if you have protons that are far away from each other, so these two protons here are far away from each other, there's still a repulsive force. The electrostatic force is still present, so they're still repelling each other. But you don't have the strong force any more. And because you don't have the strong force any more, eventually as you keep increasing the number of protons, you're increasing in the electrostatic force, and you get to a point where you need more of the strong force, and so you need to add in more neutrons to balance things out. So you need to add in more neutrons here, and that's the reason for this increased ratio. You need more neutrons as you increase the number of protons here. When you get beyond approximately 83, so let me go ahead and write this down here, so once you get an atomic number greater than 83, so bismuth, the repulsive force of the protons, this electrostatic repulsive force that we talked about here is so great that pretty much all of the nuclei are unstable, and will undergo radioactive decay. We'll talk in the next video about the types of radioactive decay that you might see.