Band of Stability

So we're gonna say here that the central idea of nuclear chemistry is that unstable nuclei will give off radiation. Alright, so remember in the nucleus we have basically are protons and our neutrons are protons are positively charged. So we're going to say that these red ones here are protons. But the thing is protons are positive like charges repel each other. So here we're gonna say that the um the basic idea is that the neutrons act like a glue to hold the protons together. So that's the whole purpose of our neutrons. Now we're gonna say like we said at the center is the nucleus that's made up of protons and neutrons. Now within this nucleus we have two major forces. We have a force that's trying to keep the nucleus together by having neutrons act as the glue. And then we have a force that's trying to rip it apart and that comes from the protons, all of which are positive. They're similar charges, want to repel each other. So are two forces that were working against are the attractive strong forces made by the neutrons which try to bring the subatomic elements together to keep the nucleus cohesive and all together. Then we have the repulsive Colombia forces caused by the similar charges of the protons where they want to just break the nucleus apart. Now the whole point point of radioactive reactions in which we do um alpha decay or beta decay or whatever is that there's an imbalance between the number of protons and neutrons within the nucleus. So we're gonna say here analyzing the neutrons the neutron to proton ratio of an element of an element is a good way for determining its nuclear stability. So this ratio neutron, the proton ratio is n oversee. Okay, so this ratio will help us determine is an isotope of an element stable enough or because there's an imbalance in the number of neutrons and protons will undergo some kind of radioactive decay. Now we're gonna stay here At an atomic number equal to or less than 20. Remember, your atomic number is based on the number of protons in your element. So if you have 20 or less protons, your neutron to proton ratio is most stable when it's one. Okay, next, um we would say if you are basically above 20 and up to 40. So between 21 and 40 we'd say that your ratio is most stable when it's around 1.25, Then if your atomic number is above 40. So 41 to around 80, its most stable when it's around 1.50. So you can see as your atomic number increases, we have more wiggle room where we don't have to be exactly equal to one. We can be within that range. And then here We're gonna say above an atomic number of stable nuclei do not exist. And in fact bismuth Which has an atomic number of 83 is the heaviest element with stable non radioactive isotopes. Okay, so this is the last element beyond that, the nuclei are too unstable to exist. So a lot of those elements will undergo different types of radioactive decays, or even capture emission capture or absorption reactions. Now, all of this fits into our idea of the valley of stability. So come back, take a look at the second half of this concept so we can get a good idea of what is meant by the valley of stability.

Hey everyone. So before we talk about the graph that we have to the left, let's label its parts. So here, we're going to say that our value of stability, we're going to say is this green portion here. Okay, so we're gonna say at the valley of stability, is that green portion above the valley of stability? We're gonna say is this blue portion in here, which we're gonna say is this then we're going to say next below the valley of stability. Let's make that yellow. So below the valley of stability is all this portion here. And they were going to say the top right. It's gonna be this portion right here to the top right corner. Alright, so let's talk about this. The value of stability is where we have different types of isotopes that are basically stable enough. Now, if we get to above the value of stability, we're gonna say in this situation, there are too many neutrons involved when there's too many neutrons involved. That means our strong nuclear force will be greater than our repulsive force. Now, in order to decrease the number of neutrons involved or to increase the number of protons that will help us move down towards the valley of stability. The green portion. How do we do this? Well, to decrease the number of neutrons or increase the number of protons we can do here, a neutron emission. So a good example of a neutron emission we can have here beryllium 13. And it's going to admit a neutron remember a neutron is 1/0 and and then our degree sign plus. So we need our numbers to still add up 2, 13 on the top. So this would have to be a 12, 12 plus one gives me 13. And then here this would still be four. So we become beryllium 12. Or what else could we do? We can do a beta emission where we emit an electron. So here a beta emission. So we're gonna write it down here. We're gonna erase these equations as we go. So here we want a good example of a beta mission. We can do with lithium eight. We're going to emit an electron. And then here this would still be eight and this would become four and becomes Berlian. Now, if we're below the valley of stability, we're gonna say that this becomes too many protons. If there's too many protons, then a repulsive force will be greater than our strong nuclear force. In this case you're going to need to increase the number of neutrons or decrease the number of protons. So how would we do that? So, to do that, we could do a positron emission or we could do an electron capture. So an example of a positron emission that we could do deals with oxygen. 15. Remember a positron is just a positive electron. So then this would still be 15 and this would have to be seven. So we just made nitrogen 15 an electron capture means that we're absorbing an electron and an electron would be reacted. So we can see that with aluminum 26. So that would be 26 for magnesium. So we just made magnesium 26. Now if your to the top right corner to the top right quarter, This happens with elements with atomic mass is equal to or greater than atomic mass units. So they have too many neutrons and protons. So here to increase the number of neutrons or decrease the number of protons, we could do an alpha decay or we could do a spontaneous vision. So here, what would that look like? Well, if we wanted to do an alpha decay, a good example here is we could do an alpha decay of uranium 2 38. So here we do eight alpha decays Plus six Beta emissions. And that would help us to create Lead 206. Now, spontaneous vision a good example of this deals with California. So here this could be Californian to 52. It gets broken down into smaller radioactive isotopes. So here we have 106 technetium Plus 1 43 sassy. Um and this would happen with Us emitting three neutrons Plus γ emissions. So of course you don't need to memorize these exact examples in order of what place you are in terms of this graph, These are just given to us examples, realize the value of stability is where we want to be in terms of stability for our different types of isotopes, but sometimes you'll be below it, above it, or too far to the top right corner. And these are just some of the things that you could do in order to shift the graph more towards the valley of stability.

So for this first example, it says determine that the following nuclei will undergo Alfa decay, beta decay or positron emission. So remember the way you approach this question is remember that if you do Alfa Decay, that usually happens if you're atomic mass, which is a is two hundred, um, am use or higher. And remember your atomic masses, the number they're giving you here would be three. So obviously it's not gonna do Alfa Decay. We're going to stay here. Beta decay, how it beta decay happened. That means you're above the valley of stability and then positron emission. We'd say that that would be below the valley of stability. So we know Alfa decay is not gonna happen because because our atomic mass is not two hundred or higher. So that's off the table. We have hydrogen three. So that means it's atomic masses. Three hydrogen has an atomic number of one. Now, hydrogen three also has another name. It's called Treaty. Um, so here we'll still put H, but usually we symbolize it with tea. What we're gonna do here is we have to figure out what the neutron to proton ratio is. So the atomic number is the number of protons, which is one. And then to find a number of neutrons, you just so track these two. So that's two. Now, remember, from the previous page, we said that Elham isotopes that have an atomic mass or actually atomic number Sorry, atomic number between one and twenty, their most stable when their ratio is equal toe one because that will put them right in the valley of stability. Here, our number is not one. It's too. That's a number that's higher than the number we want. So it would be above the valley of stability. And if you're above the valley of stability, that means you're undergo a beta decay. So we're gonna spit out an electron. Then we have to just make sure we balance the radioactive process here. So zero plus three would give me this three here and then minus one here, but we want a one at the end. So we have to put a two here that would give me helium. So we'd say that hydrogen three would undergo a beta decay in order to produce helium three. So that's the approach you take. First of all, does it have an atomic mass that is two hundred a. M. You or higher. If it does, it'll do Alfa Decay out of the three choices. Then, if it's not that, look to see what the neutron to proton ratio is. If it's above our racial that we want for the Valley of Stability, it'll do beta decay. If it's below it, it'll do. Positron emission. That's the approach you need to take. Now follow what we just did in this example to see if you can answer example to if you can, it's okay. Just come back and see how I approach this question to get the answer.

So here we have Radan to 22. So right on symbol is RN and then to 22 means that that's its atomic mass. And then if you look on the periodic table, you'll see that Radan itself has an atomic number of 86. All right, so remember beta decays. If our our neutron to proton ratio is above the value of stability, positron emission is if we're below the valley of stability and then Alfa decay is the most common type of decay. If you're atomic, mass is 200 or higher here, our atomic mass is definitely 200 or higher. So this is gonna undergo in Alfa decay, which means that we would spit out in half a particle which is four over to. And here's our symbol for Alfa. We could also do four over to for helium because it has on the same exact atomic mass and atomic number plus All right, so we need the right side to add up to 2 22 like it is here, so to 20 to minus four would mean that the new element being created would have to be having atomic mass of to 18 here. It's 86. We already have two here, so this would have to be 84. When we look on the periodic table, that gives us Pio, which is polonium. So we'd say here that raid on 2 22 undergoes an Alfa decay in order to create polonium 2 18 by Alfa Decay. And again, we know it's Alfa Decay because of the atomic mass. As long as it's 200 a. M. You are higher. Alfa Decay is the most common type of radioactive decay that will take place. So two down and one left to go. Try to see if you can answer this question if you can, it's okay, come back and see how I approach it.

So here we're doing it for magnesium 50. So that means the atomic masses 53 atomic number is 12 and this would be magnesium. Now our atomic masses, not 200 or higher. So we know that Alfa decay is not likely. Beta decay happens above the valley of stability. Positron emission happens below the valley of stability. To figure out it for above or below. We need to determine the neutron to proton ratio. So here we're going to say, if we subtract thes two, that gives me 38 for the number of neutrons, and the number 12 is the number of protons. So that's 38 divided by 12 which is 3.2 now. Remember, if you're atomic number is equal to or less than 20 than to be stable. You want your proton, your neutron to proton ratio to be equal toe one. What we got instead is 3.2, which is above that stable value since it's above it. That means we're above the valley of stability, which means beta decay is more likely to occur, so we would eject an electron. We need both sides add up to 50 in terms of atomic masses. So we put a 50 here, then on the react inside. This is 12. So we need the product side toe also be 12. So that means we have to put a 13 here. Then we think. Okay, what element has an atomic number 13 based on the periodic table, the answer would have to be aluminum. So we'd say here that Matt Magan, magnesium 50 undergoes a beta decay or beta mission in order to create aluminum 50 as our new element. So again, if you're still a little bit behind in terms of this makes you go back and take a look and my video on the value of stability, remember, based on your atomic number, you should know what's the ideal proton to neutron neutron to proton ratio for each isotope. And then remember, if you have an atomic mass of 200 or higher automatically, you should know that is Alfa decay. So based on that, you should be able to answer these three simple examples. So again, guys keep studying, keep looking over the value of stability in order to master this idea