Magic Numbers

in this video, we're going to discuss the stability of the nuclei of isotopes with a concept known as magic numbers. So here, we're gonna say, besides the ratio of neutrons two protons Remember, we talked about this when we discuss the Valley of stability. And basically the premise is for elements on the periodic table that have an atomic mass of 20 or less their most stable when this ratio is one. But as the mass increases, the ratio can deviate farther from what and when we get to the really heavy elements, um, those that have masses of greater than 200. Ideally, we want there are ratios to be less than two right. So as long as the ratio is a value less than two, um at max close to around 1.85 then it would still represent a stable isotope. Now, besides this ratio, we're now talking about actual numbers when it comes to neutrons and protons. And basically, the actual numbers for the number of protons or neutrons can also determine the overall stability of nuclei within isotopes. Now that's when we talk about magic numbers. But before we get there, let's talk about basically the distribution of protons and neutrons and how that can affect the number of stable nuclei IEDs We have for a particular element. Now, remember, number of protons can be determined by our atomic number, which is Z neutrons. Here is just end in order to figure out the number of neutrons you want or have, Right. So we'd say that would just be your atomic mass A minus your atomic number Z. So remember you'd have an element X, which you don't know what it is. It has an atomic mass A and an atomic number. Z, subtracting a from Z would give us the number of neutrons. Now, if we have an even number of protons and an even number of neutrons, then there exists around 163 different isotopes on the periodic table. Uh, that are stable. Now the some literature will show that this number maybe around 1 57 others may show it as high as 1 67 but agreed, agreed upon average is around 163. So we're going with the average now here. If we have an even number off protons and an odd number of neutrons. The number you can clearly see drops a lot. In this case. This represents another additional 53 isotopes that air still stable. Then if we switch it around where this is odd and this is even that adds an additional 50 isotopes that would be stable now for these last won, both of them. If they're odd, you can see that there's a big drop off where there's Onley, about five stable isotopes on the periodic table that have an odd number off protons and neutrons. Ah, lot of them. We already know, Um, one that we may not be familiar with. Out of these five is to over one h. So here, this is one of the isotopes of hydrogen Here's atomic masses. To hear this type of hydrogen is called deuterium. And in fact, sometimes, instead of writing h, they'll just write a D there to represent deuterium. Okay, so you could use either one of them. They're the same thing. We also have that fit in this category. Lithium six. So the atomic masses six. We could have boron 10. I'm even nitrogen. 14. Some of these work pretty familiar with in terms of elements, one that we're not as familiar with is tantalum 1 80. This would be the fifth stable isotope that has an odd number of protons and neutrons. So this is just a distribution of protons and neutrons, which help us to see that, um, if you have an even number of protons and neutrons, then there's a very good chance that that particular isotope will be stable, that it will exist somehow within nature. Now, like we said, this is all connected to magic numbers. So as we move on to the next portion, we'll talk in greater detail about what is involved in magic numbers. So make sure you come back and take a look at the following video when we continue our discussion of nuclear stability.

So we're gonna continue and saying in terms of electrons and stability, remember, the noble gasses are the group on the periodic table that all the elements try to become. Why? Because they have the ideal number of outer electrons, their outer shells air completely filled. Now, here, if we look at a normal periodic table, these here these atomic numbers, when an element is neutral that represent the number of protons but more importantly, also the number of electrons. So here these are the ideal numbers for the number of electrons you want to be. A stable is possible. Okay, so those are the numbers will write in. So we have here too. We have 10. We have 18 here. We had 36. So all we're doing is we're filling in the periodic table with the atomic numbers of each of these elements. We had 54 for Zen on 86 for Radan, and then we had 1 18 as the last one. Now, just as elements with the ideal number of electrons depict unusually high stability, so do elements with the ideal number of nuclear. Iran's nuclear is just referring to number of protons and neutrons these ideal numbers for nuclear ions are referred to as our magic numbers. So basically, if you have a new isotope that has any one of these magic numbers, it will represent ah, stable isotope for that element. Now, we're gonna say, in terms of nuclear arms and civility, the magic numbers include So for protons, they include two, 8 20 28 82 then 1 14. So these air number that you should commit to memory, Then we're going to say here that for neutrons, some of them are the same in the very beginning, so we still have to 8 20 50 and 82. So that's what they have in common with one another these initial numbers. But then we have a difference for the last two word. This is 1 26 and then this is 1 84. Okay, so those would be the magic numbers for our number of neutrons. Now, based on this, let's see if you guys can answer the following example that's on the bottom of the page. Don't worry. If you get stuck, just come back. Take a look at how I approach that question to find the correct answer

all right. So, based on your knowledge of nuclear, I'd stability determine which of the following nuclei IEDs will be most stable. The way you should approach this question is figure out the number of protons for each and figure out the number of neutrons for each. Remember, your proton number is based on the atomic number given, so this would be 49 57 and 60. And then if you subtract thes numbers, that gives you the number of neutrons. So this one will be 66. This one here would be 81. This one here would be 20. And this one here would be 84. Okay, now realize that when it comes to magic numbers, we know that, um, you should notice that all of them are even numbers, right? So magic numbers are not odd numbers. The most stable one here would be C because not only does he have the right magic number for protons, but it also has a magic number for neutrons. We're gonna say if you have magic numbers for one of them, you're definitely gonna be a stable isotope. But if you have numbers for both protons and neutrons were going to say that you These are double magic numbers. These isotopes are even more stable than usual because here, when you have the same number, if you haven't even number of protons and neutrons that are also magic numbers, that means you have the ideal number, the ideal repulsive force between the protons. The neutrons, which act as the glue, are perfectly situated in between the protons. So that way there is a perfect harmony or synergy within the nucleus. But just realize here that the answer is is C because it possesses at least one of the magic numbers, but in this case, two of them. So it's definitely very, very stable now. Here you could have stable isotopes that may not have any of the magic numbers but are still stable. Okay, you don't necessarily have to have any of these values here for to represent a stable isotope. You could have protons and neutrons that are not listed his magic numbers. But the isotope itself is still stable enough to actually exist. But in this example, see is the best one because it has double magic numbers. So again commit to memory when it comes to protons and neutrons. Not only do you need to remember the ratios when we talked about the Valley of Stability ease, but also you can use these magic numbers as a quick way of determining if this isotope exists, naturally or not.