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# Atomic radius trends on periodic table

## Video transcript

Voiceover: Let's think a little bit about the notion of atomic size or atomic radius in this video. At first thought, you might think well this might be a fairly straight-forward thing. If I'm trying to calculate the radius of some type of circular object I'm just thinking about well what's the distance between the center of that circular object and the edge of it. So the length of this line right over here. That would be the radius. And so a lot of people when they conceptualize an atom they imagine a positive nucleus with the protons in the center right over here then they imagine the electrons on these fixed orbits around that nucleus so they might imagine some electrons in this orbit right over here, just kind of orbiting around and then there might be a few more on this orbit out here orbiting around, orbiting around out here. And you might say, "well okay, that's easy to figure out the atomic radius. I just figure out the distance between the nucleus and the outermost electron and we could call that the radius." That would work except for the fact that this is not the right way to conceptualize how electrons or how they move or how they are distributed around a nucleus. Electrons are not in orbits the way that planets are in orbit around the sun and we've talked about this in previous videos. They are in orbitals which are really just probability distributions of where the electrons can be, but they're not that well defined. So, you might have an orbital, and I'm just showing you in 2 dimensions. It would actually be in 3 dimensions, where maybe there's a high probability that the electrons where I'm drawing it in kind of this more shaded in green. But there's some probability that the electrons are in this area right over here and some probability that the electrons are in this area over here, and let's say even a lower probability that the electrons are over this, like this over here. And so you might say, well at a moment the electron's there. The outermost electron we'd say is there. You might say well that's the radius. But in the next moment, there's some probability it might be likely that it ends up here. But there's some probability that it's going to be over there. Then the radius could be there. So electrons, these orbitals, these diffuse probability distributions, they don't have a hard edge, so how can you say what the size of an atom actually is? There's several techniques for thinking about this. One technique for thinking about this is saying, okay, if you have 2 of the same atom, that are- 2 atoms of the same element that are not connected to each other, that are not bonded to each other, that are not part of the same molecule, and you were able to determine somehow the closest that you could get them to each other without them bonding. So, you would kind of see, what's the closest that they can, they can kind of get to each other? So let's say that's one of them and then this is the other one right over here. And if you could figure out that distance, that closest, that minimum distance, without some type of, you know, really, I guess, strong influence happening here, but just the minimum distance that you might see between these 2 and then you could take half of that. So that's one notion. That's actually called the Van der Waals radius. Another way is well what about if you have 2 atoms, 2 atoms of the same element that are bonded to each other? They're bonded to each other through a covalent bond. So a covalent bond, we've already- we've seen this in the past. The most famous of covalent bonds is well, a covalent bond you essentially have 2 atoms. So that's the nucleus of one. That's the nucleus of the other. And they're sharing electrons. So their electron clouds actually, their electron clouds actually overlap with each other, actually overlap with each other so the covalent bond, there the electrons in that bond could spend some of their time on this atom and some of their time on this atom right over here. And so when you have a covalent bond like this, you can then find the distance between the 2 nuclei and take half of that and call that call that the atomic radius. So these are all different ways of thinking about it. Now, with that out of the way, let's think about what the trends for atomic size or atomic radii would be in the periodic table. So the first thing to think about is what do you think will be the trend for atomic radii as we move through a period. So let's say we're in the fourth period and we were to go from potassium to krypton. What do you think is going to be the trend here? And if you want to think about the extremes, how do you think potassium is going to compare to krypton in terms of atomic radius. I encourage you to pause this video and think about that on your own. Well, when you're in the fourth period, the outermost electrons are going to be in your fourth shell. Here, you're filling out 4S1, 4S2. Then you start back filling into the 3D subshell and then you start filling again in 4P1 and so forth. You start filling out the P subshell. So as you go from potassium to krypton, you're filling out that outermost fourth shell. Now what's going on there? Well, when you're at potassium, you have 19- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. You have 19 protons and you have 19 electrons. Well I'll just draw those. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, but you only have 1 electron in that outermost, in that fourth shell, so let's just say that's that electron at a moment, just for visually. It doesn't necessarily have to be there but just to visualize that. So that 1 electron right over there, you have 19, yeah, you have 19 protons. So, you have some, I guess you could say Coulom force that is attracting it, that is keeping it there. But if you go to krypton, all of a sudden you have much more positive charge in the nucleus. So you have 1, 2, 3, 4, 5, 6, 7, 8- I don't have to do them all. You have 36. You have a positive charge of 36. Let me write that, you have plus 36. Here you have plus 19. And you have 36 electrons, you have 36 electrons- I don't know, I've lost track of it, but in your outermost shell, in your fourth, you're going to have the 2S and then you're going to have the 6P. So you have 8 in your outermost shell. So that'd be 1, 2, 3, 4, 5, 6, 7, 8. So one way to think about it, if you have more positive charge in the center, and you have more negative charge on that outer shell, so that's going to bring that outer shell inward. It's going to have more I guess you could imagine one way, more Coulomb attraction right over there. And because of that, that outer most shell is going to drawn in. Krypton is going to be smaller, is going to have a smaller atomic radius than potassium. So the trend, as you go to the right is that you are getting, and the general trend I would say, is that you are getting smaller as you go to the right in a period. That's the reason why the smallest atom of all, the element with the smallest atom is not hydrogen, it's helium. Helium is actually smaller than hydrogen, depending on how you, depending on what technique you use to measure it. That's because, if we take the simplest case, hydrogen, you have 1 proton in the nucleus and then you have 1 electron in that 1S shell, and in helium you have 2, 2 protons in the nucleus and I'm not drawing the neutrons and obviously there's different isotopes, different numbers of neutrons, but you have 2 electrons now in your outer most shell. So you have more, I guess you could say, you could have more Coulomb attraction here. This is plus 2 and then these 2 combined are negative 2. They're going to be drawn inward. So, that's the trend as we go to the right, as we go from the left to the right of the periodic table, we're getting smaller. Now what do you think is going to happen as we go down the period table? As we go down the periodic table in a given group? Well, as we go down a group, each new element down the group, we're adding, we're in a new period. We're adding a new shell. So you're adding more and more and more shells. Here you have just the first shell, now the second shell and each shell is getting further and further and further away. So as you go down the periodic table, you are getting, you are getting larger. You're having a larger atomic radius depending on how you are measuring it. So what's the general trend? Well if you get larger as you go down, that means you're getting smaller as you go up. You get smaller, smaller as you go up. So, what are going to be, what's going to be the smallest ones? Well, we've already said helium is the smallest. So what are going to be some of the largest? What are going to be some of the largest atoms? Well that's going to be the atoms down here at the bottom left. So, these are going to be large, these are going to be small. So, large over here, small over here and the general trend, as you go from the bottom left to the top right you are getting, you are getting smaller.