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# Atomic and ionic radii

## Video transcript

In this video, we're going to look at atomic and ionic radii. And first, we'll start with the atomic radius. So if you think about an atom as a sphere, the idea of atomic radius is simple. You would just take this as a sphere here, and then a sphere of course would have fixed and defined radius. And so that would be one way of thinking about it. The problem is that an atom doesn't really have a fixed, defined radius like this sphere example, because there's a nucleus and then there's this electron cloud, or this probability of finding your electron. So there's no real, clear defined boundary there, and so it's difficult to have a fixed and defined radius. So what chemists do is they take two identical atoms. So let's say these are two atoms bonded together, the same element. And if you find their nuclei-- so let's say that that's their nuclei here-- and you measure the distance between those two nuclei, so this would be our distance d between our two nuclei. If you take half of that distance, that would be a good approximation of the atomic radius of one of those atoms. And so that's the idea behind the definition of atomic radius. Let's look at the trends for atomic radius, and first we'll start with group trends. And so here we have two elements found in group one, so hydrogen and lithium. And let's go ahead and sketch out the atoms first. And so we start with hydrogen, which has atomic number of 1, which means that it has one proton in the nucleus. So here's our nucleus for hydrogen, so one proton. In a neutral atom, the number of protons equals the number of electrons, and so therefore there must be one electron. So go ahead and sketch in our electron here. And we'll make things really simple and just show this simple version of the atom, even though we know it doesn't really exactly look like this. And when we do lithium, atomic number of 3, so that means three protons in the nucleus of lithium. So this is representative of lithium's nucleus with three protons and three electrons. Two of those electrons are in the inner shell. So let me go ahead and show two of lithium's electrons in the inner shell, so that would be in the first energy level. And then we would need to account for one more, so lithium's third electron is in the second energy level or at the outer shell in this example. And so here we have our two atoms. And you can see as you go down a group, you're going to get an increase in the atomic radius. And that's because as you go down a group, you're adding electrons in higher energy levels that are farther away. So in this case, we added this electron to a higher energy level which is farther away from the nucleus, which means that the atoms of course would get larger and larger. So you're adding more stuff to it, so it's kind of a simple idea. Let's look at period trends next. As you're going across a period this way, so as you're going this way, you're actually going to get a decrease in the atomic radius. And let's see if we can figure out why by once again drawing some simple pictures of our atoms. And so lithium with atomic number of 3, so we've already talked about that. So there are three protons in the nucleus of lithium. So I'm going to go ahead and write that in here. So 3 positive charge for the nucleus of lithium. And we have to account for the three electrons. So once again two of those electrons were in an inner shell, so there we go, and then we had one electron in an outer shell, so the picture is something like this. Now, let's think about what's going to happen to that outer electron as a result of where it is. So this outer electron, this one right here in magenta, would be pulled closer to the nucleus. The nucleus is positively charged, that electron is negatively charged, and so the positively charged nucleus is going to pull that electron in closer to it. At the same time, those negatively charged inner shell electrons are going to repel it. So let me go ahead and highlight these guys right here. These are our inner shell electrons. Like charges repel. And so you could think about this electron right here wanting to push this outer electron that way, and this electron wanting to push this electron that way. And so the nucleus attracts a negative charge, and the inner shell electrons repel the outer electron. And then we call this shielding, because the inner shell electrons are shielding that magenta electron from the pole of the nucleus. So this is called electronic shielding or electron screening. Now, it's going to be important concepts. So now let's go ahead and draw the atom for beryllium, so atomic number 4. And so here's our nucleus for beryllium. With an atomic number of 4, that means there are four protons in the nucleus, so a charge of four plus in our nucleus. And we have four electrons to worry about this time, so I'll go ahead and put in the two electrons in my inner orbital in our first energy level. And then we have two electrons in our outer orbital, or our second energy level. And so again, this is just a rough approximation for an idea of what beryllium might look like. And so when we think about what's happening, we're moving from a charge of 3 plus with lithium to a charge of 4 plus with beryllium. And the more positive your charges, the more it's going to attract those outer electrons. And when you think about the idea of electron screening, so once again we have these electrons in green here shielding our outer shell electrons from the effect of that positively charged nucleus. Now, you might think that outer shell electrons could shield, too. So you might think that oh, this electron right here in magenta could shield the other electron in magenta. But the problem is they're both at pretty much the same distance from the nucleus, so outer shell electrons don't really shield each other. It's more of these inner shell electrons. And because you have the same number of inner shell electrons shielding as in the lithium example-- so let me go ahead and highlight those again. So we have two inner shell electrons shielding a beryllium. We also have two inner shell electrons shielding in lithium. Because you have the same number of shielding but you have a higher positive charge, those outer electrons are going to feel more of a pull from the nucleus. And they're going to be pulled in even tighter than you might imagine, or at least tighter than our previous example. So these electrons are pulled in even more. And because of that, you're going to get the beryllium atom as being smaller than the lithium atom, hence the trend. Hence as you go across the period, you're always going to increase in the number of protons and that increased whole is going to pull those outer electrons in closer, therefore decreasing the size of the atom. All right. Let's look at ionic radius now. And ionic radius can be kind of complicated depending on what chemistry you are involved in. So this is going to be just a real simple version. If I took a neutral lithium atom again, so lithium-- so we've drawn this several times. Let me go ahead and draw it once more. So we have our lithium nucleus, which we have three electrons. So once again I'll go ahead and sketch in our three electrons real fast. Two electrons in the inner shell, and one electron in the outer shell like that. And let's say you were going to form a cation, so we are going to take away an electron from our neutral atom. So we have-- let me go ahead and draw this in here-- we had a three protons in the nucleus and three electrons those cancel each other out to be a neutral atom. And if we were to take away one of those electrons, so let's go ahead and show lithium losing an electron. So if lithium loses an electron, it's going to lose that outer electron. So the nucleus still has a plus 3 charge, because it has three protons in it. And we still have our two inner shell electrons like that, but we took away that outer shell electron. So we took away this electron in magenta, so let me go ahead and label this. So we lost an electron, so that's this electron right here, and so you could just show it over here like that. And by doing so, now we have three positive charges in our nucleus and only two electrons. And so therefore our lithium gets a plus 1 charge. So it's Li plus, it's a cation. And so we formed a cation, which is smaller than the neutral atom itself. And that just makes intuitive sense. If you take away this outer electron, now you have three positive charges in the nucleus and only two electrons here. So it's pulling those electrons in, you lost that outer electron, it's getting smaller. And so the cation is smaller than the neutralize atom. And so we've seen that neutral atoms will shrink when you convert them to cations, so it kind of makes sense that if you take a neutral atom and add an electron, it's going to get larger. And so that's our next concept here. So if we took something like chlorine, so a neutral chlorine atom, and we added an electron to chlorine, that would give it a negative charge. So we would get chlorine with a negative charge, or the chloride anion, I should say. And so in terms of sizes, let's go ahead and draw a representative atom here. So if this is our neutral chlorine atom and we add an electron to it, it actually gets a lot bigger. So the anion is bigger than the neutral atom. And let's see if we can think about why here. So if we were to draw an electron configuration, or to write a noble gas electron configuration for the neutral chlorine-- so you should already know how to do this-- you would just write your noble gas in brackets. So neon and then 3s2, 3p5, so seven electrons in the outer shell for the neutral chlorine atom. For the chloride anion, you would start off the same way. You would say neon in brackets, 3s2. And you'd be adding an electron to it. So it wouldn't be 3p5, it would be 3p6 like that. And so now we would have so this would give us eight electrons in our outer shell, and this would give us only seven electrons in our outer shell. Now, the explanation for the larger size of the chloride anion in most textbooks is, you'll see people say that the addition of this extra electron here, so that means that those electrons are going to repel each other more. You have eight of them instead of seven, and so because they repel each other more, it gets a little bit bigger. And that makes sense, but you'll see some people disagree with that explanation, and I haven't really seen a great alternative offered. And so however you want to think about it, generally the anion is larger than the neutral atom. But in terms of the explanation for that, you could think about it as electrons are repelling each other if you wanted to, despite the fact that people disagree with that. You could think about just more stuff as a really simple way of thinking about it. But again, in general for exams, think about the anion being larger.