Electron Configurations and Periodicity

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Electron Configurations and Periodicity Periodicity Periods and Atomic Size [Page 1 of 2] Just how big is an atom? That’s a much more difficult question than “How big is this bowling ball?” What the volume of the bowling ball or what the diameter of the bowling ball is, that’s an easy thing for us to do, because the bowling ball has an edge, it has a surface. But remember, an atom doesn’t. For an atom, we have to ask ourselves, “Where are we most likely to find the electron?” not “Where is the edge of the atom?” And so the hardest thing to answer about “how big is an atom?” is to define exactly what we mean by “big.” At what point do we call it “the edge”?

Let’s ask the question, “At what distance do you find 90% of the electron density?” or “At what distance from the nucleus do you find 99% of the electron density?” We have to define exactly what we mean by how big something is. And how, then, do you measure it, since, again, the electron isn’t in any particular place? If we go probing for where the electron is, we know that we disturb it and then it becomes an extremely difficult thing to do.

The way we’re going to answer that question—there are actually a number of different ways to do this, to try to get an approximation for this, but the most common is to say, “Look, if we take an atom”—and I’ll write the nucleus down here and just say, “Okay, we’ve got electron density out here someplace.” If we take that atom and we put it next to another atom”—and again, I’ll draw an electron density here—we have no idea where the edge of that atom is, but what we can say is what the distance between the two nuclei are, because the nucleus is very well defined as far as where its density is. And through scattering experiments, we can find out pretty accurately exactly where those two nuclei are. Remember, we said that electrons could be scattered off of a material to give us spacing between nuclei, and we can do the same thing here to get a pretty good idea of what the spacing is between this nucleus and this one. And if we know that distance accurately, then what we can do is say, all right, if that distance is D, then the radius of the atom would be half of that. At least we can use that as an approximate value for just how big this atom is.

Now, the only problem with that approach is that for some types of atoms, as we’re going to find out, there’s chemical bonding that’s taking place. In other words, the two nuclei are sharing some electrons between them, whereas others are more core electrons than not. Other types of atoms are going to be existing by themselves and not have any bonding between them, and that’s going to give us a very different value for what that distance is.

Now, just keeping that in the back of our minds—knowing that the numbers I’m about to show you have to be taken with a grain of salt—let’s go ahead and look at some basic trends. What we’re seeing here is, except for the transition metals, more or less a size description just by this cartoon here of how big atoms are compared to other atoms in the periodic table. The first trend becomes apparent pretty quickly, that as we go down the periodic table, the size in general increases. Now, what’s the reason for that? Well, we know that one thing in common, for instance, in the alkali metals as we go from hydrogen to lithium—and of course, hydrogen is not an alkali metal—but as we go from lithium to sodium, potassium, rubidium—and we could include hydrogen in this description—all of these have one electron in the s orbital. So electronically, they’re very similar. But what that s orbital is is going to be very different. We know in the case of hydrogen, it’s the 1s orbital. In the case of lithium, it’s a 2s orbital. Sodium: it’s the 3s orbital. Potassium: it’s the 4s orbital. What’s different about those different s orbitals is, if you recall, that the average distance that the electron is from the nucleus gets larger and larger as we go from 1s to 2s to 3s to 4s, and so on. So where the electron spends most of its time is further away from the nucleus as we get lower in the periodic table; therefore, there’s more electron density further away, and our general size of the atom is increasing as we drop down in the periodic table.

Now, what’s a little bit more difficult to understand is what happens as we go from the left to the right in the periodic table. As we go from cesium to barium to thallium, for instance, what’s going on in this case? Well, we’re adding electrons. We’re adding neutrons. We’re adding protons as we go across the periodic table. What’s determining the size? We might even think, “Jeez, we’re adding more matter; they’re getting heavier. Why aren’t they getting bigger, when in fact just the opposite seems to be true?” Well, of all the things that I mentioned, it’s the adding of protons that makes the difference. As we increase the nuclear charge, that charge pulls tighter on the electrons surrounding it, and so the electrons are drawn in closer, and thus the size decreases as we go across the periodic table.

“Now, wait a minute,” you say. “We’re also adding electrons, so we’re adding equal numbers of plus and minus charge. What’s going on?” Well, you see, the electrons that we’re putting in are valence electrons. In other words, they’re going in, as we go across the periodic table, in the same shell that the existing electrons are in. What I’m saying by this is, if you think back to the analogy with the moth circling around the light bulb, we said that if you’re a Copyright © Thinkwell Corp. All rights reserved. www.thinkwell.com

Electron Configurations and Periodicity Periodicity Periods and Atomic Size [Page 2 of 2] moth and another moth comes by, if you’re at the same distance, that other moth doesn’t very effectively shield you from the light. If it’s a moth that’s on the inside, it does a good job of blocking the light, but not if it’s in the same shell. So the basic idea is, as we go from, let’s say, lithium to beryllium to boron to carbon, although we’re adding electrons as well as protons, the electrons are being added in the valence shell, and so they don’t effectively screen other valence electrons. The net effect is that the effective nuclear charge increases. With the effective nuclear charge increasing, electrons in the valence shell are pulled in tighter, so the overall size of the atom actually decreases.

Now let’s ask a different kind of question. What about the size of an ion compared to the size of something neutral? Well, again, we can look at some data. Once again, we have to worry about exactly how we’re going to measure this. But in this case, we’re taking ionic salts, looking at the difference between two nuclei again and saying, “Okay, from there, we can roughly estimate what the size on average is of these different ions.”

Take a look at this graph here. In this case, we’re comparing what we just looked at before, and that is the size of the alkali metals. You’ll notice, again, it’s increasing. Our scale here is in picometers, so just converting that to angstroms, this is 1.5 angstroms to 2.5 angstroms. So we increase here. Now take a look at that compared to the monovalent cations, where we’ve removed one electron. If we’ve removed an electron, even if it’s a shielding electron, the overall charge of this atom has increased a bit. So the effective nuclear charge has increased a little bit, and that causes the pull on the outside electrons to be tighter. That causes the whole atom—ion, in this case—to collapse in a little bit, simply because, again, we have a higher attraction between the nucleus and the electrons. As it moves in closer, that causes us to have a smaller diameter or a smaller radius. So you’ll notice in all cases, the monovalent cation is lower, has a smaller radius, than the neutron.

Correspondingly, if we look once again at the neutral atoms, this time looking at the halogens, and then the halides— meaning the monovalent anion—we notice that adding that one extra electron without adding the extra proton gives us an overall negative charge. We’re getting even more screening by adding the electron, but we’re not compensating for it by putting in an extra proton, so the overall electron cloud moves outward because there’s more screening. It moves out to get a little bit less of that repulsion with other electrons. So the overall size again increases for negative ions and decreases for positive ions.

Finally, let’s ask, what about ions and neutrals—comparing apples and oranges, essentially—but where we keep the number of electrons exactly the same? Let’s consider sodium+, neon neutral, and fluoride. All of these have the electron configuration , , . In other words, they are isoelectronic. But they differ in one important aspect: although the number of electrons is exactly the same, the number of protons isn’t. The nuclear charge is changing from 11 to 10 to 9. And I’ll bet you can predict what’s going to happen. As our nuclear charge goes down, the existing electrons are not held as tightly, and as a result, the radius increases, or the size increases for the ion.

So we’ve made a comparison of things that are isoelectronic, meaning the same numbers of electrons. We’ve compared atoms within a given family. We’ve compared atoms across the periodic table. And we’ve compared atoms to ions. We can make sense of everything that we’ve seen so far based on this general notion of effective nuclear charge versus screening of electrons.