Periodic trends and Coulomb's law | Atomic structure and properties | AP Chemistry | Khan Academy

In this video, we're gonna look at trends for the periodic table of elements for dimensions like ionization energy, atomic and ionic radii, electron affinity, and electronegativity. To do so, we're going to start with a very fundamental idea in chemistry or physics, and that's Coulomb's law. From our point of view, we can view Coulomb's law as saying that the magnitude of the force between two charged particles is going to be proportional—just means proportional, right?—to the charge on the first particle times the charge on the second particle, divided by the distance between those two particles squared.

When we're thinking about it in the context of the periodic table of elements and various atoms, you can view q1 as the effective positive charge from the protons in the nucleus of an atom. You can view q2 as the charge of an electron. Now, any given electron is going to have the same negative charge, but as we try to understand trends in the periodic table of elements, it's really the outermost shell electrons, the valence electrons, that are most interesting because those are the ones that describe the reactivity.

So, when we think about the distance between the two charges, we're mainly going to be thinking about the distance between the nucleus and those outermost valence electrons. Now, we can view this effective charge—I'll call it Z effective—as being equal to the difference between the charge in the nucleus, so you can just view this as the atomic number or the number of protons that a given element or an atom of that element has, and the difference meaning that and what is often known as S, or how much shielding there is.

Now, there are complicated models for that, but for an introductory chemistry class, this is often approximated by the number of core electrons. Remember, we really want to think about what's going on with the valence electrons. If you imagine a nucleus here—let me do that orange color—that has protons in it, you have core electrons. These are the core electrons in the first shell, and then you have some core electrons in the second shell. Let's say the valence electrons are in the third shell; so let's say these are some valence electrons here, and they're blurred around there in these orbitals.

Those valence electrons, which have a negative charge, are going to be attracted to the positive charge in the nucleus, but they're also going to be repulsed by all these core electrons that are in between them. So, that's why an approximation of the effective charge that these valence electrons might experience is going to be the charge of the nucleus minus—and this is an approximation—the number of core electrons that you have.

So, if we use that roughly as a way to think about Z effective, what do you think are going to be the trends in the periodic table of elements? I want to be the effective charge for the Group 1 elements over here. Well, hydrogen has no core electrons, and it has an atomic number of 1, so 1 - 0 is going to have an effective charge of roughly 1. Lithium, atomic number 3, minus two core electrons that are in 1s—so, once again, you're going to have 3 minus 2—effective charge of 1.

So, roughly speaking, all of these Group 1 elements have an effective charge of 1. What if you were to go to the halogens? What's the effective charge there? If you look at fluorine, atomic number of 9, it has two core electrons in the first shell, so it has an effective charge of 7. Chlorine actually has an effective charge of 7 for the same reason; atomic number of 17 but 10 core electrons.

If you go even further to the right, to the noble gases, you see that helium is going to have an effective charge of 2, atomic number of 2 minus 0 core electrons. But then, when you get to neon, you have an atomic number of 10 and then—only two core electrons—and you'll see as you go down these noble gases, other than helium, they have an effective charge of 8.

So, the general trend is your effective charge is low at the left—effective charge low for group 1—and then when you go to the right of the periodic table, you have a Z effective. Z effective is going to be high.

So, within a given period or within a given row on the periodic table of elements, your outer electrons—valence electrons—are in the same shell, but the effective charge is increasing as you go from left to right. So, this q1 right over here is going to be increasing. What is that going to do to the radius of the atom? Well, Coulomb's law will say that the magnitude of the attractive force between those opposite charges is going to be stronger. So, even though you're adding electrons as you go from left to right within a row, within a period, the atoms in general are actually going to get smaller.

Let me write it this way: as you go from left to right, generally speaking, the radius decreases. Now, what's the trend within a column? One way to think about it is that as you go down a column, as you go down a group, you're filling shells that are further out, so you would expect the radius to increase as you go down a column or as you go down a group. Or you could say radius decreases as you go up a group. So, radius decreases.

Overall, what's the trend in the periodic table of elements? Well, radius is going to decrease as you go up and to the right. So, you could draw an arrow something like this. It is indeed the case that, by most measures, helium is considered to be the smallest atom—a neutral helium atom—and francium is considered to be the largest atom.

So, can we use this to think about other trends in the periodic table of elements? What about, for example, ionization energy? Just as a reminder, the first ionization energy is the minimum energy required to remove that first electron from a neutral version of that element. Since it's the minimum energy, it's going to be one of those outermost electrons; it's going to be one of the valence electrons.

What's going to drive that? You can imagine the ionization energy is going to be high in cases where the Coulomb forces are high. What are the situations where the Coulomb forces are high? Well, this is going to be a situation where you have a high effective charge and where you have a low radius. Lower radius makes the Coulomb forces high, and effective charge makes the Coulomb forces high.

So, where is that true? You have the lowest radii at the top right, and you have the highest effective charge at the right. So, you would expect the highest ionization energies to occur in the top right. High ionization energy—and that actually makes intuitive sense. These noble gases are very stable; they don't want to release an electron, so it's gonna take a lot of energy to take one of those electrons away.

Fluorine or chlorine—they're so close to completing a shell, the last thing they want to do is lose an electron. So, once again, it takes a lot of energy to take that first electron away. On the other hand, if you go to something like francium, it has one valence electron, and that valence electron is pretty far from the nucleus, and there is a low effective charge despite all the protons, because there's so much shielding from all those core electrons. So, it's not surprising that it doesn't take a ton of energy to remove that first electron from francium.

Now, another trend that we can think about, which is in some ways the opposite, is electron affinity. Ionization energy is talking about the energy it takes to remove an electron. Electron affinity thinks about how much energy is released if we add an electron to a neutral version of a given element.

So, high electron affinity elements—these are the ones that really want electrons—should have a high Coulomb force between their nucleus and the outermost electrons. That means they should have a high effective Z, and that also means that they should have a low R. So, one way to think about it: you're going to have a similar trend with the one difference that the noble gases don't like gaining or losing electrons. But we do know that the fluorines and the chlorines of the world can become more stable if they gain an electron; they can actually release energy.

So, you actually have high electron affinities for the top right, especially the halogens, and low electron affinities at the bottom left. Now, there's one little quirk in chemistry conventions. People will generally say that fluorine, chlorine, and the things in the top right that aren't noble gases have a high electron affinity, and it is the case that energy is released when you add an electron to a neutral version of them.

It just happens to be that the convention—and this can get a little confusing—is that when you release energy, you have a negative electron affinity. But generally speaking, people are real when they say a high electron affinity; this is going to release more energy when it's able to grab an electron.

Now, a notion that is related to electron affinity is electronegativity, and the difference between the two can sometimes be a little bit confusing. Electronegativity is all about when an atom shares a pair of electrons with another atom, how likely it is to attract that pair to itself versus for the pair to be attracted away from it to the other one.

You could imagine it correlates very strongly with electron affinity. Things that release energy when they are able to be ionized to grab an electron, if they form a bond and they're sharing a pair of electrons, they are more likely to hog those electrons. Electron affinity is easier to measure; you can actually see when these elements are in a gaseous state if you add an electron—how much energy is released. It's normally measured in kilojoules per mole of the atom in question.

While electronegativity isn't as clear-cut on how to measure it, it can be a useful concept in future videos as we think about different atoms sharing pairs of electrons and where do the electrons spend most of their time. So, I'll leave you there. We started with Coulomb forces, and we were able to intuit a whole bunch of trends just by thinking about Coulomb's law and the periodic table of elements.