Rules for Electron Configurations

I wish you'd stop being so mysterious and explain these "rules" you keep referring to.

I was just about to do that. I have to warn you, though, that the rules may seem arbitrary to you, and I won't be giving any satisfactory explanation of the reasons for them. Partly that's because I want to spare you a lot of complicated math, and partly it's because this is just the way nature is. I'll just ask you to have faith that all this numerology comes out of a sophisticated mathematical theory, and has been upheld time after time by experiment.

I can, if you like, tell you about quantum numbers; they provide a more quantitative way of understanding these rules.

For now I think I'll be satisfied if you can tell me how to predict those electron arrangements you've been showing me.

I can do that. First of all, you were correct when you guessed that those colored rows in the chart correspond to the "main energy levels"; they're often called primaryenergy levels, incidentally. Usually, a higher row means a higher energy, and energy gaps between rows tend to be quite large, in comparison with the gap between, say, s and p.

Are you ever going to explain what s and p mean?

I'll do that right now. As you surmised, the s, p, and d columns represent smaller "sublevels" of the primary rows...

Then why not just call them A, B, and C, or something else at least vaguely logical?

This is a bit of archaic notation left over from nineteenth century spectroscopy--rather silly, but everyone uses it, so we're stuck with it. If you must know, s stands for "sharp," p is for "principal," and d is for "diffuse"--supposedly they refer to the appearance of various spectral lines. The next one is called f, for "fundamental"; mercifully, the subsequent ones just go alphabetically: g, h, etc.

Electron Configurations Continued Take a look at the elements beyond lithium and see what you can discover. Let's see...the fourth element, beryllium (Be), has a second electron in the higher energy level, which means that level now has both a spin up and a spin down. So the next element should begin a third energy level--is that right? See for yourself. Try clicking on boron (B), the fifth element--you know, the one Bruce Willis was so excited about. Hey, what's going on? The fifth electron has a slightly higher energy than the other yellow ones, but it's not directly above them; it's in that column labeled "p." Ah. Do you have any ideas about what might be happening? Well...my best guess is that the colored rows, pink and yellow, represent the main energy levels, and s, p, and d are like smaller sublevels of them. Very good. So what do you think is going to happen as you keep going along that row of the periodic table? Hmm...carbon (C) has a second electron in the p column, so now s and p in the yellow row each have a spin up and a spin down. The next electron must start a whole new energy level, or maybe it goes into the d column, if that's the next higher sublevel. Sounds very logical...but now look at nitrogen (N). Hey, the seventh electron went into the p column too! How can there be three with the same energy? It gets worse. Go on. Oxygen (O), fluorine (F), neon (Ne)--more electrons just keep getting stuffed into that same state. What happened to the exclusion principle? This makes no sense at all! It makes perfect sense, once you know the rules.

Spin

Spin? What's that?

Well, it's an additional property that electrons (and other particles) possess. Here's an analogy: think about the Earth orbiting the sun--

Haven't you just been pounding into my head that electrons don't orbit like planets?

It's true, they don't--and yet that picture remains helpful and illuminating in many contexts. So bear with me for a moment: think about the Earth. Not only does it orbit around the sun once a year, it's also spinning once a day on its own axis...

And that's what spin is! Although I suppose you're going to tell me that electrons don't really spin, any more than they really orbit.

You catch on quickly. They don't spin--but it's tremendously useful to think about them as if they did, and for most practical purposes, you can. In the present case, think of the two electrons in that lowest energy level as spinning in opposite directions. It's often said that one has "spin up" and the other "spin down."

So each level has room for a spin up and a spin down--that makes sense. But you haven't explained s, p, and d yet; there must be more complications to worry about.

Indeed...

The Pauli Exclusion Principle

See what happens when you click on lithium (Li)--that's element number three in the periodic table.

There are three electrons, all right--but why is the yellow one so much higher up on the chart? In the picture, it looks like that one is a lot farther away from the nucleus than the others...hey, does that mean it's in a higher energy level?

Exactly. If you move the mouse over any electron on the chart, you'll see a little blue number appear above it. This tells you, in eV, how much energy it would take to free that electron from the clutches of the nucleus. In the case of the outermost electron, this is called the ionization energy.

Hmm...the electrons in the lower row have higher numbers listed. I guess that makes sense--the closer they are to the nucleus, the more strongly the electric force would be pulling them in. But that means the electrons in higher energy levels have lower numbers on the chart...

The terminology is a little confusing, I agree. Think of it this way: the more energy of its own an electron has, the less additional energy it needs in order to escape.

Okay, so why is that third electron in a higher level than the first two? Why not just add it to the lowest one?

Because the lowest level is "full"; it can't hold more than two electrons.

Why? That sounds totally arbitrary to me.

The rule that's operating here is called thePauli exclusion principle, first proposed byWolfgang Pauli. Pauli guessed that two electrons can't be in the same "quantum state"--I'll explain more fully what that means later. In this context, it means that two identical electrons can't be in the same energy level in the same atom.

But you just told me that the lowest energy level can hold two electrons.

Ah, yes--two electrons that are not identical. They differ in a characteristic called spin...