When electrons begin filling orbitals in an atom, they don't enter the orbitals at random; electrons follow certain rules. We can use the quantum numbers that we studied in the last video to help us understand how electrons fill orbitals. We'll apply these rules in the next video, but for now there are three main rules to understand, the first of which is called the Aufbau principle.

The Aufbau principle says that electrons will always fill the lowest energy orbitals first. As an example, let's look at boron. And I've listed the orbitals there, starting from the lowest energy, 1s, and moving up through some of the higher energy orbitals. Boron has 5 electrons, so we know that we can fit 2 in the 1s orbital, another 2 in the 2s orbital, but if we were to put the fifth electron in the 3s orbital, that's not the lowest energy orbital that's available, that's the 2p. So we would need to put that fifth electron in the 2p orbital. Now, unfortunately, figuring out what the lowest energy orbital is isn't just as simple as looking at the principal quantum number, so we have a chart that we use to help us figure that out. And that chart looks like this.

To read this chart, you simply start from the top, and follow each arrow. When you get to the end, start at the top of the next arrow down. So the lowest energy orbital that we can fill is the 1s orbital. We put a 2 there to signify that it can take 2 electrons. Then, moving on to the next arrow, the next lowest energy is the 2s orbital, which also can take 2 electrons. Then we move on to the third arrow, which starts at 2p, which can hold 6 electrons (2 in the x-direction, 2 in the y-direction, 2 in the z-direction), then it goes to the 3s orbital, which can, of course, take 2 electrons. The next arrow takes us through the 3p and 4s orbitals, and the next arrow takes us through the 3d, 4p, and 5s orbitals, and so on. As you can see, the ordering of the principal quantum numbers isn't really perfect, and so always use this as your guide when trying to decide what order to fill the orbitals in.

The next rule that electrons have to follow when filling in orbitals is called Hund's rule. Hund's rule states that when there are multiple orbitals with the same energy, every orbital must have 1 electron before any orbital will get a second. Now, when this says “multiple orbitals with the same energy,” we're talking about p- d- and f-orbitals, which have multiple orientations. So let's look at an example. As our example, let's use oxygen, which has 8 electrons. Filling this in, starting with the lowest energy, we put 2 electrons in the 1s orbital, 2 electrons in the 2s orbital. If we were to place our final 4 electrons in this way, we've violated Hund's rule, because not every equal energy orbital had 1 before some of them got a second electron. So to do this correctly, we would need to first give every single sub-orbital 1, and then put that final eighth electron, pair that up with another electron.

The third and final rule about electron filling is called the Pauli exclusion principle, which states that no two electrons in an atom can have identical quantum numbers. So let's look at how this occurs. Again, we'll use the example of oxygen. We put our first two electrons in the 1s orbital, our next two in the 2s orbital. And if we put electrons 5, 6, and 7 like this, and our eighth electron like that, unfortunately, that eighth electron shares an n value, an ℓ value, an mℓ value, and now an ms value with the electron right next to it. So in order to fix that, any two electrons that are paired like that, one has to spin up, and one has to spin down.

Let's quickly review the rules that we've covered. The first was the Aufbau principle, which says that electrons will always fill the lowest energy orbitals first. And you can use that orbital filling chart to figure out what's the lowest energy orbital that's available. The next rule was Hund's rule, which states that when there are multiple orbitals with the same energy - this occurs with p, d, and f orbitals - every orbital must have 1 electron before any orbital will get a second electron. And the third rule is the Pauli exclusion principle, which states that no two electrons in an atom can have identical quantum numbers.

In the next video, we'll apply these rules, and see how they can help us understand how electrons are arranged in an atom.