Hund's Rule – Quantum Numbers

00:01 Hund's rule states that when you've got… filling a degenerate orbital such as the 2p, where we have three orbitals which have a similar shape but just a different orientation along the axis, that they would preferably fill unpaired. This is the lowest energy configuration. So if we take, for example… Let's take, for example, this species here: carbon, okay? There'll be two electrons... Sorry, boron.

00:31 Let's take, for example, boron, in this case, where we have five possible electrons. As indicated in the previous slide, we have two electrons which fill the first principle quantum shell (1s) and then we have two electrons which will fill the next orbital in the second shell. And we finally have one electron which occupies one of the orbitals in the 2p subshell.

00:58 If we were to consider carbon, Hund's rule would mean that the next electron (because carbon possesses six electrons) would go unpaired into the adjoining 2p orbital, because they are of the same energy. It's only when all orbitals of the same energy are singly filled do you start to observe pairing of these orbitals. And this is very important, because it is unpaired electrons within individual atoms which are responsible, to a large extent, for the activity, or the reactivity, that we observe.

01:34 So for carbon, as I indicated, as we increase the number of electrons, they go into the unoccupied 2p orbitals. If we look, for example, at oxygen, which is further along the periodic table, it's only after we've complete… we've actually added one electron to each individual 2p orbital that we start to pair up the electrons. Individually occupied orbitals are, as you can see here, of lower energy than paired electrons in orbitals.

02:03 So let's have a look and break it down. As you can see here, we're looking at principal quantum number, which is shown at the beginning of the tree, rising in energy: 1, 2, and 3.

02:17 Okay? If we break down those orbitals which are available, we can consider those as subshells of the principal quantum number. So in the case of principal quantum number 1, we have a single possible orbital: the s orbital. And therefore, we have the designation 1s.

02:33 Maximum allowable electron configuration in that case is 1s2. Then, we have the second shell. Remember, we've unlocked the 2p orbitals. Now, the maximum number of electrons there is theoretically eight, because we can have two electrons in the 2s subshell, and we can have six electrons in the 2p subshell. This gives us a total number of electrons in the second shell of eight. Then we look at the third shell, bearing in mind that we've unlocked another set of orbitals, the diffuse orbitals. So now it's possible to put two electrons in the 3s, six electrons in the 3p, and 10 electrons in the 3d, as we'll come to. Now, unfortunately, nothing's ever simple, and as you can see here, we have the so-called 4s, which rather counterintuitively appears to be of lower energy than the 3d. And this ostensibly flies in the face of all we've discussed about quantum mechanics. But the reality is this: that the nature of the s orbital in this current situation actually means it's of lower energy initially than the 3d, and it is actually populated with electrons first. However, if you have a full 3d outer shell, the energy of the 4s is actually forced up, and now, the principal quantum number 4 gives a lowest energy s orbital, which exists at higher energy than the 3d orbital. And this chart shows the order of filling that you should be familiar with. Once you get to the transition metals, things change slightly, and we'll talk about that a little less… a little more later.

04:27 So now, based on your understanding, you should be able to write out the electron configuration of the first 20 elements in the periodic stable… in the periodic table. Even if you can't necessarily remember all of the chemical symbols, you should be able to do this. And by understanding what electrons are where, it's possible for you to understand how they will react. The configurations, as we've shown, refer to the ground states of the atom for the element in its atomic form. Bearing in mind, of course, in ionic forms, as we'll see, if you lose or gain electrons, the electron configuration will also, therefore, change. Putting the correct amount of energy in can lead to electrons jumping to high energy levels and giving rise to excited states, which we may touch upon later. If we look here on the periodic table extract, which I've shown you, which you can see on this board, you can observe that I've shown you hydrogen, lithium, beryllium, sodium, and magnesium again. Hydrogen, as we indicated, has electrons only in the 1s. Beryllium: The valence electrons are in the 2s. And sodium, magnesium: in the 3s.