Our conception of the atom has undergone many changes since the day the idea that matter consisted of indivisible particles was first floated by the Indians and Greeks. However it is only in this century that we have come to know something of what truly goes on inside the atom. We are all by now familiar with the iconic picture of an atom – a circle with a couple of little circles whizzing around it, rather like the moon orbits the earth. In the case of the atom, the ‘earth’ is called the nucleus and the ‘moons’ are called electrons.

What keeps the electrons hanging around the nucleus? Well, if you remember the old adage ‘like charges repel, unlike attract’: electrons have a negative charge, and the nucleus has a positive charge. The flipside of this is that the electrons need energy if they are to avoid spiralling into the nucleus. This was one of the main questions at the beginning of the century: where does this energy come from? The answer turns out to be very counterintuitive: very tiny objects, like atoms, don’t behave like we would expect them to, and instead follow the rules of the quantum world. The word ‘quantum’ implies separateness, and in the case of the atom we find that electrons are actually restricted to be at certain separate energies – an electron could have an amount of energy X, or an amount of energy Y, but it can’t have an energy between X and Y. This rules out the electron from spiralling, because in order to spiral, the electron would have to go through the whole gamut of energies all the way down to zero, and that’s just not allowed.

That’s not all. For each separate energy level, there’s only a certain amount of electrons that are allowed to be at that energy. Suppose we give each of the energy levels a number, *n*, starting from the one with the least energy (and hence closest to the nucleus) *n*=1. It turns out that *n* is one of four quantum numbers that, between them, say everything there is to say about an electron. The others are called *l, m,* and *s*, and as we shall see, the values that these numbers can have are limited by the first number *n*. These four numbers determine why there can only be a certain amount of electrons at each energy level *n*: another major law of the quantum world is that no two electrons can exist in the same atom if they have the same four numbers. It’s a little like two ladies turning up at a high society ball with the identical same outfit; you just know *somebody’s* going to have to go home and change.

What do the other three numbers mean? The *l *and *m* numbers are ‘rotational’ quantum numbers and they determine how the electron moves around the nucleus. Before we explain further, we have to interject with another major law of the quantum world, or rather an admission: we can’t actually know where exactly the electron is. This is to do with the famous ‘uncertainty principle’ which I am sure you have heard about, even if you don’t know what it means. In fact, the best we can do is say ‘Well, there’s an x-percent chance it’s here, a y-percent chance it’s there, a z-percent chance it’s somewhere else, and so on…’. That’s all. When showing the location of an electron, a common method is to draw an electron ‘cloud’, shading the cloud thickly in the areas where the electron is more likely to be, and thinly in the areas where it is less likely to be.

The *l* quantum number tells us a lot about the shape of the cloud for a particular electron. An electron on energy level *n* can have any value of *l* from 0 to *n*-1. We find that the cloud is split into *n-l* concentric bands around the nucleus, and the shape of these bands is more complex the higher *l* is (it basically looks like it has been run through with a pizza slicer *l *times). For *l*=0 the cloud is just n spherical shells around the nucleus.

We can say that *l* gives the rotation strength and m gives the angle at which the rotation axis is tilted. *m* can have any value between *-l* and *l*, and the cloud for each value of *m* (keeping *n* and *l* the same) differs only in that it is rotated a little bit around the nucleus. The last number, *s*, is called spin – as well as going around the nucleus, the electrons also rotate on their own axis! However electrons can only spin like this in two ways (again another quantum law) and so there are only two possible values for the *s* number.

Now that we know about the four numbers we can now calculate how many electrons can stay at each energy level *n*. Well if *n*=1, *l* has to be 0 and so *m* has to be zero. The only number left is *s* and that means only 2 electrons are allowed. However if *n*=2, then *l* can be either 0 or 1. If *l*=0, then we have 2 electrons just like the *n*=1 case; if *l*=1 then *m* can be -1,0 or 1 and so we will have 6 electrons when we take *s* into account. That leaves 8 in total. In this way we can calculate the number of electrons at every energy level.