The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [57]
Figure 7.2. Filling the energy levels of krypton. The dots represent electrons and the horizontal lines represent the energy levels, labelled by the quantum numbers n, l and m. We have grouped together levels with different values of m but the same values of n and l.
To understand why the filling up of the n = 3 and l = 2 levels is deferred until after calcium requires an explanation of why the n = 4, l = 0 levels, which contain the electrons in potassium and calcium, is of lower energy than the n = 3, l = 2 levels. Remember, the ‘ground state’ of an atom will be characterized by the lowest-energy configuration of the electrons, because any excited state can always lower its energy by the emission of a photon. So when we have been saying that ‘this atom contains these electrons sitting in those energy levels’ we are telling you the lowest energy configuration of the electrons. Of course, we have not made any attempt to actually compute the energy levels, so we aren’t really in a position to rank them in order of energy. In fact it is a very difficult business to calculate the allowed electron energies in atoms with more than two electrons, and even the two-electron case (helium) is not so easy. The simple idea that the levels are ranked in order of increasing n comes from the much easier calculation for the hydrogen atom, where it is true that the n = 1 level has the lowest energy followed by the n = 2 levels, then come the n = 3 levels and so on.
The obvious implication of what we just said is that the elements on the far right of the periodic table correspond to atoms in which a set of levels has just been completely filled. In particular, for helium the n = 1 level is full, whilst for neon the n = 2 level is full, and for argon the n = 3 level is fully populated, at least for l = 0 and l = 1. We can develop these ideas a little further and understand some important ideas in chemistry. Fortunately we aren’t writing a chemistry textbook, so we can be brief and, at the risk of dismissing an entire subject in a single paragraph, here we go.
The key observation is that atoms can stick together by sharing electrons – we will meet this idea in the next chapter when we explore how a pair of hydrogen atoms can bind to make a hydrogen molecule. The general rule is that elements ‘like’ to have all their energy levels neatly filled up. In the case of helium, neon, argon and krypton, the levels are already completely full, and so they are ‘happy’ on their own – they don’t ‘bother’ reacting with anything. For the other elements, they can ‘try’ to fill their levels by sharing electrons with other elements. Hydrogen, for example, needs one extra electron to fill its n = 1 level. It can achieve this by sharing an electron with another hydrogen atom. In so doing, it forms a hydrogen molecule, with chemical symbol H2. This is the common form in which hydrogen gas exists. Carbon has four electrons out of a possible eight in its n = 2, l = 0 and l = 1 levels, and would ‘like’ another four if possible to fill them up. It can achieve this by binding together with four hydrogen atoms to form CH4, the gas known as methane. It can also do it by binding with two oxygen atoms, which themselves need two electrons to complete their n = 2 set. This leads to CO2 – carbon dioxide. Oxygen could also complete its set by binding with two hydrogen atoms to make H2O – water. And so on. This is the basis of chemistry: it is energetically favourable for atoms to fill their energy levels with electrons, even if that is achieved by sharing with a neighbour.