The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [56]
What is striking is that there are two elements in row one, eight in rows two and three and eighteen in row four, and those numbers are exactly twice the numbers we just worked out by counting the allowed energy levels in hydrogen. Why is this?
As we have already mentioned, the elements in the periodic table are ordered from left to right in a row by the number of protons in the nucleus, which is the same as the number of electrons they contain. Remember that all atoms are electrically neutral – the positive electric charges of the protons are exactly balanced by the negative charges of the electrons. There is clearly something interesting going on that relates the chemical properties of the elements to the allowed energies that the electrons can have when they orbit around a nucleus.
We can imagine building up heavier atoms from lighter ones by adding protons, neutrons and electrons one at a time, bearing in mind that whenever we add an extra proton into the nucleus we should add an extra electron into one of the energy levels. The exercise in numerology will generate the pattern we see in the periodic table if we simply assert that each energy level can contain two and only two electrons. Let’s see how this works.
Hydrogen has only one electron, so that would slot into the n = 1 level. Helium has two electrons, which would both fit into the n = 1 level. Now the n = 1 level is full up. We must add a third electron to make lithium, but it will have to go into the n = 2 level. The next seven electrons, corresponding to the next seven elements (beryllium, boron, carbon, nitrogen, oxygen, fluorine and neon), can also sit in a level with n = 2 because that has four slots available, corresponding to l = 0 and l l = 1, m = −1, 0 and +1. In that way we can account for all of the elements up to neon. With neon, the n = 2 levels are all full and we must move to n = 3, starting with sodium. The next eight electrons, one by one, start to fill up the n = 3 levels; first the electrons go into l = 0, and then into l = 1. That accounts for all the elements in the third row, up to argon. The fourth row of the table can be explained if we assume that it contains all of the remaining n = 3 electrons (i.e. the ten electrons with l = 2) and the n = 4 electrons with l = 0 and 1 (which makes eight electrons), making the magic number of eighteen electrons in total. We’ve sketched how the electrons fill up the energy levels for the heaviest element in our table, krypton (which has thirty-six electrons) in Figure 7.2.
To elevate all of what we just said to science rather than numerology we have some explaining to do. Firstly, we need to explain why the chemical properties are similar for elements in the same vertical column. What is clear from our scheme is that the first element in each of the first three rows starts off the process of filling levels with increasing values of n. Specifically, hydrogen starts things off with a single electron in the otherwise empty n = 1 level, lithium starts off the second row with a single electron in the n = 2 level and sodium starts the third row with a single electron in the otherwise empty n = 3 level. The third row is a little odd because the n = 3 level can hold eighteen electrons and there are not eighteen elements in the third row. We can guess at what is happening though – the first eight electrons fill up the n = 3 levels withm l = 0 and l = 1, and then (for some reason) we should switch to the fourth row. The fourth row now contains the remaining ten electrons from the n = 3 levels with l = 2 and