WHEN we come to atoms that have more than one electron, we can no longer work out the mathematics in the same complete way as we can in the case of hydrogen and positively electrified helium. We shall see in the next chapter, however, that X-ray spectra (which are a very modern discovery) tell us a great deal about the inner rings of electrons in complex atoms, while optical spectra continue to tell us a good deal about the outer ring. As we travel up the periodic table, the first element in each period, which is an alkali, has only one electron in the outermost ring; accordingly we might expect this one electron to move more or less as the hydrogen electron does, since the positive charge on the nucleus exceeds the negative charges on the inner electrons by just the amount of the charge on an electron or a hydrogen nucleus, and the inner electrons may be expected to be never very near the outer electron, as distances go within an atom. This would lead [Pg 87] us to look out for a spectrum, in the case of an alkali, more or less similar to that of hydrogen; and in fact, this is found to be the case. Some inferences can be drawn from the fact that in all series spectra Rydberg’s constant makes its appearance. There can be no doubt that the quantum theory applies, and that the orbit of an electron (as in the case of elliptical orbits in hydrogen) is in general determined by two quantum numbers, both of them whole numbers which are usually small. There is, however, considerable uncertainty about the arrangement of the electrons when there are more than one. Already with helium, which has only two electrons, complications arise. There are two complete systems in the helium spectrum, each such as one might expect to constitute the whole spectrum of an element. This leads Bohr to the conclusion that there are two possibilities for the stable state of the second electron, in one of which it moves in an orbit similar to that of the first, while in the other it moves in an orbit considerably larger than that of the first. These two states would not be related as are the different possible orbits in the hydrogen atom; that is to say, an electron left to itself would never jump from the larger to the smaller orbit. They are both final states, after [Pg 88] all jumps have been made. The atom cannot pass from one to the other directly, but only by a roundabout process. When both electrons move in similar minimum orbits, they cannot be in the same plane. Originally it was assumed, merely in order to try simple hypothesis first, that the electrons in an atom all moved in the same plane. This hypothesis has had to be abandoned, and it is now believed that even the electrons constituting one ring are in different planes. In fact it is suggested that, in an inert gas, the eight electrons constituting the outer ring are arranged more or less like the eight corners of a cube. But according to Bohr even this hypothesis is still too simple.