The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [51]
You may have noticed that we have not explained why it is that the electron loses energy by emitting a photon. For the purposes of this chapter, we do not need an explanation. But something must induce the electron to leave the sanctity of its standing wave, and that ‘something’ is the topic of Chapter 10. For now, we are simply saying that ‘in order to explain the observed patterns of light emitted by atoms it is necessary to suppose that the light is emitted when an electron drops down from one energy level to another level of lower energy’. The allowed energy levels are determined by the shape of the confining box and they vary from atom to atom because different atoms present a different environment within which their electrons are confined.
Up until now, we have made a good fist of explaining things using a very simple picture of an atom, but it isn’t really good enough to pretend that electrons move around freely inside some confining box. They are moving around in the vicinity of a bunch of protons and other electrons, and to really understand atoms we must now think about how to describe this environment more accurately.
The Atomic Box
Armed with the notion of a potential, we can be more accurate in our description of atoms. Let’s start with the simplest of all atoms, a hydrogen atom. A hydrogen atom is made up of just two particles: one electron and one proton. The proton is nearly 2,000 times heavier than the electron, so we can assume that it is not doing much and just sits there, creating a potential within which the electron is trapped.
The proton has a positive electric charge and the electron has an equal and opposite negative charge. As an aside, the reason why the electric charges of the proton and the electron are exactly equal and opposite is one of the great mysteries of physics. There is probably a very good reason, associated with some underlying theory of subatomic particles that we have yet to discover, but, as we write this book, nobody knows.
What we do know is that, because opposite charges attract, the proton is going to tug the electron towards it and, as far as pre-quantum physics is concerned, it could pull the electron inwards to arbitrarily small distances. How small would depend on the precise nature of a proton; is it a hard ball or a nebulous cloud of something? This question is irrelevant because, as we have seen, there is a minimum energy level that the electron can be in, determined (roughly speaking) by the longest wavelength quantum wave that will fit inside the potential generated by the proton. We’ve sketched the potential created by the proton in Figure 6.8. The deep ‘hole’ functions like the square well potential we met earlier except that the shape is not as simple. It is known as the ‘Coulomb potential’, because it is determined by the law describing the interaction between two electric charges, first written down by Charles-Augustin de Coulomb in 1783. The challenge is the same, however: we must find out what quantum waves can fit inside the potential, and these will determine the allowed energy levels of the hydrogen atom.
Figure 6.8. The Coulomb potential well around a proton. The well is deepest where the proton is located.
Being blunt, we might say that the way to do this is to ‘solve Schrödinger’s wave equation for the Coulomb potential well’, which is one way to implement the clock-hopping rules. The details are technical, even for something as simple as a hydrogen atom, but fortunately we do not really learn much more than we have appreciated already. For that reason, we shall jump straight to the answer, and Figure 6.9 shows some of the resulting standing waves for an electron in a hydrogen atom. What is shown is a map of the probability to find the electron somewhere. The bright regions are where the electron is most likely to be. The real hydrogen atom is, of course, three-dimensional, and these pictures correspond to slices through