OUR EXPLORATIONS SO far tell us that the vast majority of the mass of an atom is concentrated in the nucleus. The much lighter electrons buzz around the nucleus, constrained to stay in the neighbourhood by the electromagnetic attraction between the negative charge they carry and the positively charged nucleus. This is reminiscent of a mini-Solar System, with lighter planets in orbit around a more massive star in the centre. However, we already know that electrons are not classical particles. This is another point at which their quantum-mechanical nature makes a huge difference. In this case, it dictates the way atoms bind and react to form molecules and compounds, and explains the structure of Mendeleev’s Periodic Table itself.
The reactivity of the different elements depends upon how tightly bound to the nucleus are the electrons they contain. As we tour Atom Land and visit the atoms of various different elements, we find they contain different numbers of electrons – enough to balance the positive charge of the different nuclei. But we also find that these electrons cannot have any old arbitrary energy. They have a specific set of binding energies, characteristic to the atoms of each element. These characteristic energies are what determine the ability of the atom to form molecules and other associations with neighbouring atoms. They are responsible for the whole of chemistry, and everything that follows from it. Like any curious explorer, we need to understand how this all works: what fixes these energies?
An electron of a particular energy has a particular wavelength associated with it, as we saw on our previous voyage. When travelling around freely crossing the oceans of our map, electrons can have any wavelength, and therefore whatever energy, no restrictions. But when they are confined within Atom Land, bound close to an atomic nucleus, that this is no longer true. The fact that only certain energies are allowed implies that only certain, very particular, wavelengths are allowed.
This – the fixed wavelengths – is where we can start to understand what is going on with the electrons. There are other situations where only a few special wavelengths are allowed. One example is the harmonics on a guitar string. Luckily, we have a guitarist on our boat, who will help illustrate this. In a clearing in one of the forests of Atom Land we make camp, build a fire, and sit ourselves around it to hear what she has to say, as the dusk draws in and the tiny electrons buzz around the treetops above us.
Each note that a musical instrument makes corresponds with a particular wavelength of sound. A guitar string of a certain length will make a particular note, determined by the fact that an exact number of half-wavelengths corresponding to that note have to fit into the space allowed on the string. The ends of a guitar string, at the bridge and the nut (or at a fret when the guitarist holds the string down), are fixed. They can’t vibrate like the rest of the string. So a wave on the string must have fixed points at each end, points at which the amplitude of the oscillation is zero.
This has the consequence that not all wavelengths work. A wavelength as long at the string is ok – it would have a fixed point at each end, and another fixed point in the middle, with the peak and the trough a quarter and three-quarters of the way along, swapping sides as the wave bounces back and forth.
A wavelength twice the length of the string also works, with the middle of the string oscillating up and down. This would actually be the bass harmonic of the string, the open note a guitar plays. The important point is that any wavelength that doesn’t allow stationary points at each end of the string is forbidden.
That is what happens with electrons too, when they are confined close to an atomic nucleus. The limits of the electrons’ distance from the nucleus are like the bridge and nut of the guitar – they define fixed points which the electron cannot go beyond and where the wave associated with the electron is stationary. This means only certain wavelengths are allowed, and that in turn means that only certain energies are possible, and that, in turn, explains the peculiar structures in which electrons are bound to the nucleus of the atoms we have encountered.fn1
There is a final piece of information we need to make sense of the emerging internal arrangements of Atom Land. There is a definite list of allowed energy levels for electrons bound inside an atom – the harmonics of their orbits around the massive central nucleus. But one might expect that the most stable situation for an atom is that all the electrons sink to the lowest energy level; all of them play the bass note. This is not what we see. Each energy level allows only two electrons to occupy it, and is then full. The ‘No Vacancies’ signs go up for any further electrons, which will then have to make do with the next-lowest energy level,fn2 which can then only take two of them, pushing the rest still higher, and so on. An atom in its lowest-energy state has all its electrons in the lowest available levels, with all the higher levels empty. So back to silicon, the fourteen electrons are in the seven lowest energy levels, two of them in each. Sodium has eleven electrons. They will fill the lowest five energy levels, leaving the sixth one half-filled; one electron and one vacancy.
In this way, the atoms build up ‘shells’ of electrons, with energy levels inside the shell filled and those outside empty, with sometimes a vacancy on the edge. This intricate structure of electrons and energy levels determines the size of the atom, and its propensity to react and form molecules.
There are a lot of questions that can be asked here. For example, why two electrons per energy level, not just one – or as many as we want? We do not yet know. But it is difficult to overstate the impact of the discovery itself. The fact that the energy levels are distinct and different for each type of atom, and even for different molecules when the atoms bind together, provides a way of identifying the constituent parts of materials without touching them.
When electrons jump about between the different energy levels, they emit or absorb characteristic amounts of energy, as photons of light. The science of measuring and identifying these is called spectroscopy, and it is the reason we know what the Sun, the other stars, and the dust between them are made of. Because only certain discontinuous energy levels are allowed, only certain jumps in energy are allowed. So only certain energies of photon can be absorbed or emitted, and these show up either as dark lines in the spectrum of light passing through a material, where those wavelengths of photon have been absorbed, or as bright lines in the light given off by a material when it is heated, such as the characteristic yellow lines in a sodium lamp. The exact yellow, when measured precisely in a spectrometer, is enough to identify sodium as the main component of one of those lamps. Similarly, the lines in the spectrum from other materials allow us to see what kinds of atom are present. This explains the ‘distinctive frequencies of light’ responsible for the discovery of helium in the Sun, for example.
The electronic structure of atoms and molecules – the detailed geography of Atom Land – was discovered at energy scales of a few hundred or thousand electronvolts.fn3 It was crucial in establishing the quantum nature of electrons and photons, as well as telling us what elements are present in the stars and dust of distant galaxies. It provides much inspiration, and information, for further exploration. The theory of how electrons and photons interact – QED – was the first part of the Standard Model of particle physics to be developed, and precision atomic physics measurements played a critical role in that development, as we will see as we voyage onwards.
Atom Land, and the quantum theory we picked up along the way, is the point of departure for the far reaches of particle physics. The next step of that journey takes us back once more towards the island on which we first landed, the island containing Port Electron. For as we reach the south of Atom Land, we discover there is a bridge, as well as a car rental shop. We cross the bridge, hire a car, and head off by road to explore the new territory in the hinterland of Port Electron.