• Choose a category
• All
• Classic-Fiction

6. The Music of the Atoms

The interior of an atom is a strange place. If you could stand on a proton and gaze outwards into inter-atomic space, you would see only void. The electrons would still be imperceptibly tiny even if they approached close enough for you to touch them, which they very rarely would. The proton is around 10−15 m in diameter, 0.000000000000001 metres, and is a quantum colossus compared to the electrons. If you stand on your proton at the edge of England on the White Cliffs of Dover, the fuzzy edge of the atom lies somewhere amongst the farms of northern France. Atoms are vast and empty, which means the full-size you is vast and empty too. Hydrogen is the simplest atom, comprising a single proton and a single electron. The electron, vanishingly small as far as we can tell, might seem to have a limitless arena within which to roam, but this is not true. It is bound to its proton, trapped by their mutual electromagnetic attraction, and it is the size and shape of this generous prison that gives rise to the characteristic barcode rainbow of light meticulously documented in the Handbuch der Spectroscopie by our old friend and dinner-party guest Professor Kayser.

We are now in a position to apply the knowledge we have accumulated so far to the question that so puzzled Rutherford, Bohr and others in the early decades of the twentieth century: what exactly is going on inside an atom? The problem, if you recall, was that Rutherford discovered that the atom is in some ways like a miniature solar system, with a dense nucleus Sun at the centre and electrons as planets sweeping around in distant orbits. Rutherford knew that this model couldn’t be right, because electrons in orbit around a nucleus should continually emit light. The result should be catastrophic for the atom, because if the electron continually emits light then it must lose energy and spiral inwards on an inevitable collision course with the proton. This, of course, doesn’t happen. Atoms tend to be stable things, so what is wrong with this picture?

This chapter marks an important stage in the book, because it is the first time that our theory is to be used to explain real-world phenomena. All our hard work to this point has been concerned with getting the essential formalism worked out so that we have a way to think about a quantum particle. Heisenberg’s Uncertainty Principle and the de Broglie equation represent the pinnacle of our achievements, but in the main we have been modest, thinking about a universe containing just one particle. It is now time to show how quantum theory impacts on the everyday world in which we live. The structure of atoms is a very real and tangible thing. You are made of atoms: their structure is your structure, and their stability is your stability. It would not be unduly hyperbolic to say that understanding the structure of atoms is one of the necessary conditions for understanding our Universe as a whole.

Inside a hydrogen atom, the electron is trapped in a region surrounding the proton. We are going to start by imagining that the electron is trapped in some sort of box, which is not very far from the truth. Specifically, we’ll investigate to what extent the physics of an electron trapped inside a tiny box captures the salient features of a real atom. We are going to proceed by exploiting what we learnt in the previous chapter about the wave-like properties of quantum particles, because, when it comes to describing atoms, the wave picture really simplifies things and we can make a good deal of progress without having to worry about shrinking, winding and adding clocks. Always bear in mind, though, that the waves are a convenient shorthand for what is going on ‘under the bonnet’.

Because the framework we’ve developed for quantum particles is extremely similar to that used in the description of water waves, sound waves or the waves on a guitar string, we’ll think first about how these more familiar material waves behave when they are confined