Why don't electrons fall into the nuclei of atoms?

Thanks to Cambridge University's Ben Allanach for the answer!

Will - Cast your mind back to the last time you looked at a science textbook from school, and you might remember the image of the atom being of a large circle in the centre made up of protons and neutrons with a bunch of electrons all whizzing round equidistantly on the outside. This was the original interpretation of the atom made by Niels Bohr in 1913, but unfortunately for me and my tiny brain, professor of theoretical physics at the University of Cambridge, Ben Allanach, takes issue with this image.

Ben - It's completely inaccurate, and quantum mechanics tells you how the electrons behave. They're sitting in the electric attraction of the positive nucleus, but they behave in really strange ways. So they're in a definite energy state, but they're smeared out through space in some kind of fuzzy way. Even though we think of them as points, like quantum mechanics tells you that they have a probability distribution of being almost anywhere outside of the nucleus and the energy state that they're in tells you where is more or less likely for them to be.

Will - I think what the magic man with his fancy words is saying is that it's nigh-on impossible to say exactly where any one electron is in relation to the centre or nucleus of the atom that it orbits. They are just too small and too fast to measure, certainly at this point. However, we do know what affects an electron's distance from the centre.

Ben - The electron mass, for example, tells you something about it. If the electron were heavier, it would be closer into the nucleus. If the nucleus has more electric charge, the electrons are sort of bunched up more in towards the nucleus as well. But also, like I say, it's the energy of the electrons. They're in definite energy states, and if they're in certain energy states, then it changes the shape of their probability distribution around the nucleus, and so they get more bunched up towards the inside or less bunched up towards the inside.

Will - If the electron, for example, absorbs a photon and gets a kick of energy, it will become excited and energised enough to whiz up into the outer limit of distance from the nucleus.

Ben - That's right. I mean, like I said, they're smeared, but they get more smeared towards the outside if they're in via energy states.

Will - So is there an upper limit to that distance?

Ben - Practically, of course there is. If they get far enough away, they'll be under the influence of other charges and things nearby. Yeah, there is a limit to it.

Will - So atoms, keep an eye on your excited electrons because there's always an atom nearby that might want to claim that electron as its own. Thank you to David for the question, and to Ben Allanach for the answer.