Professor Brian Cox is a physicist in England, very well-known there as a popularizer of science. The reasons for this are many-fold, including his ubiquity across media (including podcasts, Twitter, and of course TV)... but also because he has an infectious enthusiasm for science coupled with a boyish charm.
This was all on display recently when he hosted a great segment on the BBC's show A Night With The Stars, where he simply and effectively demonstrates why atoms are mostly empty space:
Pretty cool, isn't it? It helps if you can enlist Simon Pegg to help, too!
I like this demo a lot. On a very tiny scale, objects act like both particles and waves. On a big scale, like our solar system, we can think of planets as discrete particles, interacting through gravity only, and it works pretty well. Our semi-evolved brains want to think of electrons that way as well: little spheres whizzing around atomic nuclei. But that's not the way the Universe works on the quantum scale; electrons act like waves, and that means they can interfere with each other. When a crest meets a trough they cancel, when a crest meets a crest they add together. If you have a wave bouncing around inside a box the result can be chaos.
I like to use the example of sitting in a tub, and rhythmically pushing your body along its length with your toes. It's hard to do unless the rhythm is just right; otherwise the waves smack into each other chaotically and it's a mess. But get the pattern timed just right and you're in sync. That timing is just a simple multiple (like 1 or 1/2) of the time it takes a wave to move from one end of the tub to the other. You can actually feel it as you push; the correct timing just feels natural.
Electrons around an atomic nucleus work the same way. It's more complicated than your bathtub, but the principle is the same. The electrons can only exist where the wave crests and troughs add up correctly. They literally cannot exist anywhere else. They're like standing waves, as Brian shows.
We teach kids that atoms are like little solar systems, but that model is really bad! In principle, planets can orbit the Sun at any distance -- give a planet more orbital energy and it'll move away from the Sun and continue orbiting, happy as you please. But electrons can't do that. They can only be at energy levels where they don't interfere with themselves (and each other). It's more like a staircase; they can only move up or down by discrete amounts. Once you figure this out, a ton of stuff becomes possible: lasers, semiconductors, fluorescent bulbs, atomic bombs... it's quantum mechanics, and it's a huge, huge field of science.
And it's all because, as Brian demonstrates, a rope held at both ends won't vibrate at any old frequency. Amazing, isn't it?
Post script: can you imagine a show like this running on American TV? No, I can't either, unless they had a toll number you could call to vote for atoms being a hoax perpetrated by
Big Little Science.