Ask a Physicist: Why don't collapsing atoms destroy all matter in the universe?

In today's "Ask a Physicist" we look at why electrons don't fall into their atomic nuclei, destroying all matter in the universe in the process.

I'm going to skip the preamble, the dissection of the questions asked, requests for superhero questions, and needlessly wordy plugs, and do some old school quantum mechanics today. Our question comes from Lisa Hewus who asks:

Why is it that the negatively charged electrons do not "stick" to the positively charged protons of an atom when they are at their lowest energy state?

Or, to put it another way, "Why doesn't all matter in the universe immediately collapse?" I realize that this is a bit more fundamental than some of the other things we've talked about, so if you know the answer, please don't ruin it for the rest of the class.

For those who don't already have their hands wildly flailing in the air, you'd be forgiven if you had a mistaken picture of atoms like the ones drawn in the logos of the Nuclear Regulatory Commission or the Springfield Nuclear Power Plant. In the cartoon version, there's a nucleus at the middle with a bunch of electrons flying around in orbits, very much like the planets orbit the sun.

But this model has a serious problem. You need to constantly accelerate a particle to move it in an orbit, but if you accelerate a charged particle, it gives off radiation. That's how a radio transmitter works. The upshot is that if you really had a planet-like electron flying around a nucleus, it would constantly give off light.

The energy for that radiation would have to come from somewhere, and the electron is the only possible source. Just like in a gravitational field, the electron would lose energy by falling ever closer to the nucleus. This would happen ridiculously quickly. For a hydrogen atom, it would take about 1 hundred billionth of a second for the electron to slam into the nucleus, destroying the atom entirely. The fact that atoms last much longer than that is a pretty good sign that something is wrong with the model.

So if you're thinking about an electron flying around in a particular place at a particular time then you're thinking about it the wrong way. When I talked about the double-slit experiment a few weeks ago, I said that an electron doesn't go through one slit or another; it really goes through both simultaneously. In the exact same way, there isn't a "somewhere" that the electron "really" is when it's orbiting a nucleus. It literally is in many places at once – each with some probability. The distributions of probabilities are those orbital clouds that you may remember dimly from chemistry class. And it's not just our measurement uncertainty that stops us from figuring out where the electron is. The universe really doesn't know. It also doesn't know what the speed or momentum is, which is why it really doesn't make sense to think about an electron "orbiting" the nucleus.

It's this uncertainty that really prevents atoms from collapsing. After all, if the electron falls into the nucleus then you'd know exactly where to find it, and that can't be.

Quantum mechanics even tells us how to quantify our uncertainty via the famous "Heisenberg Uncertainty Principle," which says that you can't simultaneously measure the position and the momentum of a particle. In fact, you can't measure either let alone both. That means that if you tried to make miniature atoms by squeezing the electrons closer in, the uncertainty in the momentum would get higher, and you'd actually make it more likely that the whole atom gets blown apart.

Lisa and I chatted prior to this column and she asked the follow-up:

I also understand that you can't know both the position and momentum of an electron at the same time but I can't grasp what force keeps it relatively close to the nucleus but not so close that it sticks.

There isn't another force at play here. It's all about electromagnetism. But on small scales, electromagnetism has to include quantum mechanical effects. The simple "like charges repel" and "opposite charges attract" laws from high school need to be tweaked to include uncertainty. There's also a fairly non-intuitive twist to all of this. All things being equal, more massive particles can be squeezed more tightly than less massive ones.

Beyond simple atoms, this has some pretty cool implications. Particles like electrons not only take up space, but you can only put 1 of them (two, technically, because of spin – I'm sure some know-it-all would have commented otherwise) within a given volume. It's possible to pack atoms together so tightly that the electrons are essentially asses to elbows. This is precisely what will happen to our sun in another 5 billion years or so when it becomes a white dwarf. At that point, it will be about a million times as dense as it is now, and only about the size of the earth.

Because of quantum uncertainty, even gravity can't squeeze a white dwarf much smaller, but if you keep adding mass, eventually there's enough pressure to force all of the electrons and protons together to make neutrons (and a crap-ton of neutrinos). This actually happens, when red giants dump their mass onto white dwarves.

At the end of all of this (after a truly awesome supernova explosion), you're left with a neutron star. A neutron star works the same way as a white dwarf, but with the neutrons now shoved against one another. Since neutrons are much more massive than electrons (by about a factor of 2000), they can be packed much, much tighter. To put things in perspective, were the sun to turn into a neutron star, it could easily fit inside Los Angeles, though I wouldn't recommend it.

As an added bonus, you might wonder what happens if you keep piling mass onto a neutron star. Eventually, you'd get a black hole. But that's a story for another day.

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (Like us on facebook, where you can see more of Jeff's cartoons.) He is an associate professor of Physics at Drexel University. Feel free to send him your questions about the universe.

Top image by Greg Martin.