Why are atoms stable?

Question

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts.

A long time ago we had an idea about the atom as a massive nucleus with positive charge, surrounded by lightweight negative charges. But we knew that opposite charges attract. So why didn't the electrons fall into the nucleus?

We got a model for that. Masses attract, and the earth doesn't fall into the sun because it's in orbit. Maybe the electrons were in orbit around the nucleus.

But accelerated charges always radiate. Accelerated electrons would radiate away their energy. They would fall into lower and lower orbits until they fell into the nucleus. So that model failed.

At that point there were various alternatives available.

We could figure that charges don't always attract, and look for a reason that the attraction didn't happen in this specific case.

We could figure that accelerated charges don't always radiate, and look for a reason that these particular charges don't radiate.

We could postulate a hidden repulsive force, a sixth force, that balances away the charge attraction in this particular case. Why not? We did that later for the strong force and the weak force. Why not this one?

Or we could use the following reasoning: Since accelerated electrons always radiate, electrons must be mostly stationary. They continually absorb random radiation from elsewhere and radiate it away again. So they jostle around, but they don't have any consistent velocity and they give as good as they get. They are mostly stuck in place near specific areas, and we can statistically estimate where those areas are. It takes a set quantum of energy to get from one of those areas to another (or the energy is lost as radiation to go the other direction.) Those are the only places electrons can be close to a nucleus, so they can't fall in.

Or instead we could reason like this: The Uncertainty Principle says we can never know the exact position and momentum of an electron. If it was stationary at the nucleus we would know its exact position and momentum. Since that can never ever happen, electrons can never fall into the nucleus. But I can't see that as a satisfying explanation. It's like saying you can never have perpetual motion because the Second Law of Thermodynamics says you can't, therefore it can never ever happen. If you don't know the answer, it tells you what the answer has to be. But it doesn't explain it.

Here is a possible way to imagine it: Electrons have kinetic energy and potential energy. The farther an electron is from the nucleus, the more potential energy it has compared to being inside the nucleus. It follows that if it reaches the nucleus it must have tremendous potential energy. It can't radiate that energy away because it can only radiate specific amounts when it does the thing that causes radiation, and it causes no radiation when it goes from someplace distant from the nucleus into the nucleus. As electrons in p orbitals will occasionally do. So it is moving so fast that it either bounces back from the nucleus losing no energy, or it smashes through the nucleus losing no energy. It can do this quadrillions of times with no energy loss, it's as if nothing has happened. Very occasionally a nucleus is ready to do electron capture. It grabs that energy and does something with it, and uses the electron as part of the process of turning a proton into a neutron. The electron has in fact fallen in rather than just visiting.

Is this perhaps an adequate way to visualize it?

Free electrons don't have to emit quantized radiation. Electrons in a radio tower can emit any frequency the tower operator chooses. But electrons in an atom do. Why is it that electrons in atoms can only radiate quanta of radiation, when electrons elsewhere can radiate any amount? Why is it that electrons that enter or perhaps pass through a nucleus are never affected at all, except when electron capture requires that they lose their identity entirely? Why is it that electrons in atoms exist only in particular orbitals? Does that have something to do with the nucleus? If the nucleus could somehow be replaced with an undifferentiated point charge, would the electrons behave pretty much the same, because of the geometry of the situation? Or is there something special about atomic nuclei that makes it go the way it does? Are these things known on some level? Is there a way to visualize them?

I have seen some questions that are vaguely similar, but they don't seem to be asking the same things. And the answers have mostly not answered my questions.

Answer 1

First of all: an electron is nothing like anything in our everyday experience. It is not a little point zipping around in space. Nor is it a wave. You asked for a hand-wavy explanation, and I'll give you one, but remember that nothing you are likely to imagine is exactly like the reality. We can only describe the reality with mathematics, not words.

OK, keeping in mind that this is not an exact picture, electrons have both wave like and particle like properties. They're neither, but in some cases they can act like one or the other (or both). The wave like properties are particularly important for atoms. To form a stable "orbit" around the nucleus the electron "wave" has to wrap around the nucleus, i.e. there must be an integral number of wavelengths. So that's why they can't spiral in: their orbits must have a radius which is a positive multiple of their wavelength. This is also why they can only emit certain amounts of energy: the only permitted orbits are multiples of their wavelength, so only certain amounts of potential energy are legal. (Other factors, like the Pauli exclusion principle which prevents two electrons from having exactly the same state, also come into play.)

Really, though, if you want to understand this there's no substitute for a course on quantum mechanics. The math isn't terribly difficult -- it's the interpretation of the math that's the hard thing about quantum mechanics, again because quantum objects are not like classical objects.

Answer 2

For the sake of making a simple answer to why electrons don't radiate, it boils down to quantum theory.

It turns out the only possible "orbits" (more properly "states") that an electron can have around a nucleus are at well defined individual energy levels. This is unlike classical theory where the orbits can have (more or less) arbitrary energies on a continuous spectrum. In quantum theory we find the levels are discrete - not continuous.

This means to radiate energy an electron has to move to a new energy level, but that is at a fixed gap and there is a lowest possible energy level they cannot go lower than.

As they cannot get lower than that lowest state, the electronss cannot radiate more energy and hence they cannot be unstable. They are "locked in" because there is no where (in energy terms) to go on the allowed list of energy levels.