Why do Electrons Move?
Why do Electrons Move?
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For small atoms, relativistic effects aren't very big. The binding energy of the electron in hydrogen is about 13.6 eV. (That's about -27.2 potential, +13.6 kinetic.) The rest energy of an electron is about 500,000 eV. So the kinetic energy is small compared to the rest energy, and thus relativistic effects are small. For the inner electrons in big atoms the energies are large enough for the relativistic effects to be major.

The basic quantum rules (the Dirac equation, for an electron) apply whether or not the particle is in a bound state. The Dirac equation is relativistic and applies regardless of the electron's energy, unlike the approximate non-relativistic Schroedinger equation. The Dirac equation is still a wave equation. If the electron cloud is accelerated, its spatial dimensions change according to the same Lorentz transforms as any other spatial dimensions. If the cloud starts off spherical, it becomes pancake-shaped.

Mike W.

(published on 08/04/2009)

In almost every modern interpretation of quantum mechanics electrons (and all other small things) show wave-like behavior because they are indeed waves. They are, however, quantum waves, which in some regards behave quite differently from classical waves. For example, when the wave is heading toward many different-looking outcomes, you only see one, not a combination. Sometimes that's reminiscent of how a particle, heading to just one place, would act.

One interpretation, due to David Bohm, claims that these quantum objects are actually point-like coordinates influenced by a wave. So in this interpretation an electron is a wave plus a coordinate dot. That's the closest to the picture you have in mind.

So far as I know, the Bohm interpretation adds nothing (except some hassle with relativity) to the simpler interpretation that the wave is all there is.

Mike W.

(published on 10/24/2009)

Those are subtle questions.

Nothing is entirely incompressible. The near-incompressibility of the electrons we mentioned above wasn't a quantum effect. It's just that the many electrons in the metal strongly repel each other and therefore are hard to push together. There is also a quantum resistance to compression, harder to explain, that affects even single electrons.

The 'happy medium' story involved that quantum springiness. Take a hydrogen atom. The positive proton in the middle is pulling the electron cloud in. But the quantum springiness pushes the electron cloud out. As the electron cloud gets pulled in more, both those effects grow but the quantum springiness grows more. When the cloud is just atom-sized, the two effects balance each other.

Mike W.

(published on 02/07/2013)

Nice question. The answer may be simpler than you expected. No, you are not even partly correct.

As we discuss in various questions, if that picture of the electron really being somewhere were true (and the same for other smeared quantum properties), then some mathematical relations called the Bell Inequalities would have to be obeyed. They are not obeyed. Therefore those properties (exact electron position, etc.) do not exist. These experiments are the exact opposite of "ambiguous". They compare a definite prediction with a definite result, and find that the prediction is wrong. Therefore the basis of the prediction, the claim that those exact positions and so on exist, is false. It's not just that the values change rapidly, or are hard to measure, or anything else like that. They really don't exist.

You ask what comes out if we do a measurement which gives some much narrower range for the position of the electron. (No experiment gives an actual point.) We can say what happens if we do another experiment like that a little later. The electron might be anywhere over a big range. That's just what quantum mechanics predicts, because a narrow electron cloud has a big range of velocities. If you do the experiment many times, you find that quantum mechanics predicts the range very precisely.

You also ask for some more explanation of quantum reality. Here we are on less certain ground, almost in the slippery realm of philosophy. I suggest having a look at these old answers:

Mike W.

(published on 06/30/2013)

Rutherford and Bohr did say those things but they were wrong. The entire picture underlying those descriptions is mistaken. As described in the other answers, electrons and all other small objects are not classical things. The attempt to picture them as classical things, with definite positions and velocities, leads to false predictions.

Fortunately, there's another way to describe them, modern quantum mechanics. In quantum mechanics both the range of positions and the range of velocities are described by the same wave function. That means that some properties of the distribution of positions are connected with properties of the distribution of velocities. That's unlike classical physics, where the position and velcoity can be described independently. One of the implications of quantum mechanics is then that a narrow range of positions is always accompanied by a big range of momenta, with a corresponding big kinetic energy.

Mike W.

(published on 08/02/2013)

By "spin" I assume you mean "orbit", since you specify "around the nucleus". The answer is sometimes.

In the ground states of H and He, the electrons have no orbital angular momentum and cannot be said to orbit in any reasonable sense of the word. In the standard states with well-defined non-zero orbital angular momentum, e.g. one of the 2P states of H, you could sort of say that the electron orbits the nucleus. That would be misleading, however, since the distribution of positions of the electron doesn't change in time, in sharp contrast to what you probably mean by "spin around the nucleus".

You can make states with superpositions of states of higher energy with different angular momenta that do have lumps of wave-function that do orbit around the nucleus before decaying via photon emission. Since, so far as we know, the world is made of quantum objects and you do see things in classical-like orbits, you shouldn't be surprised that something like that is at least possible for electrons in atoms.

I guess I should mention one exotic possibility that would alter those answers. There's a proposed new version of quantum mechanics, not yet shown to be consistent with all the basic effects, called "Many Interacting Worlds". In that picture any one of the worlds does have particles at particular positions. If somehow that picture develops, is consistent with known effects, and manages to correctly predict any as yet unknown effects, our answers will change.

Mike W.

(published on 03/11/2015)

Great question!

You can make a list of the fixed-energy states that the electron can be in for say a hydrogen atom. We described how the lowest energy "ground" state has a size determined by a balance of minimizing kinetic and potential energy. So you ask how the electron manages to reach that ground state, if it starts of in some other state, or in some combination of other states.

Those other states have more energy. You're exactly right that the electron can't end up in the ground state without ditching that extra energy. The extra energy leaves in the form of photons.

At high temperatures there are lots of photons around, so an atom in the ground state can pick up energy and end up in a different state. It's only when things are cool enough that almost all the atoms are in the ground state.

Mike W.

p.s. Historically, realizing how much kinetic energy would be required for an electron to localize in a nucleus was a motivation for proposing the existence of neutrons, rather than just combinations of protons and electrons, to expain the different charges of nuclei with almost the same mass.

(published on 12/29/2019)