Why doesn't the electron spiral into the nucleus?

Question

Somebody asked that question earlier today, and selected an incorrect answer. I repost the question in order to give the correct answer a chance

Answer 1

they are oppositly charged

Answer 2

The very fact that the electron is bound to the nucleus leads to the requirement that the electron only be allowed to occupy combinations of particular predefined states, as determined by Schrödinger's wave equation.  

As the electron hypothetically spirals into the nucleus, it is heading towards a low energy state.  The electron existing at rest inside the nucleus would be the lowest energy state conceivable. However, the lowest energy state possible as allowed by Schrödinger's wave equation is one that keeps the electron from being exclusively inside the nucleus.  

Another way of understanding this problem is by recognizing that it would be impossible for an electron to be precisely located and at rest at the same time.  This is because of how electrons' properties are described mathematically.  More specifically, it is because of how location and velocity (a purist will say momentum instead of velocity, but for our purposes we can consider velocity) are intertwined.  

If you wanted to specify the location of an electron precisely, then this would require imposing on it a wide spread of velocities.  Therefore the electron would soon leave the place where you originally thought it was.  If on the other hand you wanted to specify the electron as being perfectly at rest, then this would require giving it a wide spread of possible locations.  So either way it's not exclusively in the nucleus for long.

Answer 3

I guess it is because electrons are stable as long as they are in their respective orbits, to preserve this stability they do not spiral into the nucleus.

Answer 4

electrons don't rotate around the nucleus, that is an old theory that has long since been replaced by quantum mechanics.

And don't ask for a clear and simple explanation of quantum mechanics, as that is just not possible.

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Answer 5

Should I just link the question.  If someone reasked every time a wrong answer gets picked, the board would be covered with repeats ;)

The questioners own answer to the question was fine really.

OK fine.  The only thing worth adding to my answer is the point Jose made indirectly by talking about electron capture.  That point is that for an electron without angular momentum, the nucleus is the most likely place to find the electron.  But the nucleus is a small place compared to the size of the electron cloud, so even if it is the most likely place to find the electron, you are not likely to find the electron there.

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The electron doesn't spiral into the nucleus because it doesn't follow Newtonian mechanics. The idea you have in your head about the electron going around the proton like a little solar system is just completely wrong.

The electron's properties are defined by a wave function that is the solution to a differential equation called Schrodinger's equation. This wave function gives you a probability distribution for the particle's position and momentum. The possible wave functions have only certain exact values of energy and orbital angular momentum that are allowed. So an electron in one of these wave function states with constant energy is static. It doesn't go anywhere. We call them stationary states (even the ones with orbital angular momentum).

If the electron were confined to a space as small as the nucleus, the uncertainty in its momentum would be enormous and the electron would get a great deal of energy--a simple problem done in undergraduate QM is to find the energy of a particle trapped in a box (or a sphere). The energy goes up as it is confined to a smaller and smaller space.

But in any case, the Coulomb potential will not confine the electron to such a small space (though the strong force does confine the nucleons to such a small space).

--Your answer is pretty good. I'd only make a couple quibbles. I don't like the use of the words "circle" and orbit, even in quotes. Not every wave function is an orbit at all. Just say states or if you want to describe it more visually, you could refer to it as a cloud. Some states just have the electron sitting in a spherical cloud not orbiting anything whatsoever.

--And why don't you find it satisfying? Why SHOULD the particle spiral in? This isn't Newtonian mechanics, and the electrons are not classical particles. This kind of goes hand in hand with your use of the word circle and orbit. You seem to be holding on to a classical picture of the atom or a Bohr model atom. You need to let that go. Stop letting your classical intuition interfere with your quantum understanding.

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One other cut you could take at an intuitive explanation is this: to explain why it doesn't spiral in, you first have to understand why it would--why the Bohr solar system with electrons orbiting due to a centrifugal electrostic attraction to the nucleus is unstable.  It is because an accelerating charge distribution radiates.  But an electron in the quantum description, however, does not move if it is in a stationary state (an eigenstate of energy).  So it doesn't radiate.

An electron doesn't radiate unless it moves from one state to another.