Why is the classical atom unstable?

[arcnets]

Hi all,
it has been stated that "the classical model of the atom is unstable because, according to classical electrodynamics, any bound electron must spiral into the nucleus, emitting radiation."

It has also been stated, even in QM, that "you can use a frame of reference in which the nucleus is at rest, because it is has so much more mass than the electron."

Both statements contradict each other because, if the nucleus is at rest, the all it causes is a Coulomb field. Which means, we get stable, Keplerian orbits. No collapse!

I don't accept the usual explanations based on calculations of the "emitted radiative power" and conservation of energy. Because they don't say what force acts on the electron, other than Coulomb.

Any help?

 

[borisleprof]

Hi, il classical electrodynamics, we learn that an accelerated charge emits light.
So an electron orbiting in a keplerian orbit do have an acceleration, than must emits continuously light, than again losing energy.

So the elctral would spirals down into the nucleus.

N. Borhs elaborate a first comprehensive model explaining the stability of the atom like hydrogen by postulating quantization of the atom's orbit.

 

[ZapperZ]

Hi all,
it has been stated that "the classical model of the atom is unstable because, according to classical electrodynamics, any bound electron must spiral into the nucleus, emitting radiation."

It has also been stated, even in QM, that "you can use a frame of reference in which the nucleus is at rest, because it is has so much more mass than the electron."

Both statements contradict each other because, if the nucleus is at rest, the all it causes is a Coulomb field. Which means, we get stable, Keplerian orbits. No collapse!

But in an ordinary Keplerian orbits as applied to orbiting planets, the accelerating mass in orbit radiates VERY LITTLE gravitational wave. Contrast this with a charged particle in a circular orbit. An accelerating charge RADIATES, even if it is in an orbit that is stable respect to classical mechanics. You need to add an electrodynamics component to the dynamics that isn't there in the classical mechanics.

You also may want to read the FAQ in the General Physics forum.

Zz.

 

[Meir Achuz]

Hi all,
it has been stated that "the classical model of the atom is unstable because, according to classical electrodynamics, any bound electron must spiral into the nucleus, emitting radiation."

It has also been stated, even in QM, that "you can use a frame of reference in which the nucleus is at rest, because it is has so much more mass than the electron."

Both statements contradict each other because, if the nucleus is at rest, the all it causes is a Coulomb field. Which means, we get stable, Keplerian orbits. No collapse!

I don't accept the usual explanations based on calculations of the "emitted radiative power" and conservation of energy. Because they don't say what force acts on the electron, other than Coulomb.

Any help?

The classical oribiting electon radiates electromagnetic energy, so by conservation of energy, it will "slowly" (in about 10^-10 sec) spiral into the nucleus. This is what also eventually happens to a low orbit Earth sattelite. For the satelllite, the retarding force is the very small drag force of molecules still exlisting at that altitude. For the electron, the force is called "radiation reaction". RR is very diffilcult to calculate in Classical EM, but conservation of energy shows that the electron must spiral in. All of that is academic, because classical physics breaks down for atoms, but the conservation of energy argument was important in showing that QM was needed.

 

[arcnets]

OK, thank you.
It seems to me that the most basic physical problem - two pointlike particles with e.m. interaction - can not be solved by Newtonian physics. Because we cannot calculate the forces.
Or am I wrong...?

 

[ZapperZ]

OK, thank you.
It seems to me that the most basic physical problem - two pointlike particles with e.m. interaction - can not be solved by Newtonian physics. Because we cannot calculate the forces.
Or am I wrong...?

I don't know what you mean by cannot be solved by Newtonian physics. If you mean as if "F=ma", technically, you can! It is just that the origin of "F" is electromagnetic in nature. You use the Lorentz force for that, and you use Maxwell Equation (specifically Gauss's Law) to find the E field that each point is subjected to.

So yes, you can calculate the force. I do that all the time. If not, I have no clue on how to accelerate the electrons that I deal with almost every day.

Zz.

 

[Meir Achuz]

There is a difference between the one-body and two-body problems.
The Rutherford atom is a one body problem which was well solved in Classical EM. The problem was that 10^-10 sec s not a long lilfe for any of us. That led eventually to QM.
The two body problem has no proper equation (much less solution) in NR Classical EM. That was the reason for the title "On the electrodynamics of moving bodies" by Einstein. Even in relativistic QM, the two body bound state cannot be formulated without gross approximation.
I hope Z's electrons don't need two body dynamics beyond perturbation theory.

 

[Stingray]

The classical 'electron' moves according to the standard Lorentz force law, which requires that one specify the electromagnetic field. This includes contributions from both the nucleus and the electron itself. One usually does not include a particle's own field when computing its motion, but this is not quite correct.

Now the self-fields of a point charge are infinite, so naively, it wouldn't even seem meaningful to include them. But consider instead an electron with a finite radius. Then each element of this charge clearly must interact with the full local electromagnetic field, which includes the body's own contribution. If the electron were isolated (and internally static), its self-field would just be Coulombic. And this clearly produces zero net force, which justifies ignoring the self-field in the usual application of Lorentz's force law.

But it is possible to show that when the charge is accelerated (i.e. if there is another charge sitting around), the self-field will become sufficiently asymmetric to induce a slight net force. For a fairly large class of charge distributions that are "approximately pointlike," this force turns out (to a first approximation) to be of two parts. The first points in the direction of the acceleration, and can therefore be lumped together with the mass. The other is independent of the details of the charge's structure. It is proportional only to the square of the charge. Note that this doesn't necessarily have anything to do with its radius.

It is this force, called the self-force or radiation reaction force, which causes the classical electron's orbit to spiral inward. It is a completely local explanation for the arguments using radiation flux.

There are a lot of caveats to what I just described; most of which weren't known 80 years ago. For instance, we now know that there are "classical atoms" which do not radiate! They are completely stable, although they do not look like the standard picture at all. For example, there's a stable configuration with an electron that's more like a wobbling cloud (with a radius larger than its separation from the nucleus). A lot of weird things happen with high spin, electric or magnetic dipole moments, etc.

In the end, though, none of this can replace quantum mechanics. But it is interesting to see how far you can get by abandoning the "spherical cow" arguments.

 

[Meir Achuz]

Carrying a theory that does not apply at such small distances, and using a fictitious extended electron only leads to confusion. If QM is needed, use QM. Trying to use a classical radiation reaction force has not worked for 100 years of trying.