Bohr's postulate: Electron not losing energy

[SweatingBear]

Hey forum.

One of the major issues physicists had at the brink of the entrance of modern physics was that an electron simply could not orbit around the nucleus since it would successively lose energy and consequently spiral into the nucleaus, collapsing the whole atom (and model as well) altogether.

But why was this an issue? From what I have understood, no work is done unto a particle subjected to centripetal accelerationen i.e. no energy is expended. Therefore, the electron shouldn't be emitting radiation and losing energy, right? Or is the electron really emitting radiation in its orbit according to the model? I do not see how.

(PS: High-school level)

 

[Doc Al]

But why was this an issue? From what I have understood, no work is done unto a particle subjected to centripetal accelerationen i.e. no energy is expended. Therefore, the electron shouldn't be emitting radiation and losing energy, right? Or is the electron really emitting radiation in its orbit according to the model? I do not see how.

It's nothing to do with the work done (or not done) on the orbiting electron. The problem comes from classical electrodynamics, where an accelerating charge (such as an electron moving in a circle) would be expected to give off electromagnetic waves and thus lose energy.

 

[jtbell]

Mathematically, the energy loss is calculated (for non-relativistic motion) by using the Larmor formula:

http://en.wikipedia.org/wiki/Larmor_formula

 

[SweatingBear]

Ah, of course, I remember that! "Accelerating charges emit electromagnetc waves"! But is it also valid if the accelerationen is perpendicular to the velocity? Centripetal movement doesn't always imply change in the particles speed.

 

[Doc Al]

But is it also valid if the acceleration is perpendicular to the velocity?

Yes.

Centripetal movement doesn't always imply change in the particles speed.

True. But it's still accelerating, which is the important thing.

 

[Jano L.]

One of the major issues physicists had at the brink of the entrance of modern physics was that an electron simply could not orbit around the nucleus since it would successively lose energy and consequently spiral into the nucleaus, collapsing the whole atom (and model as well) altogether.

But why was this an issue?

It was an issue because people thought that if the system radiates EM waves, it has to lose energy. Decrease of energy of the atom leads to collapse and this was unwanted result.

From what I have understood, no work is done unto a particle subjected to centripetal accelerationen i.e. no energy is expended.

It is not the force of the nucleus that was supposed to oppose the motion, but the additional "force of radiation reaction", which is basically the sum of forces which parts of charged body (electron) exert on themselves. In relativity, if the body is extended, this sum need not be zero (the law of action-reaction does not hold). If the electron is charged extended body, this force can be calculated approximately and it turns out to be proportional to $\dot{\mathbf a}$, which for circular motion points against the velocity. So this "self-force" would do negative work on the charged extended body and bring it down to the nucleus.

 

[SweatingBear]

Yes.

True. But it's still accelerating, which is the important thing.

Thank you for your answers, much clearer now!

It is not the force of the nucleus that was supposed to oppose the motion, but the additional "force of radiation reaction", which is basically the sum of forces which parts of charged body (electron) exert on themselves. In relativity, if the body is extended, this sum need not be zero (the law of action-reaction does not hold). If the electron is charged extended body, this force can be calculated approximately and it turns out to be proportional to $\dot{\mathbf a}$, which for circular motion points against the velocity. So this "self-force" would do negative work on the charged extended body and bring it down to the nucleus.

Hm, alright. I was comparing the circular motion with e.g. a satellite orbiting the earth, and from what I have understood no energy per se is required to keep it in its orbit, hence me wondering why the electron ought to collapse.

 

[SweatingBear]

Besides, even if the electron were to plummet into the nucleus: Wouldn't the electrostatic force repel it away from the protons?

 

[Doc Al]

Besides, even if the electron were to plummet into the nucleus: Wouldn't the electrostatic force repel it away from the protons?

No, the positively charged protons attract the electrons.

 

[SweatingBear]

Oh lord, of course, how silly of me!
Thankful to everybody for the replies.