Bohr's postulate: Electron not losing energy

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Discussion Overview

The discussion revolves around the issue of electron stability in atomic orbits, particularly addressing why classical physics suggests that an electron should lose energy and spiral into the nucleus, leading to atomic collapse. Participants explore concepts from classical electrodynamics, centripetal motion, and the implications of radiation reaction forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the premise that an electron should lose energy while orbiting the nucleus, suggesting that no work is done on a particle in centripetal motion.
  • Another participant clarifies that the issue arises from classical electrodynamics, where an accelerating charge is expected to emit electromagnetic waves and lose energy.
  • The Larmor formula is mentioned as a mathematical tool to calculate energy loss for non-relativistic motion.
  • A participant raises a question about whether acceleration perpendicular to velocity affects energy loss, to which others confirm that acceleration is still relevant.
  • Further elaboration is provided on the "force of radiation reaction," which may contribute to energy loss, particularly in extended charged bodies like electrons.
  • One participant compares electron motion to a satellite in orbit, questioning why energy loss would lead to collapse in the case of the electron.
  • A question is posed regarding the electrostatic forces between electrons and protons, specifically whether repulsion would prevent an electron from collapsing into the nucleus.
  • Another participant responds that protons attract electrons, clarifying the nature of the forces involved.

Areas of Agreement / Disagreement

Participants express differing views on the implications of centripetal motion and radiation reaction forces. There is no consensus on the resolution of the electron's stability in atomic orbits, as various models and interpretations are discussed.

Contextual Notes

Limitations include assumptions about the nature of forces acting on the electron, the applicability of classical electrodynamics to quantum systems, and the unresolved mathematical implications of radiation reaction forces.

SweatingBear
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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)
 
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SweatingBear said:
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.
 
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.
 
SweatingBear said:
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.
 
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.
 
Doc Al said:
Yes.

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

Thank you for your answers, much clearer now!

Jano L. said:
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.
 
Besides, even if the electron were to plummet into the nucleus: Wouldn't the electrostatic force repel it away from the protons?
 
SweatingBear said:
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.
 
  • #10
Oh lord, of course, how silly of me!
Thankful to everybody for the replies.
 

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