According to Bohr's atomic model, the electrons do not radiate energy when they revolve in the predefined orbits. But according to Maxwell's theory of electromagnetism, an accelerated charge produces electromagnetic waves and loses energy.

In Bohr's atomic model of an atom the electrons are in a circular motion so they are essentially accelerating thus they should lose energy due to the reasons mentioned above and eventually collapse into the nucleus. But it doesn't happen, so isn't it a violation of the EM theory?

Edit: The question is related to consensus of Bohr and Maxwell rather than Rutherford and Bohr.


Yes. Bohr's model is not really a theory at all -- it's just the observation that you get the right atomic spectra if you simply assume the particle may only have angular momentum $L = n \hbar$ and that the $n = 0$ state is stable. No reason is given for this, so of course it contradicts Maxwell's equations.

Bohr was simply trying to find the simplest assumptions that would fit the data. The real explanation is quantum mechanics, which of course is not compatible with classical electromagnetism. Roughly speaking, in quantum mechanics the configuration of the electron in a given orbital is a standing wave. Unlike classical particles, standing waves have a lowest possible frequency, which musicians know as the fundamental. When the electron is in this state, it can't lose any more energy, so it doesn't radiate.

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    $\begingroup$ So, does wave mechanics violate Maxwell's theory? Does not the electron still accelerate? $\endgroup$ – Archisman Panigrahi Oct 4 '18 at 13:24
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    $\begingroup$ @ArchismanPanigrahi You can try to have quantum matter (which is what I assume you mean by wave mechanics) along with a classical electromagnetic field. That was what was initially tried historically, and it works fine in certain regimes, but ultimately it doesn't make sense -- you can't have a sensible theory if only some things are quantized. The right theory is quantum electrodynamics, where the electromagnetic field is quantum as well, and that's very far from Maxwell's theory. $\endgroup$ – knzhou Oct 4 '18 at 13:27
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    $\begingroup$ @ArchismanPanigrahi In any case, you shouldn't speak of whether the electron is accelerating in quantum theory, because it's simply not a particle with a definite position. An electron in its ground state is in a stationary state analogous with a standing wave. It's not "going" anywhere. $\endgroup$ – knzhou Oct 4 '18 at 13:30
  • $\begingroup$ @knzhou As far as I know, Bohr's model was proposed as a replacement to Rutherford's model. And one of Rutherford's model's flaw was that it couldn't explain why doesn't the electron collapse into the nucleus despite it radiating energy. So how come was Bohr's model accepted over Rutherford's model? PS: This was by far one of the best explanations I've got! But I just wanted to clear it completely, I hope its ok... $\endgroup$ – think__tech Oct 4 '18 at 13:51
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    $\begingroup$ @think__tech It wasn't accepted as an explanation, it just fit the data better. Back then nobody knew at all how an atom worked. The Bohr model is an example of the "old quantum theory", a family of ad hoc assumptions that kind of worked, which were eventually explained and replaced by quantum mechanics as we know it. $\endgroup$ – knzhou Oct 4 '18 at 13:58

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