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In Rutherford's atomic model, an atom's nucleus can't survive because of the electromagnetic theory of Maxwell. But in Bohr's model it can survive.

My question is: in both atomic models, electrons move around the nucleus. But then why do electrons fall into the nucleus in Rutherford's model, thus making the atom unstable, while in Bohr's model the atom survives?

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    $\begingroup$ Bohr’s model didn’t solve the ‘lots of charge in a small volume’ problem. It was taken as a fact after Rutherford. Of course, that led to nuclear physics... $\endgroup$ – Jon Custer Jul 27 '18 at 0:12
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    $\begingroup$ Related: Why don't electrons crash into the nuclei they orbit? $\endgroup$ – user191954 Jul 27 '18 at 4:52
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Funny question. It is precisely "to avoid Rutherford's problem". Bohr model consists of three postulates, which means that Bohr suggests it is like that. He assumes that it is like he says, without specifying why. He takes that as true, and then he derives his results.

Among the postulates, there are (from Wikipedia):

  1. Electrons in atoms orbit the nucleus.
  2. The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.

And the thing is that Bohr's model did work reasonably well for the hidrogen atom.

Later on scientist discovered that things which worked were just a coincidence, and some other things were just wrong. However, it was probably a neccesary step in the way to QM.

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