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Since synchrotron radiation is created when charged particles are radially accelerated and electrons are definitely orbiting a nucleus (assuming a Bohr model), electron should then logically emit synchrotron radiation. However, if it does, then it lose energy and would unfortunately spiral into the nucleus, which we know doesn't happens. So, is it that atoms doesn't produce synchrotron radiation or other mechanisms are compensating the synchrotron radiation effect?

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The Bohr model is wrong. You can get a lot closer with the Schrödinger picture, and when you do that you find the orbitals which are not the same thing as orbits: they are quantum states not classical paths.

The bound states (orbitals) of atoms are not time-dependent, so they don't radiate.

Well, that's absolutely true for the ground states. The non-ground states do spontaneously couple to the photon-field but they do so more or less discretely.

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Its a good question - that seems to have no explanatory answer. So I will propose a new idea. if the electron is moving in a circle then it should emit synchrotron radiation. But if it is not moving in a circle (ie accelerating towards the centre of a circle) it will not emit radiation (photons).

So how to consider this problem? Well the obvious idea is that the electron is not orbiting the nucleus. It just seems that way - in the same way that planets orbit the sun. Maybe the same thing is happening? Does the nucleus and electron distort space-time on a microscopic level? if that were true then the electron would be travelling in a straight line (and so not radiate) but the distortion of space-time actually causes the electron to move on a curved path (eg a circle) around the nucleus.

I accept that electrostatic attraction should be greater than any relativistic space-time distortions but the space time distortion idea at least explains why there is no radiation from the orbiting electron.

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    $\begingroup$ Electrons in type s orbitals have zero orbital angular momentum. $\endgroup$
    – PM 2Ring
    Mar 24, 2022 at 12:32
  • $\begingroup$ Which is a good point. But electrons in p orbitals have a orbital angular momentum of greater than zero. So while we could focus just on s orbitals (and the complications related to "not moving") the argument can still be made for non-s orbitals. If lower orbitals are filled and an electron is stable in a p orbital - why does it not produce synchronous radiation. It electrons don't actually move (ever) in circular orbits then that would work as an argument. But then we would still be back to discussing what the orbital angular momentum actually represented. To be continued.... :0) $\endgroup$ Mar 25, 2022 at 18:48
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Excited states of atoms gradually goes into less excited states and photons, eventually stopping at the ground of state of an atom. Such a cascade of spontaneous emission is a direct continuation of the synchrotron radiation as you shrink the orbit of an electron from synchrotron scale to atomic scale. There is not much fundamentally different at the atomic scale, except for the stability of the ground state and discreteness of radiation produced.

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