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It is said that electrons will emit X-ray when it accelerate/decelerate, but inside atom it is changing velocity all the time, why Bremsstrahlung doesn't occur and finally electron will lose its all kinetic energy?

Edit: If the answer is "classical physics model doesn't work in small scale", the question would be "How quantum mechanics explain the Bremsstrahlung in a large scale?"

Crisps
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  • I am not sure if this question is the same as yours, but some of the answers will be useful. Why doesn't an electron ever hit (and stick on) a proton? – mmesser314 Oct 20 '22 at 01:21
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    The Bohr model has been dead for more than a century. In quantum mechanics, the charge density of a stationary state of an atom, such as the ground state, is… stationary. So why would it radiate? – Ghoster Oct 20 '22 at 01:44
  • @Ghoster correct, but the ground state also can't radiate even with a finite amplitude: the density of states for the final state electron is 0. (see: Fermi's Golden Rule) – JEB Oct 20 '22 at 02:06
  • This is a reasonable question. It can be confusing. If the ground state is described by a wave that doesn't change in time, why isn't the momentum identically $0$. The uncertainty principal says it isn't. If the ground state has $0$ angular momentum, why doesn't the electron stick on the nucleus? Unfortunately the answer is that is how the universe behaves. QM describes it, but it is so different from everyday experience that it violates all our ideas of common sense. We don't know why it behaves this way, just that it does. – mmesser314 Oct 20 '22 at 05:09
  • Does this answer your question? Why don't electrons crash into the nuclei they "orbit"? – John Rennie Oct 20 '22 at 16:09

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The reasons atoms exist at all is because they have a lowest possible "ground" state of energy. That is, all the energies of the electrons combined have a total energy that is some value. Below this value the atom cannot exist as a stable atom.

It does not matter what energy any individual electron has in an atom. Only the total for the atom matters. This is because in quantum theory to describe an atom we need to treat the state of the atom as a single state. Individual electron states don't have any meaning in this context.

Bremsstrahlung requires that an electron loose energy. In an atom at the ground state the total energy cannot decrease and even if the atom as a whole is in a higher energy state it cannot decrease by arbitrary amounts. It has to decease to to move to another stable energy level. We would see that as a line in a spectrum for the atom.

So Bremsstrahlung cannot happen because the atom has no way to go to a lower energy level from the ground state.

Because it cannot go lower than the ground state it cannot ever reach a zero kinetic energy state. In fact in an atom in the ground state the atom as a whole "owes" an energy "debt" - the binding energy, which means to free the electrons we have to put in energy. So the atom has no "spare" energy to release. This is different to a free electron which has "extra" kinetic energy it can release before getting to a zero kinetic energy state.

Note that while we do not always write this down, the ground state energy of an atom is negative, whereas the kinetic energy of a free electron is positive.

So there is no lower energy state to go to (and hence find energy to release) than the ground state of the atom, unlike a free electron which has a lower energy state (lots of them) which it can go to and release energy.

StephenG - Help Ukraine
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