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?"
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.
