Why doesn't an electron emit a photon when it absorbs one? Obviously, an electron cannot emit a photon when it absorbs one (I think). An electron absorbs a photon of 1.8 eV, gets excited, emits another photon of 1.8 eV and falls back down to its ground state.
I have learned that accelerating/decelerating charged particles produces electromagnetic waves. When an electron absorbs a photon, it gets bumped to a higher state, essentially causing it to accelerate/decelerate. 
So, why doesn't it emit a photon then?
 A: As per QM, the relaxing electron does not accelerate.
I actually asked a question about that:
Does a relaxing electron really accelerate?

QFT has been used to get the fine structure of atomic levels, one has to stop using classical analogues for the quantum mechanical level. The atom is an entangled system of the electron and the nucleus , the calculations give probability distributions so it has little meaning, imo, to talk of accelerating an electron as if it can be separated from the total solution.
While it is radiating, the expectation value of the energy of the mixed state goes down, the relative weight of the excited state becomes smaller, the amplitude of the oscillation becomes smaller, until it is essential equal to the ground state with its stationary probability distribution.

So basically the electron exist around the nucleus in a mixed state, and that smoothly goes does to ground level. Acceleration is a classical analogue. It would not be correct to use the classical acceleration to this QM mixed state.
A: When electron makes transition from one state to other it doesn't accelerates.If it is in an excited state then it radiates to go to a lower energy state 
