When an atom is excited by a photon and there is an electron transition from ground to excited state, from energy level 1 (E1) to energy level 2 (E2), I understand that the energy of the exciting photon must be equal to E2 – E1 = hf (h being Planck constant and f being the photon’s frequency). But my doubt is whether:
a) the electron was vibrating at frequency f and it experiences an increase in amplitude, i.e. it vibrates farther away from the nucleus or
b) the electron was vibrating at say f1 and its frequency is raised to f2 because the exciting photon has frequency f2 – f1.
I have read the two explanations.
The one I certainly prefer is a), because it is more in line with the classical analogy of a standing wave, where 1st incoming energy can only interact with a mode vibrating at same frequency as the stimulus and 2nd vibration modes are orthogonal, so incoming energy cannot propitiate a change of mode, only a change of amplitude within the mode in question…
Thus the peculiarity of quantum realm would be just that there is a minimum unit of light stimulus which is related to its frequency and defined as hf, which we call a photon. Incidentally, I would say that this would not be a great peculiarity because I can imagine that if I want to excite a string fastened at both ends, to make it vibrate at one of its natural frequencies or tones (f), I must do it with a stimulus whose intensity would be calculated in view of the nature of the challenge: as product of f (which is after all what you want the string to do, i.e. vibrate at this frequency but more intensely) times some factor playing the role of h and related (I gather) to the characteristics of the string…
But please don’t pay much attention to the latter ramblings…, the question is only: is a) or b) the right explanation about what changes in an electron transition: amplitude or frequency?
Edit: I've realized that there may be some ambiguity in the question. A likely scenario is that the atom contains no oscillation at a given frequency and after the incidence of the photon it acquires such frequency. I would say that this falls under category a) (change in amplitude), because formerly amplitude at such frequency was zero and it becomes whatever, but someone might interprete that this is a change of frequency (one frequency that was acceptable, but was latent, becomes actual). Anyhow, let us call this case c) for convenience.
I would also like to clarify what case b) means in my question: it means that a mode of oscillation existed at f1 and (because of a photon oscillating at f2 - f1) such mode f1 disappears and gives way to a mode f2.