Let's assume that an electron requires 1eV energy to get excited to the 1st excited state and requires 1.7eV to the 2nd excited state.
What would happen if we supply it with 1.5eV?
Well, in my opinion, I thought that electron will absorb the photon, excite to the 1st excited state and emit a photon of 0.5eV energy back.
I am not sure if I am right, can somebody correct me?
One could, in principle, have higher-order/non-linear processes, such as Rayleigh scattering, where a photon is replaced by a photon of different polarization and direction, but having the same energy or Raman scattering, where the photon is absorbed and a photon of lower energy is emitted in its place (here 1.5eV - 1eV = 0.5eV.)
Furthermore, due to the finite width of the higher energy levels, there is a probability that the photon is simply absorbed - all the energy selection rules are approximate in this sense.
However, I stress, that we are talking about higher-order processes here, which happen with much lower probability than the direct absorption when the energies match. In the first approximation, when discussing spectral lines, these higher order effects are neglected - to this order of precision, the photons that do not match the energy level spacing are simply not absorbed, i.e., from their point of view the atom is transparent.
