I would appreciate very much if you could help me with a puzzling question that seems a paradox to me. Every excited state of an atom (every line of the characteristic spectrum) has a “width”: the higher the width, the shorter the lifetime of the state, and when the atom de-excitates we get radiation with a range of frequencies, not with a single well-defined one. Well, let's suppose we excite some type of atoms using monochromatic light with a very well defined frequency (photon energy) that is near the low-energy edge of the line width. I'm not sure of this but I suppose when the atoms de-excitate by spontaneous emission they will produce a line with the characteristic width, regardless the precise frequency used for the excitation. Therefore, sometimes the photon emitted in the de-excitation has more frequency, and hence more energy, than the photon used for the excitation? Where does this energy come from? I do not want to go off on a tangent discussing about the energy-time uncertainty or technical details about the structure of energy levels in an atom. Just: how can we reconcile this with thermodynamics?