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I understand that if the energy of the incoming light does not match the energy required to excite an electron to n=2 or n=3 or whatever number (assuming n=1 is the starting position of that electron). What if the incoming light has enough energy to excite an electron to n=2.5? Because electrons can only jump in discrete quantities, does the electron jump to n=2? or does it not jump at all?
No, it the photon just passes right through. This can be understood through conservation of energy. The "input" photon which excites the electron must be the same value of the "output" photon when the electron drops. So it won't happen if it's 2.5, where 2 will input and the .5 will pass through and then later the 2 will be output.
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