As far as I'm aware, the energy needed to excite an electron to a different orbital is discrete. Since the frequency of light is continuous, wouldn't it be impossible for a photon to have the exact right amount of energy to excite an electron?
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$\begingroup$ please remember that light is made up of photons, but photons are not light. They have no frequency but energy connect with the ν of the light that is built up quantum mechanically by a great number of photons. this experiment shows the difference between photons and light sps.ch/artikel/progresses/… $\endgroup$– anna vApr 14 at 17:37
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There is a natural line width which is determined by the lifetime $\tau$ of the excited state. This means that you only need to be within some frequency interval of $\approx 1/\tau$ about $\omega_{\rm res}$ to have a chance of exciting the state.
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$\begingroup$ To make the best optical clocks, people generally go for a transition that is as narrow as possible. But, one challenge is that this does indeed make it very difficult to be on resonance! You have to make your laser system ultra-stable and spectrally narrow as well. $\endgroup$– RococoApr 15 at 18:13