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DDTea

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As I understand the Heisenberg Uncertainty Principle mathematically, some operators do not commute and as such, the order of measurements determines the results. In regard to spectroscopy, then, the energy of electronic transitions cannot be measured with arbitrary precision over a finite time period. That makes sense with say, UV/Vis spectroscopy of organic molecules like benzene: we see a big band around ~250 nm corresponding to the pi-->pi* shift. We can determine the energy of that shift more precisely by taking multiple measurements and averaging them.

What about atoms, though? Why do we see discrete line spectra? Wouldn't that violate the Heisenberg uncertainty principle to know *exactly* the energy of their electronic transitions over a finite period? Or rather, how exactly *do* we know the energy of their transitions? Are they the results of theoretical calculations or actual instrumental measurements?