According to the energy-time uncertainty principle, the lifetime. ∆t of a state and the uncertainty ∆E in its energy are inversely proportional. Hydrogen’s 656 nm red spectral line is the result of an electron making a transition “downward" from a quantum state whose lifetime is about 10-8 s.
(a). What inherent uncertainty in the energy of the emitted photon does this imply? (Note: Unfortunately, we might use the. symbol ∆E for the energy difference—i.e., the energy of the photon:—but. here it means the uncertainty m that energy difference.)
(b). To what range in wavelengths does this correspond? (As noted in Exercise 2.57, the uncertainty principle is one contributor to the broadening of spectral lines.)
(c). Obtain a general formula relating ∆λ to ∆t
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