An electron spends roughly 10−8 s in the first excited state of the hydrogen atom before making a spontaneous downward transition to the ground state.
(a) Use Heisenberg's uncertainty principle, Eq. (5.20), to determine the uncertainty ΔE in the energy of the first excited state.
(b) Calculate the uncertainty Δλ in the wavelength of the photon involved in a transition (either upward or downward) between the ground and first excited states of the hydrogen atom. Why can you assume that ΔE=0 for the ground state?
This increase in the width of a spectral line is called natural broadening.