Question

The transition rate of electrons from the first excited state of the hydrogen atom to
the ground state is ~108/s. What is the minimum range of energies of the resulting
photons that are emitted?

Answer 1

The energy-time uncertainty principle says

$ΔEΔt≥ℏ/2.$

Hence, the minimum range of energies of the resulting photons that are emitted

$ΔE= \frac ℏ{2Δt} ​ = \frac {1.05×10 ^{−34}}{2\times10^{-8}} ​ =5.25×10 ^{−27} J.$