Among the following specific electronic transitions occurring within a hydrogen atom, which exact tr

Question

Among the following specific electronic transitions occurring within a hydrogen atom, which exact transition will uniquely yield an absorption spectral line possessing the highest frequency?

Professor PC Thomas Classes · Answer

(b) : An absorption line of the highest frequency necessitates the largest possible energy gap ($\Delta E$) between the initial and final states, since $
u = \Delta E / h$. In the hydrogen atom, the energy spacing between adjacent levels shrinks drastically as $n$ increases. The transition originating from the tightly bound ground state ($n=1 ightarrow n=3$) features an energy gap ($13.6 	imes (1 - 1/9) \approx 12.09 \mathrm{~eV}$) vastly superior to any transitions initiating from higher, more weakly bound excited states.