Question

An electron in a hydrogen atom moves from level 3 to level 1. In a second hydrogen atom, an electron drops from level 2 to level 1. Which statement describes the most likely result?
The first atom emits light with more energy.
The second atom emits light with more energy.
The first and second atoms absorb energy without emitting light.
The first and second atoms emit light with the same amount of energy.

Answer 1

The first atom emits more energetic light.

Reason: Energy levels are E_n = -13.6 eV/n^2.
ΔE(3→1) = E1 − E3 = −13.6 − (−13.6/9) = 12.09 eV emitted.
ΔE(2→1) = E1 − E2 = −13.6 − (−3.4) = 10.20 eV emitted.

So the 3→1 transition emits the larger energy (and a shorter-wavelength photon).