Question

Light is emitted by electrons when they drop from one energy level to a lower level. Which transition results in the emission of light with the greatest energy?

level 2 to level 1

level 3 to level 2

level 4 to level 2

Answer 1

Level 2 → level 1.

Reason: Photon energy = ΔE = E2 − E1. For hydrogen-like levels E_n = −13.6 eV / n^2, so
- 2→1: ΔE = (−3.40) − (−13.6) = 10.2 eV
- 3→2: ΔE = (−1.51) − (−3.40) = 1.89 eV
- 4→2: ΔE = (−0.85) − (−3.40) = 2.55 eV

Thus the 2→1 transition emits the most energetic photon.