Understanding the energy-level diagram

Draw horizontal lines at −13.6, −3.40, −1.51, −0.85, −0.54 eV and 0 (free). Then:

• Downward arrows are emissions. The length of an arrow is proportional to the photon energy (long arrow = ultraviolet, short arrow = infrared).
• Upward arrows are absorptions. The photon must match exactly.
• All the arrows that end on the same level belong to the same series.
• Two different paths between the same pair of levels give the same total energy: a 4 → 1 jump emits 12.75 eV; a 4 → 2 followed by 2 → 1 emits 2.55 + 10.2 = 12.75 eV in two photons.
• The ratio of wavelengths for two jumps is the inverse ratio of their energies.