Reading Energy Level Diagrams

Each level on the diagram is a rung the electron can stand on, drawn as a horizontal line at its energy, usually negative because the electron is bound to the nucleus. The rungs get crowded together near the top because as the electron gets less tightly bound, less energy separates each rung from the next; the levels pile up as they approach zero, which is the energy of a free electron that has escaped the atom entirely.

To find the photon wavelengths an atom can emit, list every pair of levels the electron can drop between. For each pair, the photon energy equals the higher level's energy minus the lower level's energy, since energy lost by the electron leaves as a single photon. Convert that energy to wavelength with E = hc/lambda. A diagram with n levels gives you n choose 2 possible transitions, each producing its own distinct photon energy and wavelength.

This connects directly to why atoms absorb and emit only certain colors of light: those sharp lines in a spectrum are just this list of allowed energy gaps made visible. It also sets up the next idea, radioactive decay, where unstable nuclei behave the same way excited electrons do: both wait a random but statistically predictable time before releasing energy, governed by probability rather than a trigger.