Why does hydrogen glow in sharp, specific colours and no others? Bohr said the electron can only sit on certain rungs of an energy ladder. When it falls from a high rung to a low one, it spits out a photon of exactly the energy difference — one precise colour per jump. Slide the starting rung and read the light.
Bohr’s quantised hydrogen: the electron’s energy is Eₙ = −13.6/n² eV, allowed only at integer n. A jump from n₂ to n₁ emits a photon of energy 13.6(1/n₁² − 1/n₂²) eV, whose wavelength is 1239.84/E nm. Drops to n=2 give the visible Balmer series — Hα (3→2) is the red 656 nm line. A fail-loud self-check throws unless the 3→2 transition comes out at 656 nm, the fingerprint astronomers read in starlight.
The Bohr model is a semi-classical picture superseded by quantum mechanics (which explains fine structure and multi-electron atoms it cannot); yet its energy levels and the hydrogen spectral lines are exactly right. The Rydberg arithmetic is exact.