An electron drops from a high level to a lower one and the atom emits one photon whose energy is exactly the level difference. Pick the jump, watch the photon fly to the screen, and see where its line lands.
Balmer lines (ending on n = 2) are the visible ones. Lyman lines are ultraviolet, Paschen lines infrared.
Emit: the electron is raised to ni first (absorbing the same photon energy), then falls to nf. Cascade: at each step a lower level is chosen at random with equal odds. That is illustrative only; real branching ratios come from transition probabilities.
Drawn orbit radii are evenly spaced so six orbits fit; true radii grow as n² (36x at n = 6). Orbit speed on screen is also slowed.
Shaded band is visible light. Dim ticks are all 15 lines possible with n ≤ 6; bright ones have been emitted.
Measured values are typical vacuum wavelengths from standard tables (spot-check them). Switch to "Infinitely heavy" nucleus to see the reduced-mass effect of about 0.05 percent.
Bohr model: the electron has energies En = −RH h c / n² = −13.6 eV / n² (n = 1, 2, 3, …). Jumping from ni to nf emits one photon with E = Ei − Ef = h c / λ, which is the Rydberg formula 1/λ = RH (1/nf² − 1/ni²).
RH = R∞ / (1 + me/mp) corrects for the proton also moving about the common centre of mass (reduced mass), shifting lines by 0.054 percent. Orbit quantities: rn = n² a₀, vn = α c / n.
Simplifications: a real electron is a probability cloud, not a ball on a ring; there are no continuous orbits and the "jump" has no path (the animation is only a picture). Fine structure, spin and the Lamb shift, selection rules, line intensities and lifetimes are not modelled, and the random cascade uses equal odds as an illustration. Wavelengths are vacuum values; air values are about 0.03 percent shorter. Photon lengths on screen are scaled and not to scale with the atom.
Check method: the two formulas are evaluated by separate code paths, compared to tabulated typical line wavelengths, and cascade photon energies must sum to the level drop.