Pick a start level and an end level, then fire the transition. The orbits are drawn to scale, the ladder on the right shows where the energies actually sit, and the strip underneath marks where the photon lands in the visible spectrum — if it lands there at all.
Start level Ei = -13.6 Z² / n²
-1.511 eV
n = 3, orbit radius 0.4763 nm
End level Ef
-3.400 eV
n = 2, orbit radius 0.2117 nm
Photon energy ΔE = |Ei − Ef|
1.889 eV
emission — the atom gives this energy away
Wavelength λ = 1239.842 / ΔE
656.4 nm
Balmer series, visible
Frequency f = c / λ
4.567e14 Hz
cycles per second
Orbit radius r = n² a0 / Z
0.4763 nm
start orbit; the end orbit is 0.2117 nm
Start level ni3
End level nf2
Nuclear charge Z1 (hydrogen)
Fixed: a0 = 5.29177e-11 m and hc = 1239.842 eV·nm. One electron only, so Z = 2 is He+ and Z = 3 is Li2+, not neutral helium or lithium.
Tip: hold the end level at 2 and walk the start level up. The photon energy climbs but never past 3.4 eV — that ceiling is the Balmer series limit.