Rydberg Formula
The empirical equation predicting the wavelengths of the spectral lines emitted by a hydrogen-like atom.
Formula / equation
1/λ = R_H(1/n₁² − 1/n₂²)
Unit
m⁻¹
In depth
With the Rydberg constant R_H = 1.097 × 10⁷ m⁻¹, the formula reproduces every hydrogen line to high accuracy. Fixing n₁ selects a series: 1 gives the ultraviolet Lyman lines, 2 the visible Balmer lines and 3 the infrared Paschen lines. Bohr's model later derived the constant from first principles.
Examples in the real world
Setting n₁ = 2 and n₂ = 3 gives λ = 656 nm, the red H-alpha line seen in every hydrogen discharge tube.