The Balmer Ladder

Plate 41 speaks for itself: “Hydrogen sings four notes we can see.”

The Physics

Hydrogen's visible lines come from electrons dropping to level n = 2. Balmer found the pattern in 1885, before anyone knew why; Bohr's model and quantum mechanics later explained it.

1/λ = R_H (1/4 − 1/n²)

• λ: wavelength, m
• R_H: Rydberg constant for hydrogen ≈ 1.09678×10⁷ m⁻¹
• n: upper level, 3, 4, 5, …, dimensionless

Visible lines (air): 656.28, 486.13, 434.05, 410.17 nm. Series limit 364.6 nm. J. Balmer, 1885.

Sources

• J. J. Balmer, Ann. Phys. 261, 80 (1885).
• NIST Atomic Spectra Database (H I).

On the poster

Plate 041, “The Balmer Ladder”: the pixel-art plate with its slogan “Hydrogen sings four notes we can see.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.