• Pixel-art sticker of Rydbella, personifying Rydberg Formula, with the caption "I Only Jump In Steps."

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Rydbella

Rydberg Formula Physics

\[\frac{1}{\lambda} = R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\]
$4.99 USD
$4.99 USD
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Meet Rydbella, a hydrogen electron who drops only between allowed levels, so she emits only certain wavelengths, given by the Rydberg formula. Her jump from n = 3 to n = 2 gives the red H-alpha line at about 656 nm. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Rydbella, hydrogen's electron, who only ever jumps in steps.

A hydrogen atom can only hold certain energies, labelled by whole numbers n = 1, 2, 3 and so on. When the electron drops from a higher level n₂ to a lower level n₁, the atom gives off one photon carrying exactly the energy difference. Because the levels are fixed, the photon wavelengths are fixed too, and the Rydberg formula gives them all: one over the wavelength equals the Rydberg constant times (1/n₁² − 1/n₂²).

Take the drop from n = 3 to n = 2. With R_H ≈ 1.0968×10⁷ per metre, the formula gives about 656 nanometres: the red H-alpha line. Drops that end on n = 2 make the visible Balmer series; drops that end on n = 1 make the ultraviolet Lyman series.

These lines are how astronomers spot hydrogen across the universe. The red glow of many nebulae is mostly H-alpha.

The formula, found from measured spectra before quantum mechanics, works so well for hydrogen because it has one electron. Atoms with more electrons need corrections, and tiny effects such as fine structure split even hydrogen's lines slightly.

Equations

\[\frac{1}{\lambda} = R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\]
SymbolMeaningUnit
\(\lambda\) wavelength of the emitted light \(\mathrm{m}\)
\(R_H\) Rydberg constant for hydrogen (≈ 1.0968×10⁷ m⁻¹) \(\mathrm{m⁻¹}\)
\(n_1\) lower energy level (whole number) —
\(n_2\) upper energy level, n₂ > n₁ —

Sources

  1. OpenStax University Physics Vol. 3 — Bohr's Model of the Hydrogen Atom
  2. NIST CODATA — Rydberg constant
  3. Wikipedia — Rydberg formula

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