• Pixel-art sticker of Orbel, personifying Bohr Radius, with the caption “Level Up, Four Times Wider.”

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Orbel

Bohr Radius Physics

\[r_n = n^2 a_0\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Orbel, a proton whose electron moves much farther out with each step up in energy. In Bohr's model orbit radius grows as n² times the Bohr radius, 5.29 × 10⁻¹¹ m: four times wider at n = 2, nine times at n = 3. 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 Orbel, a proton whose electron moves much farther out with each step up in energy.

In Niels Bohr's model of hydrogen, the electron can only orbit at certain distances. Each allowed orbit has a whole number n. The smallest, n = 1, has a radius called the Bohr radius, a₀.

The orbit radius grows as rₙ = n²a₀. With a₀ ≈ 5.29 × 10⁻¹¹ m, the n = 2 orbit is about 0.212 nm from the centre, four times wider. The n = 3 orbit is nine times wider, about 0.476 nm.

Modern quantum mechanics replaces neat orbits with clouds of probability, but the Bohr radius is still the most likely distance of the electron from the nucleus in the ground state.

It sets the natural size scale for atoms. Most atoms, whatever their element, are only a few Bohr radii across, around a tenth of a nanometre or so. Larger orbits need more energy, and the electron jumps between them by absorbing or giving out light.

Equations

\[r_n = n^2 a_0\]
Symbols
SymbolMeaningUnit
\(r_n\) radius of orbit n \(\mathrm{m}\)
\(n\) orbit number \(\mathrm{dimensionless}\)
\(a_0\) Bohr radius \(\mathrm{m}\)