• Pixel-art sticker of Alphon, personifying Fine-Structure Constant, with the caption “About 1/137, No Units.”

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Alphon

Fine-Structure Constant Physics

\[\alpha = \frac{e^2}{4\pi\varepsilon_0 \hbar c}\]
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Meet Alphon, a tiny electron who carries a number with no units at all. The fine-structure constant, about 1/137.036, measures how strongly light and charges interact. In the Bohr model it sets the electron's lowest-orbit speed at under 1 percent of light speed. 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 Alphon, a tiny electron who carries a number that has no units at all.

The fine-structure constant α combines the charge of the electron, the vacuum permittivity, the reduced Planck constant and the speed of light. All their units cancel, so it is a pure number. It measures how strongly light and charged particles interact.

Its value is about 1/137.036, or 0.0072974. In the simple Bohr model of hydrogen, the electron's speed in the lowest orbit is αc. That is about 2.19 × 10⁶ m/s, under 1 percent of the speed of light.

Because α is small, physicists can calculate electric effects step by step, each step smaller than the last. This makes quantum electrodynamics one of the most precise theories ever tested.

No one knows why α has the value it does. If it were very different, atoms and the chemistry of life could not exist as they do. Physicists still test whether it has changed over billions of years, and so far it has not.

Equations

\[\alpha = \frac{e^2}{4\pi\varepsilon_0 \hbar c}\]
SymbolMeaningUnit
\(\alpha\) fine-structure constant \(\mathrm{dimensionless}\)
\(e\) elementary charge \(\mathrm{C}\)
\(\varepsilon_0\) vacuum permittivity \(\mathrm{F/m}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(c\) speed of light \(\mathrm{m/s}\)

Sources

  1. NIST CODATA — fine-structure constant
  2. Wikipedia — Fine-structure constant

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