Bohr Radius

The most probable distance between proton and electron in ground-state hydrogen, about half an ångström.

Specifications & Metrics

symbol

a₀

status

Measured (CODATA 2022)

value

5.29177210544 × 10⁻¹¹ ± 8.2 × 10⁻²¹ m

Relative Scale in Constants

Core Principles & Analysis

• Equals 5.29 × 10⁻¹¹ m — the radius scale of every atom's electron cloud.
• In Bohr's 1913 model it was the ground-state orbit radius; in quantum mechanics, the most probable electron-proton distance in hydrogen.
• Equals ħ divided by mₑ·c·α, so it would shrink if the electron were heavier or electromagnetism stronger.

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