r_e

The classical electron radius, often denoted as r_e or r₀, is a fundamental physical constant defining a length scale that equates the electron’s rest mass energy (mc²) to its electrostatic potential energy(

. According to the 2022 CODATA recommendation, its value is

$$r_e = 2.8179403205(13) \times 10^{-15}\ \text{m}$$

Key details regarding this value:

• Definition: It is where the elementary charge, the electron mass, $$the speed of light, and the vacuum permittivity are in relation.
• Physical Meaning: While it represents a “radius” in classical electrodynamics, modern quantum theory treats the electron as a point particle. The classical electron radius is instead interpreted as the scale where classical field theory breaks down and quantum electrodynamics (QED) becomes significant.
• Significance: It is roughly the length scale of nuclear dimensions $$and is used in scattering cross-sections, such as Thomson scattering.
• Uncertainty: The standard uncertainty is  m (4.7 × $$ relative standard uncertainty).
• CODATA Value: 2.8179403205(13) × 10⁻¹⁵ meters

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