Electron Radius (Classical) to Bohr Radius Converter
Unit Converter
Instant · Precise · Universal
32 units available
6 categories total
How to Convert Electron Radius (Classical) to Bohr Radius
To convert to meters: multiply by 2.8179403262 × 10⁻¹⁵.
re = e²/(4πε₀mec²) ≈ 2.8179 × 10⁻¹⁵ m, where e is electron charge and me is electron mass.
For example, 1 Electron Radius (Classical) (re) = 0.00005325135452 Bohr Radius (a₀).
Electron Radius (Classical) to Bohr Radius — Common Values
| Electron Radius (Classical) (re) | Bohr Radius (a₀) |
|---|---|
| 0.1 | 0.000005325135452 |
| 0.5 | 0.00002662567726 |
| 1 | 0.00005325135452 |
| 2 | 0.000106502709 |
| 5 | 0.0002662567726 |
| 10 | 0.0005325135452 |
| 25 | 0.001331283863 |
| 50 | 0.002662567726 |
| 100 | 0.005325135452 |
| 500 | 0.02662567726 |
| 1000 | 0.05325135452 |
About Electron Radius (Classical) (re)
Definition
The classical electron radius is a theoretical length scale derived from the electron's charge and mass, approximately 2.818 × 10⁻¹⁵ meters.
Mathematical Relationship
re = e²/(4πε₀mec²) ≈ 2.8179 × 10⁻¹⁵ m, where e is electron charge and me is electron mass.
Conversion Formula
To convert to meters: multiply by 2.8179403262 × 10⁻¹⁵.
Practical Applications
Used in calculating X-ray and gamma-ray scattering probabilities off electrons (Thomson and Compton scattering).
Interesting Facts
Despite its name, the electron is a point particle in quantum theory — the 'classical radius' is a theoretical construct, not the electron's actual size.
Common Mistakes
Assuming this is the actual physical size of the electron — quantum mechanics shows the electron has no measurable size.
Educational Tips
Think of it as the scale at which classical electromagnetic self-energy equals the electron's mass-energy.
About Bohr Radius (a₀)
Definition
The Bohr radius is the most probable distance between the nucleus and the electron in a ground-state hydrogen atom, approximately 5.292 × 10⁻¹¹ meters.
Mathematical Relationship
a₀ = ℏ/(mec α) = 4πε₀ℏ²/(mee²) ≈ 5.29177 × 10⁻¹¹ m, where α is the fine-structure constant.
Conversion Formula
To convert Bohr radii to meters: multiply by 5.29177210903 × 10⁻¹¹.
Practical Applications
Sets the characteristic scale for atomic sizes. Most atoms have radii of 1–3 Bohr radii.
Interesting Facts
The Bohr radius gives atoms their characteristic size of ~1 Å (10⁻¹⁰ m), explaining why matter has the volume it does.
Common Mistakes
Confusing Bohr radius with atomic radius — the Bohr radius is specific to hydrogen; other atoms have different sizes.
Educational Tips
The Bohr radius tells you 'how big atoms are' — about 0.5 angstroms. It's the atomic analog of a ruler for atomic-scale physics.