Electron Radius (Classical) to Planck Length Converter
Unit Converter
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32 units available
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How to Convert Electron Radius (Classical) to Planck Length
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) = 1.743500e+20 Planck Length (ℓP).
Electron Radius (Classical) to Planck Length — Common Values
| Electron Radius (Classical) (re) | Planck Length (ℓP) |
|---|---|
| 0.1 | 1.743500e+19 |
| 0.5 | 8.717499e+19 |
| 1 | 1.743500e+20 |
| 2 | 3.487000e+20 |
| 5 | 8.717499e+20 |
| 10 | 1.743500e+21 |
| 25 | 4.358750e+21 |
| 50 | 8.717499e+21 |
| 100 | 1.743500e+22 |
| 500 | 8.717499e+22 |
| 1000 | 1.743500e+23 |
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 Planck Length (ℓP)
Definition
The Planck length is the fundamental natural unit of length, approximately 1.616 × 10⁻³⁵ meters, below which the conventional concepts of space may cease to exist.
Mathematical Relationship
ℓP = √(ℏG/c³) ≈ 1.616255 × 10⁻³⁵ m.
Conversion Formula
To convert Planck lengths to meters: multiply by 1.616255 × 10⁻³⁵.
Practical Applications
No practical applications — purely theoretical. It represents the scale at which quantum gravity effects become significant.
Interesting Facts
The Planck length is about 10⁻²⁰ times the diameter of a proton. It's as far below a proton as a proton is below a grain of sand.
Common Mistakes
Thinking the Planck length is the 'smallest possible length' — it's the scale where our current physics models break down, not a proven minimum.
Educational Tips
The Planck length arises from combining the three constants that govern quantum mechanics (ℏ), gravity (G), and relativity (c).