Electron Radius (Classical) to Astronomical Unit Converter
Unit Converter
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32 units available
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How to Convert Electron Radius (Classical) to Astronomical Unit
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) = 1.883677e-26 Astronomical Unit (AU).
Electron Radius (Classical) to Astronomical Unit — Common Values
| Electron Radius (Classical) (re) | Astronomical Unit (AU) |
|---|---|
| 0.1 | 1.883677e-27 |
| 0.5 | 9.418384e-27 |
| 1 | 1.883677e-26 |
| 2 | 3.767354e-26 |
| 5 | 9.418384e-26 |
| 10 | 1.883677e-25 |
| 25 | 4.709192e-25 |
| 50 | 9.418384e-25 |
| 100 | 1.883677e-24 |
| 500 | 9.418384e-24 |
| 1000 | 1.883677e-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 Astronomical Unit (AU)
Definition
The astronomical unit is a unit of length approximating the mean Earth-Sun distance, defined as exactly 149,597,870,700 meters.
Mathematical Relationship
1 AU = 149,597,870,700 m ≈ 149.598 Gm ≈ 499 light-seconds ≈ 8.317 light-minutes.
Conversion Formula
To convert AU to km: multiply by 149,597,870.7. To convert AU to light-years: divide by 63,241.
Practical Applications
Spacecraft mission planning, expressing planetary orbit sizes, and solar system scale models.
Interesting Facts
Light takes about 8 minutes and 20 seconds to travel 1 AU. Mars is about 1.52 AU from the Sun, Jupiter about 5.2 AU.
Common Mistakes
Thinking the AU is the exact Earth-Sun distance — Earth's actual distance varies from ~147 to ~152 Gm over the year due to orbital eccentricity.
Educational Tips
AU makes the solar system manageable: Mercury ≈ 0.39 AU, Venus ≈ 0.72, Earth = 1, Mars ≈ 1.52, Jupiter ≈ 5.2, Saturn ≈ 9.5.