Convert Classical Electron Radius to X-unit
Convert classical electron radii to x-units instantly. 1 classical electron radius = 0.0281203505 x-unit — use the live calculator, the exact formula, a conversion table and worked examples. Also check the X-unit to Classical Electron Radius converter for the reverse conversion.
Units explained
Classical Electron Radius
The classical electron radius is approximately 2.818×10⁻¹⁵ meters. It is the radius an electron would have if its mass were entirely electromagnetic and its charge distributed over its surface.
Defined classically in the early 20th century. The CODATA 2018 value of 2.8179403262×10⁻¹⁵ m is derived from the elementary charge, electron rest mass, and the Coulomb constant.
The classical electron radius appears in scattering theory (Thomson scattering cross-section), particle physics estimates, and historical electromagnetism. It is a calculational tool, not the actual size of an electron, which has no measured extent.
Concept dates to the early 20th-century classical electromagnetism; CODATA 2018 provides the current reference value.
X-unit
The X-unit (or siegbahn) is a historical X-ray crystallography unit of approximately 1.0021×10⁻¹³ meters. It was used before X-ray wavelengths could be measured directly in meters.
Introduced by Manne Siegbahn in 1925 as a self-consistent unit for X-ray crystallography. The 'X-unit' was defined to make the X-ray wavelength of the molybdenum K-alpha line a round number.
X-units appear in X-ray crystallography literature from 1925 through the 1960s. Modern crystallography uses meters or angstroms; X-units are mostly of historical interest now.
Defined by Manne Siegbahn in 1925; superseded by direct SI measurement of X-ray wavelengths after the 1960s; retained in literature for historical comparison.
Classical Electron Radius to X-unit conversion formula
The relationship between classical electron radii and x-units:
To convert classical electron radii to x-units, multiply the value in classical electron radii by 0.0281203505. To reverse, multiply x-units by 35.5614343811.
How to use this converter
Type a value into the calculator. The result in x-units updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the X-unit to Classical Electron Radius converter for the reverse direction.
Step-by-step: convert classical electron radii to x-units
- Write down the value in classical electron radii (rₑ).
- Multiply that value by the factor 0.0281203505.
- The product is the equivalent value in x-units (X).
- To reverse, multiply the x-unit value by 35.5614343811.
Worked examples
Example 1 — Convert 1 rₑ to X:
1 × 0.0281203505 = 0.0281203505 X
Example 2 — Convert 100 rₑ to X:
100 × 0.0281203505 = 2.8120350526 X
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 classical electron radii) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 rₑ × 0.0281203505 = 0.0562407011 X
Real-world example — Wavelengths across the spectrum
Optical and atomic-scale phenomena are routinely cross-converted between sub-micron units. A photon of wavelength 800 classical electron radii can be re-expressed in x-units for direct comparison with another instrument's calibration data sheet.
800 rₑ × 0.0281203505 = 22.4962804207 X
Classical Electron Radius to X-unit conversion table
Standard reference values for converting classical electron radii to x-units:
| Classical Electron Radius [rₑ] | X-unit [X] |
|---|---|
| 0.01 | 0.0002812035 |
| 0.1 | 0.0028120351 |
| 1 | 0.0281203505 |
| 2 | 0.0562407011 |
| 3 | 0.0843610516 |
| 4 | 0.1124814021 |
| 5 | 0.1406017526 |
| 10 | 0.2812035053 |
| 20 | 0.5624070105 |
| 30 | 0.8436105158 |
| 40 | 1.124814021 |
| 50 | 1.4060175263 |
| 100 | 2.8120350526 |
| 500 | 14.0601752629 |
| 1000 | 28.1203505259 |
Frequently asked questions
How many x-units is 1 classical electron radius?
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How do I convert x-units back to classical electron radii?
How many x-units is 100 classical electron radii?
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Metric / SI (4 units)
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Sources & references
Conversion factor (1 rₑ = 0.0281203505 X) verified against the following authoritative sources:
- BIPM — The International System of Units (SI Brochure 9th ed.)
Official BIPM publication defining the seven SI base units (including the meter) and the rules for their use. The global authority on units of measurement.
- NIST — Guide to the SI
US National Institute of Standards and Technology reference covering the SI base and derived units with definitions and usage rules for US technical practice.
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Detailed NIST guide covering exact conversion factors between SI and US customary units along with formatting and rounding conventions.
- NIST — Refinement of values for the yard and pound (Federal Register 1959)
The treaty (signed by US
- International Astronomical Union — System of Astronomical Constants
The IAU defines astronomical units including the AU (149597870700 m exactly) light-year and parsec used in astronomy and astrophysics.