Bohr Radius to Femtometer Converter
Unit Converter
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How to Convert Bohr Radius to Femtometer
To convert Bohr radii to meters: multiply by 5.29177210903 × 10⁻¹¹.
a₀ = ℏ/(mec α) = 4πε₀ℏ²/(mee²) ≈ 5.29177 × 10⁻¹¹ m, where α is the fine-structure constant.
For example, 1 Bohr Radius (a₀) = 52917.72109 Femtometer (fm).
Bohr Radius to Femtometer — Common Values
| Bohr Radius (a₀) | Femtometer (fm) |
|---|---|
| 0.1 | 5291.772109 |
| 0.5 | 26458.86055 |
| 1 | 52917.72109 |
| 2 | 105835.4422 |
| 5 | 264588.6055 |
| 10 | 529177.2109 |
| 25 | 1322943.027 |
| 50 | 2645886.055 |
| 100 | 5291772.109 |
| 500 | 26458860.55 |
| 1000 | 52917721.09 |
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.
About Femtometer (fm)
Definition
The femtometer is a unit of length equal to 10⁻¹⁵ meters, commonly used to measure the size of atomic nuclei.
Mathematical Relationship
1 fm = 10⁻¹⁵ m = 1,000 am = 10⁻⁶ nm. One meter equals 10¹⁵ femtometers.
Conversion Formula
To convert fm to meters: multiply by 10⁻¹⁵. To convert meters to fm: multiply by 10¹⁵.
Practical Applications
Describing the size of protons (~0.87 fm radius) and nuclear diameters (1–15 fm depending on the element).
Interesting Facts
A proton's charge radius is approximately 0.87 fm. The diameter of a uranium-238 nucleus is about 15 fm.
Common Mistakes
Confusing femtometers with nanometers — a femtometer is one million times smaller than a nanometer.
Educational Tips
Remember: atoms are ~0.1 nm, but nuclei are ~1–10 fm — nuclei are about 100,000 times smaller than the whole atom.