Bohr Radius to Nanometer Converter
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32 units available
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How to Convert Bohr Radius to Nanometer
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) = 0.05291772109 Nanometer (nm).
Bohr Radius to Nanometer — Common Values
| Bohr Radius (a₀) | Nanometer (nm) |
|---|---|
| 0.1 | 0.005291772109 |
| 0.5 | 0.02645886055 |
| 1 | 0.05291772109 |
| 2 | 0.1058354422 |
| 5 | 0.2645886055 |
| 10 | 0.5291772109 |
| 25 | 1.322943027 |
| 50 | 2.645886055 |
| 100 | 5.291772109 |
| 500 | 26.45886055 |
| 1000 | 52.91772109 |
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 Nanometer (nm)
Definition
The nanometer is a unit of length equal to 10⁻⁹ meters, or one billionth of a meter.
Mathematical Relationship
1 nm = 10⁻⁹ m = 10 Å = 1,000 pm = 10⁻³ µm. One micrometer equals 1,000 nanometers.
Conversion Formula
To convert nm to meters: multiply by 10⁻⁹. To convert nm to micrometers: divide by 1,000.
Practical Applications
Semiconductor chip feature sizes (5 nm, 3 nm transistors), UV light wavelengths, virus dimensions, and thin-film coatings.
Interesting Facts
A human hair is about 80,000–100,000 nm thick. The COVID-19 virus is approximately 100 nm in diameter.
Common Mistakes
Confusing nanometers with micrometers — they differ by a factor of 1,000. Be careful with nm vs. µm in specs.
Educational Tips
Visible light wavelengths (380–700 nm) are a great anchor: red light ≈ 700 nm, violet light ≈ 380 nm.