Bohr Radius to Astronomical Unit Converter
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How to Convert Bohr Radius to Astronomical Unit
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) = 3.537331e-22 Astronomical Unit (AU).
Bohr Radius to Astronomical Unit — Common Values
| Bohr Radius (a₀) | Astronomical Unit (AU) |
|---|---|
| 0.1 | 3.537331e-23 |
| 0.5 | 1.768666e-22 |
| 1 | 3.537331e-22 |
| 2 | 7.074662e-22 |
| 5 | 1.768666e-21 |
| 10 | 3.537331e-21 |
| 25 | 8.843328e-21 |
| 50 | 1.768666e-20 |
| 100 | 3.537331e-20 |
| 500 | 1.768666e-19 |
| 1000 | 3.537331e-19 |
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 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.