Bohr Radius to Earth's Equatorial Radius Converter
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How to Convert Bohr Radius to Earth's Equatorial Radius
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) = 8.296736e-18 Earth's Equatorial Radius (R⊕ (eq)).
Bohr Radius to Earth's Equatorial Radius — Common Values
| Bohr Radius (a₀) | Earth's Equatorial Radius (R⊕ (eq)) |
|---|---|
| 0.1 | 8.296736e-19 |
| 0.5 | 4.148368e-18 |
| 1 | 8.296736e-18 |
| 2 | 1.659347e-17 |
| 5 | 4.148368e-17 |
| 10 | 8.296736e-17 |
| 25 | 2.074184e-16 |
| 50 | 4.148368e-16 |
| 100 | 8.296736e-16 |
| 500 | 4.148368e-15 |
| 1000 | 8.296736e-15 |
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 Earth's Equatorial Radius (R⊕ (eq))
Definition
The Earth's equatorial radius is the distance from Earth's center to the equator, approximately 6,378.137 km.
Mathematical Relationship
R⊕(eq) = 6,378,137 m = 6,378.137 km. Earth's oblateness = (R_eq − R_pol)/R_eq ≈ 1/298.257.
Conversion Formula
To convert Earth radii to meters: multiply by 6,378,137.
Practical Applications
GPS calculations, satellite orbit determination, map projections, and geophysical modeling.
Interesting Facts
Earth is not a perfect sphere — the equatorial radius is about 21 km (0.3%) larger than the polar radius due to rotational flattening.
Common Mistakes
Using the equatorial radius as if Earth were a sphere — for precision, you must account for the oblate spheroid shape.
Educational Tips
Earth's equatorial radius (6,378 km) vs. polar radius (6,357 km) shows the planet bulges at the equator due to spinning.