Bohr Radius to Earth's Polar Radius Converter
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Instant · Precise · Universal
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How to Convert Bohr Radius to Earth's Polar 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) = 8.324647e-18 Earth's Polar Radius (R⊕ (polar)).
Bohr Radius to Earth's Polar Radius — Common Values
| Bohr Radius (a₀) | Earth's Polar Radius (R⊕ (polar)) |
|---|---|
| 0.1 | 8.324647e-19 |
| 0.5 | 4.162324e-18 |
| 1 | 8.324647e-18 |
| 2 | 1.664929e-17 |
| 5 | 4.162324e-17 |
| 10 | 8.324647e-17 |
| 25 | 2.081162e-16 |
| 50 | 4.162324e-16 |
| 100 | 8.324647e-16 |
| 500 | 4.162324e-15 |
| 1000 | 8.324647e-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 Polar Radius (R⊕ (polar))
Definition
The Earth's polar radius is the distance from Earth's center to either pole, approximately 6,356.752 km.
Mathematical Relationship
R⊕(polar) = 6,356,752.3 m. It is about 21.385 km shorter than the equatorial radius.
Conversion Formula
To convert Earth polar radii to meters: multiply by 6,356,752.3.
Practical Applications
Geodetic calculations, gravity modeling, and precise cartography near the poles.
Interesting Facts
At the poles, you are about 21 km closer to Earth's center than at the equator — you weigh very slightly more!
Common Mistakes
Approximating Earth as a perfect sphere — the difference between equatorial and polar radii matters for precision applications.
Educational Tips
Earth's shape (oblate spheroid) is like a slightly squished ball — wider at the equator, flatter at the poles.