Bohr Radius to Petameter Converter
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How to Convert Bohr Radius to Petameter
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) = 5.291772e-26 Petameter (Pm).
Bohr Radius to Petameter — Common Values
| Bohr Radius (a₀) | Petameter (Pm) |
|---|---|
| 0.1 | 5.291772e-27 |
| 0.5 | 2.645886e-26 |
| 1 | 5.291772e-26 |
| 2 | 1.058354e-25 |
| 5 | 2.645886e-25 |
| 10 | 5.291772e-25 |
| 25 | 1.322943e-24 |
| 50 | 2.645886e-24 |
| 100 | 5.291772e-24 |
| 500 | 2.645886e-23 |
| 1000 | 5.291772e-23 |
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 Petameter (Pm)
Definition
The petameter is a unit of length equal to 10¹⁵ meters, or about 0.1 light-years.
Mathematical Relationship
1 Pm = 10¹⁵ m ≈ 0.1057 light-years ≈ 0.0324 parsecs.
Conversion Formula
To convert Pm to light-years: divide by 9.461. To convert Pm to parsecs: divide by 30.857.
Practical Applications
No practical everyday applications. Would describe distances to nearby stars in metric.
Interesting Facts
1 light-year ≈ 9.46 Pm. The Oort Cloud extends to roughly 15,000 Pm from the Sun.
Common Mistakes
Case sensitivity is critical: Pm (petameter) vs. pm (picometer) differ by a factor of 10²⁷!
Educational Tips
Remember: 1 light-year ≈ 9.46 Pm, so a few Pm is a fraction of the distance to the nearest star.