Bohr Radius to Centimeter Converter
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How to Convert Bohr Radius to Centimeter
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-9 Centimeter (cm).
Bohr Radius to Centimeter — Common Values
| Bohr Radius (a₀) | Centimeter (cm) |
|---|---|
| 0.1 | 5.291772e-10 |
| 0.5 | 2.645886e-9 |
| 1 | 5.291772e-9 |
| 2 | 1.058354e-8 |
| 5 | 2.645886e-8 |
| 10 | 5.291772e-8 |
| 25 | 1.322943e-7 |
| 50 | 2.645886e-7 |
| 100 | 5.291772e-7 |
| 500 | 0.000002645886055 |
| 1000 | 0.000005291772109 |
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 Centimeter (cm)
Definition
The centimeter is a unit of length equal to one hundredth of a meter (10⁻² m), or 10 millimeters.
Mathematical Relationship
1 cm = 0.01 m = 10 mm = 0.3937 inches. There are 2.54 cm in one inch.
Conversion Formula
To convert cm to inches: divide by 2.54. To convert inches to cm: multiply by 2.54.
Practical Applications
Measuring height, waist circumference, screen sizes, furniture dimensions, and map scales.
Interesting Facts
The CGS system was the primary scientific system for over a century. 1 cm is roughly the width of an adult fingernail.
Common Mistakes
Confusing cm and inches — a common error in international contexts. Always verify which system a measurement uses.
Educational Tips
Your fingernail width is roughly 1 cm — a handy mental reference that's always available.