Bohr radius
Atomic & nuclearMeasured
= 5.291 772 105 44(82) × 10−11 m
- Value
- 5.291 772 105 44 × 10−11 m
- Standard uncertainty
- 8.2 × 10−21 m
- Relative uncertainty
- 1.5 × 10−10 (155 parts per trillion)
- Status
- Measured
- Symbol
- Source
- CODATA 2022 via NIST · NIST entry
Use in a calculation
# Bohr radius, CODATA 2022 (NIST)
a_0 = 5.29177210544e-11 # m, standard uncertainty 8.2e-21
# SciPy: scipy.constants.physical_constants['Bohr radius']What it is
The radius of the smallest electron orbit in Bohr's model of hydrogen, and in quantum mechanics the most probable distance of the electron from an infinitely heavy nucleus in the ground state. It is the atomic unit of length, about half an ångström.
Equations
- definition
In other units
| Unit | Value | |
|---|---|---|
| CGS (cm) | 5.291 772 105 44 × 10−9 | |
| nm nanometre | 0.052 917 721 0544 | |
| pm picometre | 52.917 721 0544 | |
| fm femtometre | 52 917.721 0544 | |
| Å ångström | 0.529 177 210 544 | |
| a₀ bohr (atomic unit) | 1 | unit is itself measured |
Converted with ConstantID's unit table; digits are rounded to the precision of the value, and a long exact value is rounded only for display. The relative uncertainty is unchanged by conversion to an exactly defined unit.
How the value changed, 1998–2022
Each point is one CODATA adjustment, plotted as its difference from the 2022 value; the bars show one standard uncertainty (an arrowhead means the bar runs off the chart).
Relative uncertainty
| CODATA | Value (uncertainty) | Relative uncertainty | Change from previous |
|---|---|---|---|
| 2022 | 5.291 772 105 44(82) × 10−11 | 1.5 × 10−10 | −4.5 σ of 2018 |
| 2018 | 5.291 772 109 03(80) × 10−11 | 1.5 × 10−10 | +1.9 σ of 2014 |
| 2014 | 0.529 177 210 67(12) × 10−10 | 2.3 × 10−10 | −1.5 σ of 2010 |
| 2010 | 0.529 177 210 92(17) × 10−10 | 3.2 × 10−10 | +6.5 σ of 2006 |
| 2006 | 0.529 177 208 59(36) × 10−10 | 6.8 × 10−10 | −1.2 σ of 2002 |
| 2002 | 0.529 177 2108(18) × 10−10 | 3.4 × 10−9 | +1.3 σ of 1998 |
| 1998 | 0.529 177 2083(19) × 10−10 | 3.6 × 10−9 |
“Change from previous” is the shift in the value divided by the standard uncertainty of the previous adjustment. Earlier values are converted into the current unit where NIST changed it (for example J s to J Hz⁻¹).