a₀ is the radius of the first orbit in Bohr's model of hydrogen. Orbit radii grow as n²: rₙ = 0.529 n²/Z Å.
Value of a₀ in different units
| Value | Use it when |
|---|---|
| 5.29 × 10⁻¹¹ m | SI. |
| 0.529 Å | The value used in atomic-structure questions. |
| 52.9 pm | Picometres. |
Formulas that use a₀
- rₙ = 0.529 n²/Z Å
- a₀ = 4πε₀ħ²/(mₑe²)
Other constants
- Gas constant (R): 8.314 J mol⁻¹ K⁻¹
- Planck's constant (h): 6.626 × 10⁻³⁴ J s
- Avogadro's number (Nₐ): 6.022 × 10²³ mol⁻¹
- Speed of light (c): 3 × 10⁸ m/s
- Charge of an electron (e): 1.602 × 10⁻¹⁹ C
- Mass of an electron (mₑ): 9.109 × 10⁻³¹ kg
- Mass of a proton (mₚ): 1.673 × 10⁻²⁷ kg
- Mass of a neutron (mₙ): 1.675 × 10⁻²⁷ kg
- Universal gravitational constant (G): 6.674 × 10⁻¹¹ N m² kg⁻²
- Acceleration due to gravity (g): 9.8 m/s²
- Boltzmann constant (k): 1.381 × 10⁻²³ J/K
- Faraday constant (F): 96 485 C/mol
- Permittivity of free space (ε₀): 8.854 × 10⁻¹² C² N⁻¹ m⁻²
- Permeability of free space (μ₀): 4π × 10⁻⁷ T m/A
- Rydberg constant (R): 1.097 × 10⁷ m⁻¹
- Stefan–Boltzmann constant (σ): 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Wien's constant (b): 2.898 × 10⁻³ m K
- Bohr radius (a₀): 0.529 Å
- Molar volume of a gas at STP (Vₘ): 22.4 L/mol
The full list, searchable, is on the physical constants page.
Questions students ask
What is the value of Bohr radius?
a₀ = 0.529 Å. In other units: 5.29 × 10⁻¹¹ m; 0.529 Å; 52.9 pm.
What is a₀ in physics and chemistry?
a₀ is the radius of the first orbit in Bohr's model of hydrogen. Orbit radii grow as n²: rₙ = 0.529 n²/Z Å.
Which value of a₀ should I use?
5.29 × 10⁻¹¹ m: SI. 0.529 Å: The value used in atomic-structure questions. 52.9 pm: Picometres.