Bohr Radius

a_0 = \frac{4\pi\varepsilon_0\hbar^2}{m_e e^2} \approx 5.29 \times 10^{-11}\text{ m}

The most probable distance between electron and nucleus in a hydrogen atom ground state.

Variables

a₀

Bohr radius

ε₀

Permittivity of free space

F/m

ℏ

Reduced Planck constant

J·s

m_e

Electron mass

Electron charge

Your notes

0/5000

Constants in this formula

a₀

Bohr Radius

5.292 × 10⁻¹¹. Measured (CODATA 2018).

ε₀

Vacuum Permittivity

8.854 × 10⁻¹². Measured (CODATA 2018).

F/m

ℏ

Reduced Planck Constant

1.054 571 817… × 10⁻³⁴. Exact by definition.

J·s

m_e

Electron Mass

9.109 × 10⁻³¹. Measured (CODATA 2018).

Elementary Charge

1.602 176 634 × 10⁻¹⁹. Exact by definition.

Other modern physics formulas with the same quantities

Electron Wavelength (Accelerated) (Quantum Mechanics) shares Electron mass, Electron charge
Stopping Potential (Quantum Mechanics) shares Electron charge
Heisenberg Uncertainty Principle (Quantum Mechanics) shares Reduced Planck constant
Energy-Time Uncertainty (Quantum Mechanics) shares Reduced Planck constant
Time-Dependent Schrödinger Equation (Quantum Mechanics) shares Reduced Planck constant
Compton Scattering (Quantum Mechanics) shares Electron mass

Where this formula is listed

Modern Physics formulas, under Atomic Physics, alongside Hydrogen-like Atom Energy, Electron Orbital Radius and Moseley's Law.
In the modern physics list it comes after Electron Wavelength (Accelerated) and before Bohr Energy Levels.
Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Bohr Radius formula?

Bohr Radius is written a₀ = 4πε₀ℏ²/(m_e e²) ≈ 5.29 × 10⁻¹¹ m. The most probable distance between electron and nucleus in a hydrogen atom ground state. It belongs to Modern Physics, under Atomic Physics.

What are the units in a₀ = 4πε₀ℏ²/(m_e e²) ≈ 5.29 × 10⁻¹¹ m?

In SI units, a₀ is bohr radius, measured in m; ε₀ is permittivity of free space, measured in F/m; ℏ is reduced planck constant, measured in J·s; m_e is electron mass, measured in kg; e is electron charge, measured in C.