In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. In the simplest atom, that of hydrogen, a single electron orbits, and the smallest possible orbit for the electron, that with the lowest energy, is the one at a distance from the nucleus called the Bohr radius.

The Bohr radius has a value of 5.291772108×10^-11 m (i.e. 53 pm), or about half an angstrom.

Technical description

The Bohr radius (a₀) is the radius of the lowest energy orbit in the hydrogen atom:

where:

is the permittivity of vacuum

is Dirac's constant or the "reduced Planck's constant"

m_e is the electron rest mass

and

e is the elementary charge

The Bohr radius is often used as a unit in atomic physics, typically in perturbative expansions of wave function solutions.