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(18)×10-11 m (according to 2002 CODATA), i.e., approximately 53 pm or 0.53 angstroms. This value can be computed in terms of other physical constants:

[itex]a_0 = {{4\pi\varepsilon_0\hbar^2}\over{m_e e^2}} = {{\hbar}\over{m_e c \alpha}}[itex]

where:

[itex]\varepsilon_0[itex] is the permittivity of vacuum
[itex]\hbar[itex] is Dirac's constant or the "reduced Planck's constant"
[itex]m_e[itex] is the electron rest mass
[itex]e[itex] is the elementary charge
[itex]c[itex] is the speed of light
[itex]\alpha[itex] is the fine structure constant

The Bohr radius is often used as a unit in atomic physics, see atomic units.de:Bohrscher Radius it:Raggio di Bohr ja:ボーア半径 sl:Bohrov polmer

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