Bohr radius

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 (<math>a_0<math>) is the radius of the lowest energy orbit in the hydrogen atom:

<math>a_0 = {{4\pi\varepsilon_0\hbar^2}\over{m_e e^2}}<math>

where:

<math>\varepsilon_0<math> is the permittivity of vacuum

<math>\hbar<math> is Dirac's constant or the "reduced Planck's constant"

<math>m_e<math> is the electron rest mass

and

<math>e<math> is the elementary charge

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