Bohr radius

Categories: Units of length | Atomic physics | Constants

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:

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

<math>e</math> is the elementary charge

<math>c</math> is the speed of light

<math>\alpha</math> is the fine structure constant

The Bohr radius is often used as a unit in atomic physics, see atomic units.

Note that the definition of Bohr radius does not include the effect of reduced mass, and so it is not precisely equal to the orbital radius of the electron in a hydrogen atom in the more physical model where reduced mass is included. This is done for convenience: the Bohr radius as defined above appears in equations relating to atoms other than hydrogen, where the reduced mass correction is different. If the definition of Bohr radius included the reduced mass of hydrogen, it would be necessary to include a more complex adjustment in equations relating to other atoms.de:Bohrscher Radius es:Radio de Bohr fr:Rayon de Bohr it:Raggio di Bohr ja:ボーア半径 pt:Raio de Bohr ru:Боровский радиус sl:Bohrov polmer