Editing Bohr radius (section)

== History ==
[[File:Bohr_model.jpg|thumb|right|alt=Picture of a hydrogen atom using the Bohr model|Picture of a hydrogen atom using the Bohr model]]
In the [[Bohr model]] for [[atom]]ic structure, put forward by Niels Bohr in 1913, [[electrons]] orbit a central [[atomic nucleus|nucleus]] under electrostatic attraction. The original derivation posited that electrons have orbital angular momentum in integer multiples of the reduced Planck constant, which successfully matched the observation of discrete energy levels in emission spectra, along with predicting a fixed radius for each of these levels. In the simplest atom, [[hydrogen]], a single electron orbits the nucleus, and its smallest possible orbit, with the lowest energy, has an orbital radius almost equal to the Bohr radius. (It is not ''exactly'' the Bohr radius due to the [[reduced mass|reduced mass effect]]. They differ by about 0.05%.)

The Bohr model of the atom was superseded by an electron probability cloud adhering to the [[Schrödinger equation]] as published in 1926. This is further complicated by spin and quantum vacuum effects to produce [[fine structure]] and [[hyperfine structure]]. Nevertheless, the Bohr radius formula remains central in [[atomic physics]] calculations, due to its simple relationship with fundamental constants (this is why it is defined using the true electron mass rather than the reduced mass, as mentioned above). As such, it became the unit of length in [[atomic units]].

In Schrödinger's quantum-mechanical theory of the hydrogen atom, the Bohr radius is the value of the radial coordinate for which the radial probability density of the electron position is highest.  The [[expected value]] of the radial distance of the electron, by contrast, is&nbsp;{{tmath|\tfrac{3}{2} a_0}}.<ref>{{cite web |last1=Nave |first1=Rod |title=The Most Probable Radius: Hydrogen Ground State |url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html |website=[[HyperPhysics]] |publisher=Dept. of Physics and Astronomy, Georgia State University |access-date=2 October 2021 |quote=The Schrodinger equation confirms the first Bohr radius as the most probable radius.}}</ref>