Bohr radius  The Bohr radius ("a"0) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state (non-relativistic and with an infinitely heavy proton). It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is   The Bohr radius is:  where:  The CODATA value of the Bohr radius (in SI units) is   The Bohr model derives a radius for the "n"th excited state of a hydrogen-like atom. The Bohr radius corresponds to . In the Bohr model for atomic structure, put forward by Niels Bohr in 1913, electrons orbit a central 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 lowest energy, has an orbital radius almost equal to the Bohr radius. (It is not "exactly" the Bohr radius due to the reduced mass effect. They differ by about 0.05%.) The Bohr model of the atom was superseded by an electron probability cloud obeying the Schrodinger equation, which is further complicated by spin and quantum vacuum effects to produce fine structure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 in part to its simple relationship with other fundamental constants. (This is why it is defined using the true electron mass rather than the reduced mass, as mentioned above.) For example, it is the unit of length in atomic units. An important distinction is that the Bohr radius gives the radius with the maximum radial probability density, not its expected radial distance. The expected radial distance is 1.5 times the Bohr radius, as a result of the long tail of the radial wave function. Another important distinction is that in three-dimensional space, the maximum probability density occurs at the location of the nucleus and not at the Bohr radius, whereas the radial probability density peaks at the Bohr radius, i.e. when plotting the probability distribution in its radial dependency. The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelength of the electron formula_9 and the classical electron radius formula_10.