Bohr radius

The characteristic length scale of the hydrogen atom’s ground state, equal to about 5.29 × 10⁻¹¹ metres. In the Bohr model it is the radius of the electron’s lowest-energy orbit.

Hydrogen atom: The simplest atom, consisting of one proton and one electron. The Bohr radius sets the characteristic spatial scale of its ground state.
Planck constant: The fundamental constant that sets the scale of quantum action. It enters the Bohr radius squared in the numerator.
Radial distribution function: A probability density describing how likely a particle is to lie at a given distance from an origin. For hydrogen’s ground state, its most probable radius is one Bohr radius.
Classical electron radius: A length derived by equating an electron’s electrostatic self-energy with its rest energy. It is much smaller and does not represent an electron’s orbital size.
Bohr model: A model of hydrogen that assigns electrons quantized circular orbits around the nucleus. It treats the Bohr radius as the radius of the lowest-energy orbit.
Vacuum permittivity: A physical constant that characterizes electric fields in vacuum. It appears in the Coulomb interaction used to derive the radius.
Hydrogen-like atom: An atom or ion with one electron bound to a nucleus of charge Z. Its orbital length scale is the Bohr radius divided by Z, with reduced-mass correction.
Compton wavelength: The wavelength associated with a particle’s momentum scale, defined from Planck’s constant and its mass. The electron’s Compton wavelength is smaller than the Bohr radius by the fine-structure constant.
Coulomb potential: The electrostatic potential energy between charged particles, varying inversely with their separation. Its attraction between proton and electron helps determine the characteristic length.
Electron mass: The rest mass of an electron, approximately 9.11 × 10⁻³¹ kilograms. It appears in the denominator of the standard Bohr-radius formula.

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ÅngströmCompared with: This atomic-scale constant is a physical length, unlike the defined unit ångström.