Bohr Radius


Named after Niels Bohr, the Bohr radius is the most probable distance between an electron and proton in a hydrogen atom (ground state). The ground state is the lowest level of energy – the first orbital in the atom.  

The Bohr radius was derived in detail in the Atomic Orbitals paper.  It is based on a proposed pentaquark structure of the proton, where an alignment of particles in a proton creates a repelling force.  The pentaquark structure includes four electrons and a positron at high energies resembling quarks.  The positron has an attractive force (F1) on the electron.  There is a repelling force (F2) when the electron is aligned on an axis with two or more “quarks”.  This creates a probability function for the electron as it is only repelled when aligned at an axis.  The repelling force is strong near the core, increasing in wave amplitude at the square of the inverse fine structure constant after passing through two “quarks”, but then declining at the cube of distance.  This allows an orbital – a position where the attractive, Coulomb force (which declines at the square of distance) is equal to the repelling force.


Bohr Radius Explained



Derivation – Bohr Radius

The Bohr radius is based on the fine structure constant (α), which is the coupling constant for the strong force.  It is the first hint that orbitals are based on the strong force – creating a new orbital force.  The complete derivation is found in Atomic Orbitals by setting the electric force and the orbital force to be equal.


Classical Constant Form

Bohr Radius Derivation

Wave Constant Form

Bohr Radius Derivation Wave Constant Form

Using classical constants Using energy wave constants


Calculated Value: 5.2918E-11
Difference from CODATA: 0.000%
Calculated Units: meters (m)
G-Factor: gλ


Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.