## Background

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.

In energy wave theory, this value is important as the wavelength count to the Bohr radius is the method for calculating transverse wavelengths and energies for the first orbital.

## Energy Wave Constants – Equivalent

The following is the representation of this fundamental physical constant expressed in energy wave theory. Using energy wave constants, its value was calculated and shown to match the known value in the Summary of Calculations table.

### Bohr Radius

The Bohr radius is based on the fine structure constant (α) and thus not required as a separate constant for the energy wave equations. However, for the purpose of equation readability, its symbol will be used here in this section.

The distance for the first orbital shell in hydrogen (Bohr radius) along with all the orbital shells of hydrogen were derived and calculated in the *Particle Energy and Interaction *paper. It can be modeled as the distance, in electron wavelengths (K), proportional to the square of the fine structure constant. To get the number of wavelengths (n) for the first orbital shell, the following is used:

**n _{1s}=**187,789 wavelengths

This provides the number of wavelengths from the atom’s core. However, the Bohr radius is measured in meters. It needs to be multiplied by the electron’s radius (K λ_{l}):

Since the fine structure constant is a derived term, it can be substituted above and the Bohr radius can be described completely in wave constants.

**Calculated Value**: 5.2918E-11

**Difference from CODATA:** 0.000%

**Calculated Units**: meters (m)

*The complete derivation of this constant is available in the Fundamental Physical Constants paper.*