Deriving the Bohr radius

The Bohr radius is the size of the hydrogen atom's ground-state orbit, about 0.0529 nanometers. Standard quantum mechanics obtains it by solving the Schrödinger equation. RSI proposes a mechanical derivation that needs two ingredients.

The first is the electron's topological footprint, its reduced Compton wavelength of about 3.861 × 10⁻¹³ m. The second is the proton's acoustic broadcast frequency. Because the atom's phase-lock regulates that broadcast, RSI holds that the proton broadcasts at the 137-Escapement, the inverse fine structure constant of about 137.036. The first resonant Acoustic Valley (n = 1) forms where this standing wave meshes with the electron's footprint. Multiplying the two values gives 5.29 × 10⁻¹¹ m, the Bohr radius.

The outer shells (n = 2, n = 3) follow the Bohr scaling rₙ = n²a₀, and their energies reproduce the Rydberg formula for spectral lines, 1/λ = R(1/n₁² − 1/n₂²). Deriving that n² spacing from the medium's standing waves is still to be done.