Chapter 45: The Hydrogen Atom: Bohr Radius and Rydberg Constant

Hydrogen is the simplest atom and the first co-rotor system built from the nuclear modes of Part V. In Category τ, the hydrogen atom is not “a proton plus an electron”: it is a single torus τ² carrying two coupled bulk modes—proton core and electron orbit. This chapter derives the ground state, the Bohr radius a₀, the Rydberg constant R_∞, and the complete electromagnetic calibration cascade from τ³ → (M, L, ℏ) → (α, a₀, R_∞, c). Ionisation is reinterpreted as a surface transition on T², not the escape of a particle.