Constraining the Electron: From Bohr's Atom to Energy-Efficiency Theory

Bohr’s atomic model, though superseded by quantum mechanics, retains pedagogical value for its intuitive picture of quantized orbits. This paper reinterprets Bohr’s model within Energy-Efficiency Theory (EET), revealing its deep connection to the energy ratio η = E˙ resp/E˙ main. We show that the principal quantum numbern corresponds to the inverse square of η: ηn ∝ 1/n2 . In the ground state (n = 1), η ≪ 1, and the electron is particle-like; in highly excited states (n ≫ 1), η approaches 1, and the electron becomes wave-like. This provides a continuous picture of the transition from quantum to classical behavior, and offers a pedagogical bridge from Bohr’s model to modern quantum theory.