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This research demonstrates connections between Bohr's atomic model and energy efficiency in electron behavior, suggesting educational implications.
Bohr’s atomic model, though superseded by quantum mechanics, retains pedagogical value for its intuitive picture of quantized orbits.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.
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Hongpu Yang (2026) studied this question.
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