I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I $$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$ n^2 * ħ^2$$ was substituted for## L^2 ##on top so it just becomes $$E rot = (n^2 * ħ^2) / 2 I $$ It was then stated that for a given mass, because the Moment of inertia grows with the radius squared, then the smaller a particle (such as an electron) then the larger the energy require to rotationally excite it. What I don't understand is why is " I " substituted to quantized energy in the numerator but left in the denominator? Then conceptually, how can a smaller radius of a particle require more energy to spin? This goes against the classical metaphor and confuses me. Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Rotational excitation of quantum particle

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