![]() ![]() Here we have four obvious principal axes: only possible if What about a symmetrical three dimensional molecule? The moment of inertial about either of theseĪxes will be one-half that about the perpendicular-to-the-plane axis. Obviously, one principal axis is through the centroid,Įstablished that any axis of symmetry is a principal axis, so there areĮvidently three principal axes in the plane, one along each bond! The only interpretation is that there is aĭegeneracy: there are two equal-value principal axes in the plane, and any two Lowest angular momentum state E = L 2 / 2 I = ℏ 2 / 2 I , is lower for molecules with bigger moments of This was not the case for heavier diatomic gases, since the energy of the Was so low that a lot of energy was needed to excite the first quantized The resolution was that the moment of inertia ![]() Though they constantly collided with each other. Temperatures, apparently these diatomic molecules didn’t spin around, even Which gave an excellent account of the specific heats of almost all gases, ![]() In the nineteenth century, the mystery was that equipartition of energy, Two point masses m a fixed distance a apart gives I = 1 2 m a 2. The moment of inertia of the hydrogen molecule wasįind: the nuclei (protons) have 99.95% of the mass, so a classical picture of Michael Fowler Examples of Moments of Inertia Molecules
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