Question R13 Q18 - MIT Science Bowl 2022

Diatomic hydrogen can be modeled as two spherical protons with nonzero mass connected by a massless rod, where the length of the rod is much larger than the radii of the spheres. The equipartition theorem predicts that, on average, the thermal energy of rotation is the same for all three axes. However, only rotation about the two axes perpendicular to the rod is typically observed. Which of the following statements is the best explanation for this phenomenon?

W) The moment of inertia about the rod is much smaller, so the energy scale is comparatively small and difficult to observe

X) Protons are better modeled as point masses, so rotation about the rod has no effect

Y) The moment of inertia about the rod is much smaller, and quantization of angular momentum causes the lowest nonzero rotational energy level to be much larger than the thermal energy

Z) Rotation about the rod is much harder to observe experimentally due to the comparatively small size of the protons

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