Consider the model of the diatomic gas oxygen (O2) shown in Figure 9.3. (a) Assuming the atoms are point particles separated by a distance of 121 pm, find the rotational inertia Ix for rotation about the x axis. (b) Now compute the rotational inertia of the molecule about the z axis, assuming almost all of the mass of each atom is in the nucleus, a nearly uniform solid sphere of radius 3.0 × 10-15 m. (c) Compute the rotational energy associated with the first (/ = 1) quantum level for a rotation about the x axis. (d) Using the energy you computed in (c), find the quantum number/ needed to reach that energy level with a rotation about the z axis. Comment on the result in light of what the equipartition theorem predicts for diatomic molecules.
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