Consider the model of a diatomic gas sodium (Na,) shown in the figure. atom Rigid connector (massless) atom (a) Assuming the atoms are point particles separated by a distance of 0.31 nm, find the rotational inertia I, (in kg · m²) for rotation about the x-axis. kg - m2 (b) Now compute the rotational inertia (in kg - m2) 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 3.40 x 10-1s m. kg - m2 (c) Compute the rotational energy (in J) associated with the first (f = 1) quantum level for a rotation about the x-axis.

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Consider the model of a diatomic gas sodium (Na,) shown in the figure.
atom
`Rigid connector
(massless)
atom
(a) Assuming the atoms are point particles separated by a distance of 0.31 nm, find the rotational inertia I, (in kg · m²) for rotation about the
x-axis.
kg - m2
(b) Now compute the rotational inertia (in kg - m2) 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 3.40 x 10-15 m.
kg - m2
(c) Compute the rotational energy (in J) 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.
Transcribed Image Text:Consider the model of a diatomic gas sodium (Na,) shown in the figure. atom `Rigid connector (massless) atom (a) Assuming the atoms are point particles separated by a distance of 0.31 nm, find the rotational inertia I, (in kg · m²) for rotation about the x-axis. kg - m2 (b) Now compute the rotational inertia (in kg - m2) 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 3.40 x 10-15 m. kg - m2 (c) Compute the rotational energy (in J) 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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