?The potential energy of the rotation of one \(\mathrm{CH}_{3}\) group relative to its

Chapter 7, Problem P7E.16

(choose chapter or problem)

The potential energy of the rotation of one \(\mathrm{CH}_{3}\) group relative to its neighbour in ethane can be expressed as \(V(\phi)=V_{0} \cos 3 \phi\). Show that for small displacements the motion of the group is harmonic and derive an expression for the energy of excitation from v = 0 to v = 1. (Hint: Use a series expansion for \(\cos 3 \phi\).) What do you expect to happen to the energy levels and wavefunctions as the excitation increases to high quantum numbers?

Text Transcription:

CH_3

V(phi) = V_0 cos 3phi

cos 3phi

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