Discussion
A non-linear molecule of N atoms has how many fundamental vibrational modes?
Answer: A
Correct answer: \( 3N - 6 \)
A molecule of \( N \) atoms has \( 3N \) degrees of freedom. Three are taken by translation of the whole molecule and three by rotation about its principal axes, leaving
\[ 3N - 6 \]vibrational modes. A linear molecule has only two rotational degrees of freedom, since rotation about the molecular axis moves nothing, so it has \( 3N - 5 \) vibrations instead.
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