Discussion
How many fundamental vibrations does a non-linear molecule of \( N \) atoms have?
Answer: C
Of the three degrees of freedom per atom, three describe translation and three rotation, leaving 3N minus 6 vibrational modes. A linear molecule has only two rotational degrees of freedom and so has 3N minus 5. Counting the modes tells you how many bands to expect at most, though degeneracy, inactivity and overlap always reduce the number actually seen.
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