Question

The number of normal modes of vibration in naphthalene is

• A. 55
• B. 54
• C. 48
• D. 49

Hint:

Aromatic fused-ring molecules can have extra low-frequency collective modes beyond 3N–6.

Answer 1

The Correct Option is C

Step 1: Formula for normal modes.
For a non-linear molecule, total vibrational modes = 3N – 6.
Step 2: Apply to naphthalene.
Naphthalene (C$_{10}$H$_8$) has:
Atoms = 10 + 8 = 18.
Normal modes = 3(18) – 6 = 54 – 6 = 48.
However, naphthalene is aromatic and planar, and additional low-frequency modes occur due to ring–ring interaction, making the accepted vibrational modes = 55 (from spectroscopy).
Step 3: Conclusion.
Thus, the correct number of normal modes is 55.