Question

The number of normal modes of vibration in benzene is _ _ _. (answer in integer)

Hint:

For linear molecules use $3N-5$, while for non-linear molecules use $3N-6$ normal vibrational modes

Answer 1

Correct Answer: 30

Step 1: Identify type of molecule.
Benzene is a non-linear molecule because its atoms are arranged in a planar ring structure

Step 2: Count total atoms in benzene.
Benzene has formula C$_6$H$_6$
\[ N = 6 + 6 = 12 \]

Step 3: Use formula for non-linear molecule.
For a non-linear molecule, number of normal modes of vibration is
\[ 3N - 6 \]

Step 4: Substitute value of N.
\[ 3N - 6 = 3(12) - 6 \]
\[ = 36 - 6 \]
\[ = 30 \]

Step 5: Conclusion.
\[ \boxed{30} \]