Which of the following is an optically active compound?

The correct answer is option 2. 

The structure ans names of the given compounds are :

An optically active compound is a molecule that can exist in two non-superimposable mirror image forms called enantiomers. These mirror images have the same chemical formula and bonding but differ in the spatial arrangement of their atoms.

For a molecule to be optically active, it requires a chiral center. A chiral center is a carbon atom that has four different substituents attached to it.

Let us analyze each option:

Pentan-2-ol: This molecule has two chiral centers. However, it also has a plane of symmetry. Molecules with a plane of symmetry can superimpose on their mirror image and are therefore achiral (not optically active).

3-methylhexan-3-ol: This molecule has a chiral center at the third carbon atom. The four substituents around this carbon are different (H, CH₃, CH₂CH₂CH₃, and OH). Since there is no plane of symmetry, this molecule can exist in two non-superimposable mirror images, making it optically active.

4-methylheptane: This molecule only has primary carbon atoms (bonded to four different substituents). Primary carbon atoms cannot be chiral centers. Therefore, the molecule is achiral.

5,5-dimethylnonane: Similar to option 3, both central carbon atoms are bonded to four identical substituents (two methyl groups each). These carbons cannot be chiral centers, making the molecule achiral.

Therefore, only 3-methylhexan-3-ol possesses a chiral center and lacks a plane of symmetry, fulfilling the requirements for an optically active compound.