Why –(-) butan- 2 -ol is optically inactive ?

The compound you mentioned is (–)-butan-2-ol, which is also known as (S)-butan-2-ol. The reason for its optical inactivity is due to the presence of a plane of symmetry. Optical activity in a molecule is related to its chirality, and a chiral molecule lacks a plane of symmetry.

In (–)-butan-2-ol, the carbon atom with the hydroxyl group (OH) is attached to four different substituents (H, CH3, CH2CH3, and CH2OH). However, the molecule overall has a plane of symmetry, which divides it into two mirror-image halves. This plane of symmetry allows the molecule to be superimposed on its mirror image, making it achiral and optically inactive.

In general, a molecule is optically active if it is chiral (lacks a plane of symmetry) and has no internal symmetry elements. If a molecule has a plane of symmetry or other internal symmetry elements, it is considered achiral and optically inactive.