(S)-3-Methylhexane undergoes radical bromination to yield optically inactive 3-bromo-3-methylhexane as the major product. Is the product chiral

No, the product is not chiral

Explanation:

The compound (S)-3-Methylhexane is chiral. However, the bromination of this compound via free radical mechanism yields an achiral intermediate as shown in the image attached to this answer.

This achiral intermediate is a flat and planar tertiary radical. Attack on either face of this radical specie is possible. This leads us to obtain a 50-50 mixture of (R) and (S) - 3-bromo-3-methylhexane.

This is a racemic mixture hence it is optically inactive.

the mantle

explanation:

earth is divided into three layers: the crust or the outermost layer on which we live; the underlying, middle layer - the mantle - and the core (the innermost layer of earth).