In an S N1 reaction of alkyl halide on chiral centres there is inversion more than retention to partial racemization.
A mix of retention and inversion occurs in SN1 mechanism. In case of optically active alkyl halides. SN1 reaction is followed by racemisation. The carbocation formed in the slow step being sp2 hybridised is planar and attack of nucleophile may take place from either side resulting in a mixture of products, one having the same configuration and other having inverted configuration.