In an $S_{N}1$ reaction on chiral  centres,  there is

In case of optically active alkyl halides, $S_{N}1$ reaction is accompanied by racemisation. The carbocation formed in the slow step being $s{p}^2$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. The isomer corresponding to inversion is present in slight excess because $S_{N}1$ also depends upon the degree of shielding of the front side of the reacting carbon.