In an SN1 reaction on chiral  centres,  there is

In case of optically active alkyl halides, SN1 reaction is accompanied by racemisation. The carbocation formed in the slow step being sp2hybridised 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 SN1 also depends upon the degree of shielding of the front side of the reacting carbon.