In SN1 reaction, the racemisation takes place due to:
Both a and b
In the 1st step of mechanism a carbocation is formed which is planar .Therefore the nucleophile can attack the carbocation from both the sides. When a nucleophile attacks the carbocation from the side where initially halogen was there,the product with retention in configuration is produce and when nucleophile attacks the carbocation from backside, the product with inversion in configuration is produce. Hence 50% of the product will be with retention in configuration and rest 50% will be with inversion in configuration. This produces a racemic mixture which is optically inactive.