The correct option is D Rate depends on R-X
Polar protic solvent solvates the halide ion formed due to C-X bond breaking. Therefore, polar protic solvent favours the SN1 reaction.
The nucleophile is not involved in the RDS in SN1 reaction. thus it does not affect the rate of SN1 reaction.
However, a stronger nucleophile may lead to side reactions. So, weak & moderate nucleophiles are preferred.
Rate of the reaction ∝[R−X]1[Nu]0
Hence correct option is d.