Explain the mechanism of a unimolecular nucleophilic substitution $(S_N1)$ reaction with a suitable example.

(N/A) The $S_N1$ reaction between tert-butyl bromide and hydroxide ion $(OH^-)$ yields tert-butyl alcohol.
$(CH_3)_3C-Br + OH^- \longrightarrow (CH_3)_3C-OH + Br^-$
Characteristics of $S_N1$ reaction:
$(a)$ Unimolecular kinetics: The rate of reaction depends only on the concentration of the substrate,tert-butyl bromide.
$(b)$ Nucleophilic substitution: The leaving group $Br^-$ is replaced by the nucleophile $OH^-$.
$(c)$ Two-step process: $S_N1$ reactions proceed in two steps.
Step $I$ (Slow step): The $C-Br$ bond undergoes heterolytic cleavage to form a carbocation $(CH_3)_3C^+$ and a bromide ion $Br^-$. This is the rate-determining step.
Step $II$ (Fast step): The nucleophile $OH^-$ attacks the carbocation to form the final product,tert-butyl alcohol.