Explain the mechanism of `S_N1` reaction taking 2-bromo-2-methyl propane (t-butyl bromide)

Explanation

`S_(N)1` - Unimolecular nuclephilic substitution.
`CH_(3)-overset(CH_(3))overset("| ")underset(CH_(3))underset("| ")"C "-Br+KOH_((aq))rarr CH_(3)-overset(CH_(3))overset("| ")underset(CH_(3))underset("| ")"C "-OH+KBr`
The reaction follows first order kinetics and occurs in two steps.
Step 1 : - Br eliminates as leaving group and produce `3^(@)` carbocation.
`CH_(3)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)C-Br rarr CH_(3)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)Co++Br^(-)-"Slow step"`
Step 2 :- The nucleophile `OH^(-)` attacks the carbocation and forms t - butyl alcohol