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No, an $"S"_"N"1$ reaction involves two steps.

In a typical nucleophilic substitution reaction, a nucleophile Nu⁻ attacks a substrate R-LG.

Nu⁻ + R-LG → Nu-R + LG⁻

The leaving group LG departs, and the Nu replaces (substitutes) it in the substrate.

An $"S"_"N"1$ substitution reaction consists of two steps.

Step 1: Loss of the leaving group, LG, to generate a carbocation intermediate.

R-LG → R⁺ + LG⁻

Step 2: Attack of the nucleophile on the electrophilic carbocation to form a new σ bond

Nu⁻ + R⁺ → Nu-R

Step 1 is the rate determining step. Only the substrate is involved in this step, so this is a unimolecular reaction.

$"S"_"N"1$ means substitution, nucleophilic, unimolecular.

The "1" in $"S"_"N"1$ does not refer to the number of steps.

An $"S"_"N"1$ substitution is a two-step reaction.