Step 1: Understanding the reaction type.
This reaction involves the substitution of the bromine atom in \( \text{C}_2\text{H}_5\text{Br} \) with the hydroxide ion (OH⁻), which is a nucleophile. The reaction is a typical example of nucleophilic substitution.
Step 2: Analysis of options.
(A) Electrophilic substitution: This is incorrect because electrophilic substitution involves an electrophile, and the reaction here involves a nucleophile.
(B) Nucleophilic substitution: Correct — The hydroxide ion (OH⁻) is a nucleophile that replaces the bromine atom.
(C) Both (A) and (B): This is incorrect because the reaction is clearly nucleophilic substitution, not electrophilic.
(D) None of these: This is incorrect because (B) is the correct answer.
Step 3: Conclusion.
The correct answer is (B) because the reaction is a nucleophilic substitution where the nucleophile (OH⁻) replaces the leaving group (Br⁻).