Step 1: Understanding nucleophilicity.
Nucleophilicity refers to the ability of a species to donate a pair of electrons to form a bond with an electrophile. It depends on the species' electron density and size. More negatively charged and less electronegative species are generally better nucleophiles.
Step 2: Analyze the options.
- \( \text{F}^- \): Fluoride ion is highly electronegative and its electron density is tightly held, making it a weaker nucleophile.
- \( \text{OH}^- \): Hydroxide ion is a good nucleophile, but not the strongest among the given options.
- \( \text{CH}_3^- \): The methyl anion (\( \text{CH}_3^- \)) is a very strong nucleophile because the negative charge is localized on a small, less electronegative carbon atom.
- \( \text{NH}_2^- \): The amide anion (\( \text{NH}_2^- \)) is a good nucleophile, but not as good as the methyl anion.
Step 3: Conclusion.
The correct answer is (3), \( \text{CH}_3^- \), as it is the most nucleophilic species among the options.