Reaction:

${\mathrm{CH}}_3\mathrm{Br}\stackrel{\mathrm{Nu}-}{\to }$

Order of reactivity of nucleophile:

OH^-, CH₃COO^-, PhO^-, ClO₄^-

Correct Answer:
The correct order of reactivity of the nucleophiles is OH^- > PhO^- > CH₃COO^- > ClO₄^-.

Step-by-Step Explanation:

1. Understanding the Reaction Type:
The given reaction is the nucleophilic substitution of methyl bromide:

${\mathrm{CH}}_3\mathrm{Br}+{\mathrm{Nu}}^{-}\to {\mathrm{CH}}_3\mathrm{Nu}+{\mathrm{Br}}^{-}$

Since methyl bromide is an unhindered primary alkyl halide, the reaction proceeds via an S_N2 mechanism. In an S_N2 reaction, the rate depends directly on the nucleophilicity of the attacking nucleophile (Nu^-).

2. Relation Between Nucleophilicity and Resonance Stabilization:
All four given nucleophiles (OH^-, PhO^-, CH₃COO^-, ClO₄^-) carry a negative charge on an oxygen atom. When the nucleophilic atom is the same (oxygen), nucleophilicity generally parallels basicity.
A stronger base holds its electron pair less tightly and is more readily available to donate to the carbon atom. Conversely, if the negative charge on the oxygen atom is stabilized by resonance or strong inductive effects, the electron density on oxygen decreases, making it a weaker base and a poorer nucleophile.

3. Analyzing the Electron Density on Oxygen for Each Ion:

• OH^- (Hydroxide ion): The negative charge is localized entirely on a single oxygen atom with no resonance stabilization. Hence, it has the highest electron density, making it the strongest base and the most reactive nucleophile in this series.

• PhO^- (Phenoxide ion): The negative charge on oxygen is delocalized over the aromatic benzene ring through resonance. This reduces the negative charge density on oxygen compared to OH^-, making it less reactive than OH^-.

• CH₃COO^- (Acetate ion): The negative charge is delocalized over two electronegative oxygen atoms through resonance. Resonance stabilization between two equivalent oxygen atoms is stronger than aromatic delocalization in phenoxide, making acetate a weaker nucleophile than phenoxide.

• ClO₄^- (Perchlorate ion): The negative charge is delocalized over four highly electronegative oxygen atoms via resonance. Due to extreme resonance stabilization and powerful electron-withdrawing effects, ClO₄^- is the conjugate base of a superacid (HClO₄). It has extremely low electron density on its oxygen atoms, making it an exceptionally weak base and the least reactive nucleophile.

4. Conclusion:
Comparing the extent of charge delocalization, the nucleophilicity order decreases as resonance stabilization increases:
OH^- > PhO^- > CH₃COO^- > ClO₄^-