The correct order of relative reactivity of alkyl halides towards \(S_N1\) reaction is:

(I) \(PhCH_2Cl\)       (II) \(Ph_2CHCl\)       (III) \(Ph_3C-Cl\)

III > II > I

The correct answer is option 3. III > II > I.

The \(S_N1\) reaction involves a two-step process:

1. Formation of Carbocation: The leaving group departs, leaving behind a positively charged carbon known as a carbocation. The rate-determining step is the formation of this carbocation intermediate.

2. Nucleophilic Attack: A nucleophile then attacks the carbocation to complete the substitution.

The stability of the carbocation intermediate is crucial in determining the overall reactivity. Carbocations are stabilized by adjacent alkyl groups through a phenomenon called hyperconjugation. More alkyl groups adjacent to the positively charged carbon lead to greater stability.

In \(S_N1\) reactions (substitution nucleophilic unimolecular), the rate-determining step involves the formation of a carbocation intermediate. The stability of the carbocation intermediate is crucial in determining the overall reactivity. Carbocations are stabilized by adjacent alkyl or aryl groups through a phenomenon called hyperconjugation. More alkyl or aryl groups adjacent to the positively charged carbon lead to greater stability. The stability of the carbocation significantly influences the reaction rate. The general order of carbocation stability is:

\(\text{tertiary} > \text{secondary} > \text{primary} > \text{methyl} \)

Now, let us analyze each alkyl halide given:

(I) \(PhCH_2Cl\) - This is a primary alkyl halide, and the carbocation formed would be a primary carbocation. Primary carbocations are less stable than secondary or tertiary carbocations.

(II) \(Ph_2CHCl\) - This is a secondary alkyl halide. The carbocation formed would be a secondary carbocation, which is more stable than a primary carbocation but less stable than a tertiary carbocation.

(III) \(Ph_3C-Cl\) - This is a tertiary alkyl halide. The carbocation formed would be a tertiary carbocation, which is the most stable among the three options.

Based on the carbocation stability order, the relative reactivity in \(S_N1\) reactions is:

\(\text{III > II > I}\)

So, the correct order of relative reactivity of alkyl halides towards \(S_N1\) reaction is: 3. III > II > I