For an SN\(_1\) reaction, the reactivity is influenced by the stability of the carbocation formed during the reaction. The order of reactivity follows the trend: allyl>benzyl>primary.
Let’s analyze the compounds:
- Compound A, C\(_6\)H\(_5\)CH\(_2\)Cl: The benzyl chloride undergoes SN\(_1\) easily due to the resonance stabilization of the benzyl carbocation. It is highly reactive.
- Compound B, C\(_6\)H\(_5\)Cl: This is a simple aryl chloride, and the carbocation formed is not stabilized by resonance as in the case of benzyl chloride, so it is less reactive.
- Compound C, CH\(_2\)=CH–Cl: This is an allyl chloride, which can form a resonance-stabilized carbocation. However, the double bond conjugation decreases its reactivity compared to benzyl chloride.
- Compound D, CH\(_3\)–CH\(_2\)–Cl: This is a primary alkyl chloride, and it forms a primary carbocation, which is the least stable, hence the least reactive. Thus, the order of reactivity towards SN\(_1\) is: \[ B<D<C<A \]
If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are $ a $, $ b $, and $ c $ respectively, then the corresponding ratio of increase in their lengths would be: