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: \[ B<D<C<A \]
Arrange stability of the given carbon cation in decreasing order:
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: