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(B) The reaction of an alkyl halide with aqueous $AgNO_3$ proceeds via an $S_N1$ mechanism,where the rate-determining step is the formation of a carbo

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$N$-(Bromomethyl)piperidine

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(B) The reaction of an alkyl halide with aqueous $AgNO_3$ proceeds via an $S_N1$ mechanism,where the rate-determining step is the formation of a carbocation: $R-X + aq. AgNO_3 \xrightarrow{RDS} R^{\oplus} + AgX \downarrow (PPT)$.The rate of precipitate formation depends on the stability of the intermediate carbocation $(R^{\oplus})$.In the given options,the carbocations formed are:$(a)$ $CH_3CH_2-O-CH_2^{\oplus}$$(b)$ Piperidine ring attached to $CH_2^{\oplus}$ (stabilized by resonance from the nitrogen lone pair)$(c)$ $Ph-N(Et)-CH_2^{\oplus}$$(d)$ $p-MeO-C_6H_4-N(Et)-CH_2CH_2^{\oplus}$The carbocation in option $(b)$ is highly stabilized by the resonance effect of the nitrogen lone pair,making it the most stable among the choices. Therefore,$N$-(bromomethyl)piperidine forms the precipitate most readily.

Which of the following compounds will form the precipitate with aqueous $AgNO_3$ solution most readily?

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