benzyl ethyl ether on reaction with HI gives benzyl iodide and ethyl alcohol.. why not ethyl iodide and benzyl alcohol?

The reaction can be written as :
 
Reason for product: Primary and secondary alkyl ethers react by an SN2 mechanism, while tertiary, benzylic, and alicylic ethers cleave by an SN1 mechanism. Benzyl ethyl ether is a benzylic ether so the substitution will follow the SN1 path. The two carbocations are possible in rate determining step. Benzyl carbocation and ethyl carbocation. Out of these two, benzyl carbocation is more stabilised hence more favourable and will form benzyl iodide. Remaining ethoxide will form ethanol.

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