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Protonation followed by Nucleophilic addition is the process.
Explanation:
The reactant is tertiary butyl methyl ether.
The reagent is hydrogen bromide.
The hydrogen bromide undergoes heterolytic fission.
It produces bromide and a Proton.
This Proton attacks the oxygen of ether to produce a hydronium intermediate.
This intermediate then undergoes heterolytic cleavage to produce methanol and tertiary butyl cation.
This tertiary butyl cation is then attacked by bromide ion to produce the tertiary butyl bromide.
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