Additional evidence for the halogenation mechanisms that we just presented comes from the following facts:
(a) Optically active 2-methyl-1-phenylbutan-1-one undergoes acid-catalyzed racemization at a rate exactly equivalent to the rate at which it undergoes acid- catalyzed halogenation.
(b) 2-Methyl-1-phenylbutan-1-one undergoes acid-catalyzed iodination at the same rate that it undergoes acid-catalyzed bromination.
(c) 2-Methyl-1- phenylbutan-1-one undergoes base-catalyzed hydrogen-deuterium exchange at the same rate that it undergoes base-promoted halogenation. Explain how each of these observations supports the mechanisms that we have presented.