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(1) As Asymmetrical ketones, that group migrate which is better able to supply electron (ERG). Thus order of ease of migration is ….
The substituent’s which can stabilize the positive charge can migrate readily. The migratory aptitude of various substituents is approximately:
3o-Alkyl > Cyclohexyl > 2o- Alkyl > Benzyl > Aryl > 1o - Alkyl > Methyl
(2) The electron withdrawing groups (-I groups) on peroxy acids enhance the rate of the reaction.
(3) As the rearrangement is a concerted process, the configuration of the migrating chiral substituent is retained.
(4) In case of aldehydes, usually the hydrogen atom is migrated preferentially and thus by furnishing carboxylic acids. But formates are also produced when the migrating group is other than the hydrogen. This is possible when the other substituent is a tertiary alkyl group or electron rich vinyl or aryl group.
    -H > 3o-Alkyl > 2o- Alkyl > Benzyl > Aryl > 1o - Alkyl > Methyl
(5) One of the competing reactions is the formation of epoxide when a double bond is present in the molecule especially at low temperatures in neutral solvents.

(6) The aldehyde is oxidized to formate due to preferential migration of aryl group. But it undergoes hydrolysis under the reaction conditions to yield a phenol.
(7) As illustrated below, the aldehyde group is oxidized to carboxylic acid due to preferential migration of the hydride ion. The aryl group with electronegative halogen groups has less migratory aptitude. Remember the groups which can stabilize positive charge possess greater migratory aptitude.
(8) The greater migratory aptitude of aryl group over the -CH2 group can be observed in the following example.
(9) The -CH2 group is migrated preferentially in the following reaction. The -CH-CF3 group has less migratory aptitude due to electron withdrawing nature.
(10) The lactone formed can be reduced to a dihydric alcohol.

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