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(a) It is because their d-orbitals are incompletely filled.
(b) Eo[Zn/Zn2+] is negative because of the conversion of
gives it a filled d5 configuration which is very stable whereas, conversion of Cu to Cu2+ does not give any extra stabity, hence it has positive Eo value.
(c)This is because in case of oxygen, Mn forms pπ-dπ multiple bonding using 2p orbitals of oxygen and 3d orbitals of Mn.
With F, Mn shows +4 because of the single bond formation caused by the unavailability of 2p orbitals in F for multiple bonding.