A 3d series transition metal M exhibits an exceptionally high positive E ^ ( M ³⁺ / M ²⁺ ) value because its M ²⁺ ion attains a stable half-filled d -subshell. The spin-only magnetic moment of the M ³⁺ ion in aqueous solution is approximately:

Step-by-step solution

The metal M belongs to the 3d series. Its M ²⁺ ion has a stable half-filled d -subshell, which means the electronic configuration of M ²⁺ is [ Ar ] 3d^5 . This identifies the metal M as Manganese ( Mn ), which has a ground state configuration of [ Ar ] 3d^5 4s^2 . The question asks for the spin-only magnetic moment of the M ³⁺ ion ( Mn ³⁺ ). The electronic configuration of Mn ³⁺ is [ Ar ] 3d^4 . The number of unpaired electrons ( n ) in Mn ³⁺ is 4 . The spin-only magnetic moment ( ) is calculated as: = n(n+2) = 4(4