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The oxidation number of Cobalt in the complex ion `[Co(CN)_6]^(3-)` is +3.
Originally, Cobalt has the electronic configuration of [Ar]3d74s2,
It loses three of its outermost electrons to produce `Co^(3+)` , which has the electronic configuration of [Ar]3d6.
The complex ion `[Co(CN)_6]^(3-)` is octahedral. During its formation, owing to the effect of the field created by six negatively charged incoming ligands from the direction of six corners of a regular octahedron, the d-orbitals of Co3+ ion is supposed to undergo further splitting, giving it a `t_(2g)-e_g` type of splitting. This requies the degeneracy of five d-orbitals wil be lifted and two new sets of degenerate d-orbitals will result; one lower, `t_(2g)` , containing theree orbitals, and the other higher, possessing two orbitals, named `e_g` .
In the given example, though, scanning through the number of electrons in d-orbitals only gives a clue about the correct answer without going into further niceties. Out of the given options, only option A has six electrons in the d-orbital set, therefore, this is the correct answer.
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