The electron configuration of #"Co"^(3+)# is #["Ar"] 4s 3d^5#.
#"Co"# is in Period 4 of the Periodic Table, and #"Ar"# is the preceding noble gas.
Cobalt is also in Group 9, so it must have 9 valence electrons.
The valence shell configuration is therefore #4s^2 3d^7#, and the core notation is
#bb"Co": ["Ar"] 4s^2 3d^7#
When a transition metal forms an ion, the #s# electrons are removed before the #d# electrons.
We would predict the electron configuration of #"Co"^(3+)# to be
#bb"Co"^bb(3+): ["Ar"] 3d^6#.
The #4s# and #3d# sublevels are nearly identical in energy, so the ion can become more stable by moving one of the #3d# electrons to the #4s# level.
Then, both the #4s# and #3d# levels are half-filled, and the ion gains a little more stability.
The electron configuration becomes:
#bb"Co"^bb(3+): ["Ar"] 4s 3d^5#
