Is someone going to answer the question that was asked?
Simply stating because "half-filled" and "completely filled" is more stable is not even an answer.
Atoms can't desire or want to be "filled" - that is anthropomorphistic (as stated by Ferdinand in the post above).
The "half filled" 3d orbital of Cr is more stable because the 4s energy level is close to the 3d energy levels - therefore moving electrons from the 4s energy level into the 3d minimizes the repulsion between the electrons, and entropy is favored (if the two electrons stay in the 4s there is more order).
I do not understand the "completely filled" state. I thought that the "+" charged nucleus of an atom (z effective) for a 4s is more "penetrating", which means that further away electrons (such as the 3d) are more shielded (by the spherical s shell electrons which block the "+" charge) and therefore "feels" less attraction towards the nucleus.
Why does Cu obtain an [Ar]4s^(1)3d^(10)? You can't use the entropy argument (or electron repulsion argument) any more because the electron would not favor either 4s or 3d more... and it seems that due to the 4s being more penetrating (closer to the "+" nucleus with less sheilding) that the electron would be more stablized to be in the 4s energy level?
Confused. ):