Final answer:
The orbital diagram for cobalt's ground state arranges electrons based on Hund's rule and the Pauli exclusion principle, with a [Ar] 3d7 4s2 electron configuration indicating five singly occupied 3d orbitals and two with paired electrons, as well as a full 4s orbital.
Step-by-step explanation:
To draw the orbital diagram for the ground state of cobalt, which has the electron configuration [Ar] 3d7 4s2, we should visualize each orbital and the distribution of electrons within them according to Hund's rule and the Pauli exclusion principle.
In the 4s subshell, we have two electrons that can be paired in one orbital box. For the 3d subshell, which can hold up to 10 electrons, we have 7 electrons. Following Hund's rule, these electrons will occupy the five 3d orbitals in a way that maximizes the number of unpaired electrons by filling them singly before any pairing occurs. An exception is made for chromium and copper, but cobalt falls into the regular filling rule. Therefore, the first five orbitals will each have one electron, and then the remaining two electrons will pair up in two of the three singly occupied orbitals.
Here's the sequence of filling: [Ar] (3d with singly filled five orbitals and two paired in the sixth and seventh orbitals) (4s with one pair of electrons).