The number of unpaired electrons in an atom of cobalt in its ground state can be determined using its electron configuration. The electron configuration of cobalt (Co) is:

[Ar] 3d^7 4s^2

In this configuration, the 3d orbitals are partially filled. The 3d orbitals consist of five degenerate orbitals, and the seven electrons in cobalt's 3d orbitals distribute among these orbitals in a way that minimizes the electron-electron repulsion.

According to Hund's rule, electrons in the same orbital tend to have the same spin, but with the maximum possible spin multiplicity. In other words, electrons will occupy degenerate orbitals singly before pairing up.

In cobalt's case, the seven 3d electrons occupy the five 3d orbitals, with four of the electrons having their spins aligned in one direction (spin-up) and the remaining three electrons having their spins aligned in the opposite direction (spin-down).

Therefore, an atom of cobalt in its ground state has three unpaired electrons.