Final answer:
The ground state electron configuration of manganese, using the building-up principle, is written as [Ar] 3d5 4s2.
Step-by-step explanation:
To obtain the electron configuration of the ground state of manganese using the building-up (Aufbau) principle, we follow the sequence of increasing energy of atomic sublevels. Manganese has an atomic number of 25, which means it has 25 electrons in its neutral ground state.
Starting from the first shell and moving up, we fill the 1s, 2s, 2p, 3s, 3p, and 4s sublevels, which are lower in energy compared to the 3d sublevel. The electron configuration for manganese is therefore: [Ar] 3d5 4s2. This notation indicates that the first two electrons occupy the 4s sublevel.
The core of argon configuration and that the next five electrons are in the 3d sublevel. For manganese, the 4s sublevel is filled before starting to fill the 3d sublevel even though the 3d comes after the 4s in the periodic table, due to the particular arrangement of orbital energies.