Identify the atomic number of barium (Ba), which is 56. This tells us the total number of electrons to place in the electron configuration.
Recall the order of filling electron orbitals based on the Aufbau principle, which generally follows the sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, and so on.
Start filling the orbitals with electrons according to their capacities (s holds 2, p holds 6, d holds 10, f holds 14) until you reach 56 electrons in total.
Check the given options and compare their electron configurations to the expected filling order and total electron count for barium.
Confirm that the correct configuration ends with 6s^2 after filling up to 5p^6, since barium's electrons fill up to the 6s orbital after xenon core ([Xe]) configuration.