Final answer:
The correct chemical formula for barium oxide is BaO, resulting from the +2 oxidation state of barium, in accordance with its position as an alkaline earth metal, balancing the -2 oxidation state of oxygen.
Step-by-step explanation:
The chemical formula for barium oxide, given the oxidation numbers of barium as +2 and oxygen as -2, is BaO. To determine the formula, the total positive oxidation number must balance out the total negative oxidation number. Since barium has an oxidation number of +2 (not +4 as was initially stated in the question) and oxygen has an oxidation number of -2, one barium ion will balance with one oxygen ion, which leads to the chemical formula BaO.
Barium typically exhibits a +2 oxidation state, which corresponds to its group 2 (alkaline earth metals) position on the periodic table. Thus, the provided oxidation state of +4 for barium seems to be a typo or a mistake in the question.