Final answer:
The IUPAC name for Mn(BrO₂)₂ is manganese(II) bromite, where manganese has a +2 oxidation state and 'bromite' is the name of the BrO₂ anion.
Step-by-step explanation:
The correct IUPAC name for Mn(BrO₂)₂ is manganese(II) bromite. In this compound, manganese has a +2 oxidation state, indicated by the roman numeral II. The anion BrO₂ is named bromite, which is the polyatomic ion with a single bromine atom and two oxygen atoms. While naming such compounds according to IUPAC conventions, the cation is named first followed by the anion with appropriate oxidation numbers provided for the transition metals.
When naming ionic compounds with polyatomic ions, the cation's name (here manganese) is followed by its oxidation state in parentheses. Next, the name of the anion (bromite) is written. Since there are two bromite ions, the numeral II within the parenthesis after manganese indicates the oxidation state or the valency of manganese, which balances the charge from the two bromite ions.