The correct IUPAC name of $$K_2MnO_4$$ is:

We need to find the correct IUPAC name of $$K_2MnO_4$$. To do this, we first determine the oxidation state of manganese by letting it be $$x$$ and solving the equation $$2(+1) + x + 4(-2) = 0$$. Simplifying, we get $$2 + x - 8 = 0$$, so $$x = +6$$, which means manganese is in the +6 oxidation state.

Next, we apply the modern IUPAC 2005 nomenclature rules for oxoanions. The cation is named first as potassium, with no prefix for quantity because its stoichiometry is clear. For the anion $$MnO_4^{2-}$$, the name is formed by stating the number and type of ligands (four oxide ligands become tetraoxido), followed by the metal name with an -ate suffix (manganate), and then the oxidation state in Roman numerals (VI).

Putting these parts together, the IUPAC name of $$K_2MnO_4$$ is Potassium tetraoxidomanganate(VI). Option 1 is incorrect because it uses “tetraoxo” and “permanganate,” Option 3 is wrong in stating the oxidation state as VII, and Option 4 incorrectly uses “manganese” instead of “manganate.” Therefore, the correct answer is Option 2: Potassium tetraoxidomanganate(VI).