To determine the empirical formula of manganese oxide, we need to know the relative proportions of manganese and oxygen in the compound. This information can be obtained through elemental analysis, which involves measuring the masses of each element present in the compound.

Let's assume that we have a sample of manganese oxide and we perform elemental analysis on it. The results show that the sample contains 43.45% manganese and 56.55% oxygen by mass.

To calculate the empirical formula, we need to convert these mass percentages to mole fractions. We can do this by dividing the mass of each element by its respective atomic mass and then dividing by the sum of these values:

Mole fraction of manganese (Mn) = (43.45 g / 54.94 g/mol) / (43.45 g / 54.94 g/mol + 56.55 g / 16.00 g/mol) = 0.474

Mole fraction of oxygen (O) = (56.55 g / 16.00 g/mol) / (43.45 g / 54.94 g/mol + 56.55 g / 16.00 g/mol) = 0.526

Next, we need to simplify the mole fractions to the simplest whole-number ratio. To do this, we can divide both mole fractions by the smallest mole fraction:

Simplified mole fraction of manganese (Mn) = 0.474 / 0.474 = 1

Simplified mole fraction of oxygen (O) = 0.526 / 0.474 = 1.11

Since the simplified mole fractions are close to whole numbers of 1 and 1, the empirical formula for manganese oxide is approximately MnO.

Therefore, the empirical formula for manganese oxide is MnO.