In metal oxide, the oxide ions are arranged in corners as well as on face centers and metal cation occupy $\frac{2}{3}$ of tetrahedral voids. What is the formula of the compound?

M₄O₃

The correct answer is option 4. M₄O₃.

Number of oxide ions (O) = $\frac{1}{8}$ x 8 + $\frac{1}{2}$ x 6 = 1 + 3 = 4

Number of metal cations (M) = $\frac{2}{3}$ x T-voids = $\frac{2}{3}$ x 8 = $\frac{16}{3}$

M : O = $\frac{16}{3}$ : 4

M : O = 16 : 12

or M : O = 4 : 3

Hence, the formula of the compound is M₄O₃.