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.