Given,
Oxide ions occupy [tex]\frac{1}{2}[/tex] octahedral and [tex]\frac{1}{2}[/tex] tetrahedral voids.
To Find,
The formula of the oxide.
Solution,
We can solve this mathematical problem using mathematical formulas.
Total Octahedral voids = 4
Total Tetraherdal voids = 4
Let Metal ion of ccp = Metal ion of fcc = x
Number of Octahedral voids = x
Number of Tetrahedral voids = 2x
According to question,
Octahedral voids = x = 4 × [tex]\frac{1}{2}[/tex] = 2
Tetrahedral voids = 2x = 2 × 4 × [tex]\frac{1}{2}[/tex] = 4
So, Total number of oxides = Number of Octahedral + Number of Tetrahedral.
⇒ 2 + 4 = 6
Formula for oxide = M₄O₆
Further simplification ⇒ M₂O₃
Hence, The formula of the oxide is M₂O₃.