In the compound MgAl2O4,the oxide ions are in fcc . if only the oxide ions of face centres are doped by the ion Y^-3 ,the formula of the oxide is (1)MgAl2O4 (2) MgAl2Y2O2 (3) MgAl2Y2O (4) Mg3Al6Y8g

To tackle this question, we first need to understand the structure of the compound MgAl2O4, commonly known as spinel. In this structure, oxide ions (O²⁻) are arranged in a face-centered cubic (fcc) lattice, and the magnesium (Mg²⁺) and aluminum (Al³⁺) ions occupy specific interstitial sites within this lattice. Now, when we consider doping the oxide ions at the face centers with Y³⁻ ions, we must analyze how this affects the overall formula of the compound.

Analyzing the Doping Process

In the original MgAl2O4 structure, there are a total of 4 oxide ions per formula unit, as the fcc arrangement contains 4 formula units of the oxide. When we replace some of these oxide ions with Y³⁻ ions, we need to maintain charge neutrality in the compound. The Y³⁻ ions will replace the O²⁻ ions at the face centers, which means we need to consider the implications of this substitution.

Charge Balance Considerations

Each Y³⁻ ion carries a -3 charge, while each O²⁻ ion carries a -2 charge. If we replace one O²⁻ with one Y³⁻, we are effectively increasing the negative charge by 1 unit (from -2 to -3). To maintain charge neutrality, we need to adjust the overall composition of the compound accordingly.

• Original charge from MgAl2O4: 2 (from 4 O²⁻) + 2 (from 2 Mg²⁺) + 6 (from 2 Al³⁺) = 10 (total positive charge)
• After doping with Y³⁻: The charge from Y³⁻ will need to be balanced by adjusting the number of Al³⁺ or Mg²⁺ ions, or by adding more oxide ions.

Determining the New Formula

When we replace the oxide ions with Y³⁻ ions, we can consider the following potential formulas:

• MgAl2O4: This is the original compound without any doping.
• MgAl2Y2O2: This suggests that we have two Y³⁻ ions replacing two O²⁻ ions, which would not balance the charge correctly.
• MgAl2Y2O: This implies that we have two Y³⁻ ions and only one O²⁻ ion left, which also does not maintain charge neutrality.
• Mg3Al6Y8g: This formula appears to be incorrect as it does not follow the stoichiometry of the original compound.

Conclusion on the Correct Formula

Given the need for charge neutrality and the structure of the original compound, the most plausible formula after doping the oxide ions with Y³⁻ ions is MgAl2Y2O2. This formula maintains the overall charge balance while incorporating the doped Y³⁻ ions. Therefore, the correct answer to your question is option (2) MgAl2Y2O2.