In aluminium oxide, the oxide ions are arranged in hexagonal close packed (hcp) arrangement and the aluminium occupy `2//3` of octahedral voids. What is the formula of oxide ?

Explanation

To find the formula of aluminium oxide based on the given information, we can follow these steps:

### Step 1: Determine the number of oxide ions in the hexagonal close-packed (hcp) arrangement.
In an hcp arrangement, the number of oxide ions (O²⁻) per unit cell is 6.

### Step 2: Calculate the number of octahedral voids.
In a close-packed arrangement, there is one octahedral site for each atom in the lattice. Since there are 6 oxide ions, the number of octahedral voids will also be 6.

### Step 3: Determine the number of aluminium ions occupying the octahedral voids.
According to the problem, aluminium occupies \( \frac{2}{3} \) of the octahedral voids. Therefore, the number of aluminium ions (Al³⁺) can be calculated as:
\[ \text{Number of Al ions} = \text{Number of octahedral voids} \times \frac{2}{3} = 6 \times \frac{2}{3} = 4 \]

### Step 4: Write the empirical formula.
Now that we have the number of aluminium ions and oxide ions, we can write the empirical formula. We have 4 aluminium ions and 6 oxide ions, which gives us:
\[ \text{Formula} = \text{Al}_4\text{O}_6 \]

### Step 5: Simplify the formula.
To simplify the formula, we can divide both the subscripts by 2:
\[ \text{Al}_4\text{O}_6 \rightarrow \text{Al}_2\text{O}_3 \]

### Conclusion:
The formula of aluminium oxide is \( \text{Al}_2\text{O}_3 \).

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