How many aluminium ions are present per unit cell of corundum `(Al_2O_3)` ?

Answer

To determine how many aluminium ions are present per unit cell of corundum (Al₂O₃), we can follow these steps:

### Step 1: Understand the Structure of Al₂O₃
Corundum (Al₂O₃) has a specific crystal structure where oxide ions (O²⁻) occupy a hexagonal close-packed (HCP) arrangement.

**Hint:** Remember that in HCP, the arrangement of ions is crucial for determining the number of voids.

### Step 2: Identify the Number of Oxide Ions
In the HCP structure, the number of oxide ions per unit cell can be determined. For HCP, there are 6 oxide ions per unit cell.

**Hint:** Consider how many atoms are in a unit cell of HCP.

### Step 3: Determine the Number of Octahedral and Tetrahedral Voids
In the HCP arrangement:
- There are 6 octahedral voids.
- There are 12 tetrahedral voids (which is twice the number of atoms in the unit cell).

**Hint:** Recall the relationship between the number of atoms and the number of voids in a close-packed structure.

### Step 4: Calculate the Number of Aluminium Ions
In Al₂O₃, aluminium ions (Al³⁺) occupy two-thirds of the octahedral voids. Since there are 6 octahedral voids in total, the number of aluminium ions can be calculated as follows:
- Number of aluminium ions = (2/3) × 6 = 4.

**Hint:** Focus on the fraction of octahedral voids occupied by aluminium ions.

### Step 5: Determine the Total Number of Aluminium Ions per Unit Cell
Each formula unit of Al₂O₃ contains 2 aluminium ions. Since there are 6 formula units in a unit cell of corundum:
- Total aluminium ions = 6 (formula units) × 2 (aluminium ions per formula unit) = 12.

**Hint:** Remember to multiply the number of formula units by the number of aluminium ions per formula unit.

### Conclusion
Therefore, the total number of aluminium ions present per unit cell of corundum (Al₂O₃) is **12**.