An ionic compound crystallises in FCC type structure with 'A' ions at the centre of each face and 'B' ions occupying corners of the cube. The formula of compound is -

Options

A. `AB_(4)`
B. `A_(3)B`
C. `AB`
D. `AB_(3)`

Answer

To determine the formula of the ionic compound that crystallizes in a face-centered cubic (FCC) structure with 'A' ions at the center of each face and 'B' ions occupying the corners of the cube, we can follow these steps:

### Step 1: Understand the FCC Structure
In a face-centered cubic (FCC) structure:
- There are atoms at each of the corners of the cube and at the center of each face.

### Step 2: Count the Contribution of 'A' Ions
- The 'A' ions are located at the center of each of the 6 faces of the cube.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared between two adjacent unit cells.
- Therefore, the total contribution from the 'A' ions is:
\[ \text{Total contribution from A} = 6 \text{ faces} \times \frac{1}{2} = 3 \text{ A ions} \]

### Step 3: Count the Contribution of 'B' Ions
- The 'B' ions are located at the 8 corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 adjacent unit cells.
- Therefore, the total contribution from the 'B' ions is:
\[ \text{Total contribution from B} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ B ion} \]

### Step 4: Write the Formula
Combining the contributions from both types of ions, we find:
- Total A ions = 3
- Total B ions = 1
Thus, the formula of the compound is:
\[ \text{Formula} = A_3B \]

### Step 5: Identify the Correct Option
From the options provided, the correct formula for the compound is \( A_3B \).

### Final Answer
The formula of the compound is \( A_3B \).

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