A unit cell consists of a cube in which anions (B) are present at each corner and cations (A) at centre of the alternate faces of the unit cell. What is the simplest formula of the compound ?

Explanation

To determine the simplest formula of the compound based on the given unit cell structure, we will analyze the contributions of the anions (B) and cations (A) in the unit cell.

### Step-by-Step Solution:

1. **Identify the Position of Anions (B) and Cations (A)**:
- Anions (B) are located at each corner of the cube.
- Cations (A) are located at the center of the alternate faces of the cube.

2. **Calculate the Contribution of Anions (B)**:
- There are 8 corners in a cube.
- Each corner contributes \( \frac{1}{8} \) of an anion (B) to the unit cell.
- Therefore, the total contribution of anions (B) from the corners is:
\[ \text{Total B} = 8 \times \frac{1}{8} = 1 \]

3. **Calculate the Contribution of Cations (A)**:
- There are 6 faces in a cube, and cations (A) are present at the center of alternate faces. This means cations are present at 3 faces.
- Each face center contributes \( \frac{1}{2} \) of a cation (A) to the unit cell.
- Therefore, the total contribution of cations (A) is:
\[ \text{Total A} = 3 \times \frac{1}{2} = \frac{3}{2} \]

4. **Determine the Simplest Formula**:
- Now we have 1 anion (B) and \( \frac{3}{2} \) cations (A).
- To express this in the simplest whole number ratio, we can multiply both by 2 to eliminate the fraction:
- Cations (A): \( \frac{3}{2} \times 2 = 3 \)
- Anions (B): \( 1 \times 2 = 2 \)
- Therefore, the simplest formula of the compound is:
\[ A_3B_2 \]

### Final Answer:
The simplest formula of the compound is \( A_3B_2 \).

---