A unit cell consists of a cube in which there are anions Y at each corner and cations X at the centres of alternate faces of 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 follow these steps:

### Step 1: Identify the number of anions (Y) in the unit cell
- The anions Y are located at each corner of the cube.
- A cube has 8 corners, and each corner contributes \( \frac{1}{8} \) of an anion to the unit cell.

**Calculation:**
\[ \text{Effective number of anions (Y)} = 8 \times \frac{1}{8} = 1 \]

### Step 2: Identify the number of cations (X) in the unit cell
- The cations X are located at the centers of alternate faces of the cube.
- There are 6 faces on a cube, and since cations are present at alternate faces, there will be cations on 3 faces.
- Each face center contributes \( \frac{1}{2} \) of a cation to the unit cell.

**Calculation:**
\[ \text{Effective number of cations (X)} = 3 \times \frac{1}{2} = \frac{3}{2} \]

### Step 3: Write the empirical formula
- From the calculations, we have:
- Anions (Y): 1
- Cations (X): \( \frac{3}{2} \)

Thus, the formula can be represented as:
\[ \text{Formula} = Y \cdot X^{\frac{3}{2}} \]

### Step 4: Simplify the formula
- To express the formula in whole numbers, we can multiply both sides by 2 to eliminate the fraction.

**Calculation:**
\[ \text{Multiplying by 2:} \quad 2Y \cdot 3X \quad \Rightarrow \quad Y_2X_3 \]

### Conclusion
The simplest formula of the compound is:
\[ \text{Formula} = X_3Y_2 \]

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