A compound formed by element `X` and `Y` crystallizes in the cubic structure when `Y` atoms are at the corners of the cube and `X` atoms are at the alternate faces. What is the formula of the compound?

Explanation

To determine the formula of the compound formed by elements X and Y, we need to analyze the arrangement of the atoms in the cubic structure as described in the question.

### Step-by-Step Solution:

1. **Identify the Positions of Atoms**:
- The problem states that Y atoms are located at the corners of the cube.
- X atoms are located at alternate faces of the cube.

2. **Count the Contribution of Y Atoms**:
- In a cube, there are 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared by 8 adjacent cubes.
- Therefore, the total contribution of Y atoms in the unit cell is:
\[ \text{Total Y atoms} = 8 \times \frac{1}{8} = 1 \]

3. **Count the Contribution of X Atoms**:
- The problem states that X atoms are at alternate faces. In a cube, there are 6 faces.
- However, since X atoms occupy alternate faces, only 3 faces will have X atoms.
- Each face atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared with one adjacent unit cell.
- Therefore, the total contribution of X atoms in the unit cell is:
\[ \text{Total X atoms} = 3 \times \frac{1}{2} = 1.5 \]

4. **Determine the Formula**:
- From the contributions calculated:
- Y contributes 1 atom.
- X contributes 1.5 atoms.
- To express the formula in the simplest whole number ratio, we can multiply both contributions by 2 to eliminate the fraction:
- X: \( 1.5 \times 2 = 3 \)
- Y: \( 1 \times 2 = 2 \)
- Therefore, the formula of the compound can be expressed as \( X_3Y_2 \).

### Final Answer:
The formula of the compound is \( X_3Y_2 \).