A compound formed by elements X and Y crysstallixzes in the cubic struture where Y atoms are at the corners of the cube and X atoms are at the alterante 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 Position of Y Atoms:**
- The problem states that Y atoms are located at the corners of the cube. In a cubic unit cell, there are 8 corners.

2. **Calculate the Contribution of Y Atoms:**
- Each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of Y atoms from the corners can be calculated as:
\[ \text{Contribution of Y} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ Y atom} \]

3. **Identify the Position of X Atoms:**
- The question mentions that X atoms are located at alternate faces of the cube. In a cubic structure, there are 6 faces.

4. **Calculate the Contribution of X Atoms:**
- Since X atoms occupy alternate faces, we can assume that they occupy 3 out of the 6 faces (for example, if X is on the front, back, and one side face).
- Each face atom is shared by 2 adjacent unit cells. Thus, the contribution of X atoms from the faces can be calculated as:
\[ \text{Contribution of X} = 3 \text{ faces} \times \frac{1}{2} = 1.5 \text{ X atoms} \]

5. **Determine the Empirical Formula:**
- Now we have the contributions:
- Y: 1 atom
- X: 1.5 atoms
- To express this in the simplest whole number ratio, we can multiply both by 2 to eliminate the fraction:
- Y: \(1 \times 2 = 2\)
- X: \(1.5 \times 2 = 3\)
- Therefore, the empirical formula of the compound is:
\[ \text{Formula} = X_3Y_2 \]

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