A compound formed by elements `X` and `Y` crystallises in a cubic structure in which the `X` atoms are at the corners of a cube and the `Y` atoms are at the face centres.The formula of the compound is

Options

A. `XY_(3)`
B. `X_(3)Y`
C. `XY`
D. `XY_(2)`

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.

### Step-by-Step Solution:

1. **Identify the Positions of Atoms**:
- The X atoms are located at the corners of the cube.
- The Y atoms are located at the face centers of the cube.

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

3. **Calculate the Contribution of Y Atoms**:
- In a cube, there are 6 faces.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell (since each face atom is shared by 2 adjacent cubes).
- Therefore, the total contribution of Y atoms in the unit cell is:
\[ \text{Total Y atoms} = 6 \times \frac{1}{2} = 3 \text{ atoms of Y} \]

4. **Write the Empirical Formula**:
- From the contributions calculated:
- There is 1 atom of X.
- There are 3 atoms of Y.
- Thus, the empirical formula of the compound can be written as:
\[ \text{Formula} = XY_3 \]

### Final Answer:
The formula of the compound is \( XY_3 \).