In a cubic structure of compound which is made from X and Y, where X atoms are at the corners of the cube and Y at the face centres of the cube. The molecular formula of the compound is

Options

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

Answer

To determine the molecular formula of the compound formed by X and Y in a cubic structure, we need to analyze the positions of the atoms and their contributions to the unit cell.

### Step-by-Step Solution:

1. **Identify the positions of atoms**:
- X atoms are located at the corners of the cube.
- 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.
- Therefore, the total contribution of X atoms is:
\[ \text{Contribution of X} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]

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.
- Therefore, the total contribution of Y atoms is:
\[ \text{Contribution of Y} = 6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Combine the contributions to find the molecular formula**:
- From the contributions calculated, we have:
- 1 atom of X
- 3 atoms of Y
- Thus, the molecular formula of the compound is:
\[ \text{Molecular Formula} = XY_3 \]

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

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