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 made from X and Y in a cubic structure, we need to analyze the positions of the atoms and their contributions to the formula.

### 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**:
- There are 8 corners in a cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution of X atoms is:
\[ \text{Total contribution of X} = 8 \times \frac{1}{8} = 1 \]

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

4. **Combine the contributions**:
- From the calculations, we have:
- Total X atoms = 1
- Total Y atoms = 3
- Thus, the molecular formula of the compound can be written as:
\[ \text{Molecular formula} = X_1Y_3 \Rightarrow XY_3 \]

5. **Final Answer**:
- The molecular formula of the compound is \( XY_3 \).

### Conclusion:
The correct option is option number 4: \( XY_3 \).