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

Options

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

Answer

To determine the formula of the compound formed by elements X and Y, we will analyze the given information about the arrangement of the atoms in the cubic structure.

### Step-by-Step Solution:

1. **Identify the Position of Atoms:**
- Atoms of element X are located at the corners of the cube.
- Atoms of element Y are located at two non-adjacent face centers.

2. **Count 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 because it is shared among 8 adjacent unit cells.
- Therefore, the total contribution of X atoms in the unit cell is:
\[ \text{Total contribution of X} = 8 \times \frac{1}{8} = 1 \text{ atom of X} \]

3. **Count the Contribution of Y Atoms:**
- There are 2 Y atoms located at the face centers.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared between two adjacent unit cells.
- Therefore, the total contribution of Y atoms in the unit cell is:
\[ \text{Total contribution of Y} = 2 \times \frac{1}{2} = 1 \text{ atom of Y} \]

4. **Determine the Formula of the Compound:**
- Since there is 1 atom of X and 1 atom of Y in the unit cell, the formula of the compound can be expressed as:
\[ \text{Formula} = XY \text{ or } X_1Y_1 \]

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

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