A crystal is formed by two elements X and Y in cubic structure. X atoms are at the corners of a cube while Y atoms are at the face centre . The formula of the compound will be

Options

A. XY
B. `XY_2`
C. `X_2Y_3`
D. `XY_3`

Explanation

To determine the formula of the compound formed by elements X and Y in a cubic structure, we can follow these steps:

### Step 1: Identify the positions of the atoms
- X atoms are located at the corners of the cube.
- Y atoms are located at the face centers of the cube.

### Step 2: Calculate the contribution of X atoms
- In a cubic unit cell, there are 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution from X atoms is:
\[ \text{Total contribution from X} = 8 \times \frac{1}{8} = 1 \]
- Thus, there is 1 X atom per unit cell.

### Step 3: Calculate the contribution of Y atoms
- In a cubic unit cell, there are 6 faces.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total contribution from Y atoms is:
\[ \text{Total contribution from Y} = 6 \times \frac{1}{2} = 3 \]
- Thus, there are 3 Y atoms per unit cell.

### Step 4: Write the empirical formula
- Now that we have the number of X and Y atoms in the unit cell, we can write the formula of the compound.
- The formula will be:
\[ \text{Formula} = X_1Y_3 \rightarrow XY_3 \]

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

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