A compound formed by elements X, Y and Z has a cubic structure in which X atoms are at the corner of the cube and also at alternate face centres. Y atoms are present at the body centre and Z atoms are present at the alternate edge centre. Then the molecular formula of the compound is

Options

A. `XYZ`
B. `XY_2 Z`
C. `XYZ_3`
D. `X_2 YZ`

Answer

To determine the molecular formula of the compound formed by elements X, Y, and Z, we need to analyze the contributions of each type of atom based on their positions in the cubic structure.

### Step-by-Step Solution:

1. **Identify the positions of the atoms**:
- X atoms are located at the corners of the cube and at alternate face centers.
- Y atoms are located at the body center.
- Z atoms are located at alternate edge centers.

2. **Calculate the contribution of X atoms**:
- There are 8 corners in a cube, and each corner atom contributes \( \frac{1}{8} \) to the unit cell.
- Total contribution from corner X atoms:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \]
- There are 6 faces in a cube, and since X is at alternate face centers, we consider 2 face centers.
- Each face center contributes \( \frac{1}{2} \):
\[ \text{Contribution from face centers} = 2 \times \frac{1}{2} = 1 \]
- Total contribution from X:
\[ X_{\text{total}} = 1 + 1 = 2 \]

3. **Calculate the contribution of Y atoms**:
- There is 1 Y atom at the body center, which contributes fully:
\[ Y_{\text{total}} = 1 \]

4. **Calculate the contribution of Z atoms**:
- There are 12 edges in a cube, and Z atoms are at alternate edge centers, which means we consider 4 edges.
- Each edge contributes \( \frac{1}{4} \):
\[ \text{Contribution from edges} = 4 \times \frac{1}{4} = 1 \]
- Total contribution from Z:
\[ Z_{\text{total}} = 1 \]

5. **Combine the contributions**:
- Now we can write the molecular formula based on the contributions of each atom:
\[ \text{Molecular formula} = X_2Y_1Z_1 = XYZ \]

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