If there elements X, Y & Z crystallize in cubic solid latice with X atoms at corners, Y atoms at cube centre & Z-atoms at the edges, then the formula of the compound is

Options

A. XYZ
B. `XYZ_2`
C. `XYZ_3`
D. `X_2Y_2Z`

Explanation

To determine the formula of the compound formed by elements X, Y, and Z in a cubic solid lattice, we will analyze the contribution of each type of atom based on their positions in the lattice.

### Step-by-Step Solution:

1. **Identify the positions of the atoms:**
- X atoms are located at the corners of the cube.
- Y atoms are located at the center of the cube.
- Z atoms are located at the edges 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:
\[ \text{Contribution of X} = 8 \times \frac{1}{8} = 1 \]

3. **Calculate the contribution of Y atoms:**
- There is 1 atom at the center of the cube.
- This atom contributes fully to the unit cell.
- Therefore, the total contribution of Y atoms is:
\[ \text{Contribution of Y} = 1 \]

4. **Calculate the contribution of Z atoms:**
- There are 12 edges in a cube.
- Each edge atom contributes \( \frac{1}{4} \) of an atom to the unit cell.
- Therefore, the total contribution of Z atoms is:
\[ \text{Contribution of Z} = 12 \times \frac{1}{4} = 3 \]

5. **Combine the contributions to form the empirical formula:**
- From the contributions calculated:
- X contributes 1 atom.
- Y contributes 1 atom.
- Z contributes 3 atoms.
- Thus, the formula of the compound can be written as:
\[ \text{Formula} = X^1 Y^1 Z^3 = XYZ^3 \]

6. **Conclusion:**
- The formula of the compound is \( XYZ^3 \).

### Final Answer:
The formula of the compound is \( XYZ^3 \).