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. `XY_(3)Z`
C. `XYZ_(3)`
D. `X_(3) YZ`

Explanation

To determine the formula of the compound formed by elements X, Y, and Z in a cubic solid lattice, we need to calculate the number of atoms of each element in the unit cell.

### Step 1: Count the number of X atoms
- X atoms are located at the corners of the cube.
- Each corner atom is shared by 8 adjacent cubes.
- Therefore, the contribution of X atoms from the corners is:

\[ \text{Number of X atoms} = 8 \text{ corners} \times \frac{1}{8} = 1 \]

### Step 2: Count the number of Y atoms
- Y atoms are located at the center of the cube.
- The center atom is not shared with any other cube.
- Therefore, the contribution of Y atoms is:

\[ \text{Number of Y atoms} = 1 \text{ (the center atom)} \]

### Step 3: Count the number of Z atoms
- Z atoms are located at the edges of the cube.
- Each edge atom is shared by 4 adjacent cubes.
- There are 12 edges in a cube.
- Therefore, the contribution of Z atoms is:

\[ \text{Number of Z atoms} = 12 \text{ edges} \times \frac{1}{4} = 3 \]

### Step 4: Write the empirical formula
Now that we have the number of atoms for each element:
- Number of X = 1
- Number of Y = 1
- Number of Z = 3

The empirical formula of the compound can be written as:

\[ \text{Formula} = X^1 Y^1 Z^3 = XY Z^3 \]

### Conclusion
Thus, the formula of the compound is \( XY Z^3 \).

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