A solid has a structure in which Y atoms are located at the corners of cubic lattice, Z atoms at the centre of edges and X atoms at the centre of body. The formula of compound is

Options

A. XYZ
B. `XY_8Z_3`
C. `XYZ_4`
D. `XYZ_3`

Answer

To determine the formula of the compound based on the given atomic arrangement in the solid structure, we will analyze the contributions of each type of atom (Y, Z, and X) in the unit cell.

### Step-by-Step Solution:

1. **Identify the Position of Y Atoms**:
- Y atoms are located at the corners of the cubic lattice.
- A cube has 8 corners.

2. **Calculate the Contribution of Y Atoms**:
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell since it is shared among 8 adjacent unit cells.
- Therefore, the total contribution of Y atoms in the unit cell is:
\[ \text{Contribution of Y} = 8 \times \frac{1}{8} = 1 \]
- So, there is 1 Y atom per unit cell.

3. **Identify the Position of Z Atoms**:
- Z atoms are located at the center of the edges of the cube.
- A cube has 12 edges.

4. **Calculate the Contribution of Z Atoms**:
- Each edge atom contributes \( \frac{1}{4} \) of an atom to the unit cell since it is shared between 4 unit cells.
- Therefore, the total contribution of Z atoms in the unit cell is:
\[ \text{Contribution of Z} = 12 \times \frac{1}{4} = 3 \]
- So, there are 3 Z atoms per unit cell.

5. **Identify the Position of X Atoms**:
- X atoms are located at the center of the body of the cube.
- There is only 1 body-centered atom per unit cell.

6. **Calculate the Contribution of X Atoms**:
- The contribution of X atoms is simply:
\[ \text{Contribution of X} = 1 \]
- So, there is 1 X atom per unit cell.

7. **Write the Formula of the Compound**:
- Now, we can summarize the contributions:
- Y: 1
- Z: 3
- X: 1
- Therefore, the formula of the compound is:
\[ \text{Formula} = X_1Y_1Z_3 \text{ or simply } XYZ_3 \]

### Final Answer:
The formula of the compound is \( XYZ_3 \).

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