A solid is made of two element `X` and `Z` .The atoms `Z` are in `C CP` arrangement while the atoms `X` occupy all the terahedral sites .What is the formula of the compound ?

Options

A. XZ
B. `X_(2)Z`
C. `X_(2)Z_(3)`
D. `XZ_(2)`

Answer

To find the formula of the compound formed by elements X and Z, we need to analyze the arrangement of the atoms and the number of sites occupied by each element.

### Step-by-Step Solution:

1. **Identify the arrangement of atoms:**
- The atoms of element Z are arranged in a Close Packed Cubic (CCP) structure.

2. **Determine the number of Z atoms in the unit cell:**
- In a CCP arrangement, the number of atoms per unit cell is 4. This is because:
- There are 8 corner atoms (each contributes 1/8 to the unit cell) and 6 face-centered atoms (each contributes 1/2 to the unit cell).
- Therefore, the total number of atoms = \(8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4\).
- Thus, \(Z = 4\).

3. **Identify the tetrahedral sites:**
- In a CCP structure, the number of tetrahedral sites is twice the number of octahedral sites.
- There are 4 octahedral sites in a CCP unit cell, hence the number of tetrahedral sites = \(2 \times 4 = 8\).

4. **Determine the number of X atoms:**
- Since the atoms of element X occupy all the tetrahedral sites, the number of X atoms = 8.

5. **Find the ratio of X to Z:**
- We have \(Z = 4\) and \(X = 8\).
- The simplest whole number ratio of Z to X is \(4:8\), which simplifies to \(1:2\).

6. **Write the formula of the compound:**
- Based on the ratio, the formula can be expressed as \(ZX_2\) or \(Z_1X_2\).
- Therefore, the formula of the compound is \(XZ_2\).

### Final Answer:
The formula of the compound is \(XZ_2\).