In Zinc blende structure, `Zn^(+2)` ions are present in alternate tetrahedral voids and `S^(-2)` in ccp. The coordination number of `Zn^(+2)` and `S^(-2)` are respectively

Options

A. 8,8
B. 4,4
C. 4,8
D. 8,4

Answer

To determine the coordination numbers of \( \text{Zn}^{2+} \) and \( \text{S}^{2-} \) in the zinc blende structure, we can follow these steps:

### Step 1: Understand the Structure
In the zinc blende structure, \( \text{S}^{2-} \) ions form a cubic close-packed (CCP) arrangement, while \( \text{Zn}^{2+} \) ions occupy alternate tetrahedral voids.

### Step 2: Determine the Number of Atoms in CCP
In a CCP structure (also known as face-centered cubic or FCC), there are 4 atoms per unit cell. This is calculated as follows:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) to the unit cell: \( 8 \times \frac{1}{8} = 1 \)
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \): \( 6 \times \frac{1}{2} = 3 \)
- Total = \( 1 + 3 = 4 \)

### Step 3: Calculate the Number of Tetrahedral Voids
In a CCP structure, the number of tetrahedral voids is given by \( 2n \), where \( n \) is the number of atoms in the unit cell. Since \( n = 4 \):
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]

### Step 4: Determine the Occupied Tetrahedral Voids
According to the problem, \( \text{Zn}^{2+} \) ions occupy alternate tetrahedral voids. Therefore, only half of the tetrahedral voids are occupied:
\[ \text{Occupied tetrahedral voids} = \frac{8}{2} = 4 \]

### Step 5: Coordination Number of \( \text{Zn}^{2+} \)
The coordination number is defined as the number of nearest neighbors surrounding an ion. In this case, each \( \text{Zn}^{2+} \) ion in the tetrahedral void is surrounded by 4 \( \text{S}^{2-} \) ions. Thus, the coordination number of \( \text{Zn}^{2+} \) is:
\[ \text{Coordination number of } \text{Zn}^{2+} = 4 \]

### Step 6: Coordination Number of \( \text{S}^{2-} \)
In the CCP structure, each \( \text{S}^{2-} \) ion is surrounded by 4 \( \text{Zn}^{2+} \) ions (since \( \text{Zn}^{2+} \) occupies tetrahedral voids). Therefore, the coordination number of \( \text{S}^{2-} \) is also:
\[ \text{Coordination number of } \text{S}^{2-} = 4 \]

### Final Answer
The coordination numbers of \( \text{Zn}^{2+} \) and \( \text{S}^{2-} \) are respectively:
\[ \text{Coordination number of } \text{Zn}^{2+} = 4, \quad \text{Coordination number of } \text{S}^{2-} = 4 \]

### Summary
Thus, the final answer is:
- Coordination number of \( \text{Zn}^{2+} \): 4
- Coordination number of \( \text{S}^{2-} \): 4