Which of following statements is correct in the zinc-blende-type structure of an ionic compound?

Options

A. Co-ordination number of each cation and anion is two
B. Co-ordination number of each cation and anion in four
C. Co-ordination number of each cation and anion in six
D. Co-ordination number of each cation and anion in eight

Answer

To determine the correct statement regarding the zinc-blende-type structure of an ionic compound, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Zinc Blende Structure**:
- The zinc blende structure is commonly represented by zinc sulfide (ZnS). In this structure, the sulfide ions (S²⁻) form a cubic close-packed (CCP) lattice.

2. **Identifying the Lattice Type**:
- The cubic close-packed (CCP) structure is also known as face-centered cubic (FCC). In an FCC unit cell, there are a total of 4 atoms.

3. **Calculating the Number of Sulfide Ions**:
- In the FCC lattice:
- There are 8 corner atoms, each contributing 1/8 to the unit cell.
- There are 6 face-centered atoms, each contributing 1/2 to the unit cell.
- Total contribution:
- From corners: \( 8 \times \frac{1}{8} = 1 \)
- From faces: \( 6 \times \frac{1}{2} = 3 \)
- Therefore, the total number of S²⁻ ions in the unit cell is \( 1 + 3 = 4 \).

4. **Calculating Tetrahedral Voids**:
- The number of tetrahedral voids in a CCP structure is twice the number of atoms present. Since there are 4 S²⁻ ions, the total number of tetrahedral voids is \( 2 \times 4 = 8 \).

5. **Placing Zinc Ions in Tetrahedral Voids**:
- Zinc ions (Zn²⁺) occupy half of the tetrahedral voids. Thus, the number of Zn²⁺ ions is \( \frac{1}{2} \times 8 = 4 \).

6. **Determining Coordination Numbers**:
- The coordination number is defined as the number of nearest neighbors surrounding an ion.
- For the S²⁻ ion, there are 4 nearest Zn²⁺ ions, giving it a coordination number of 4.
- For the Zn²⁺ ion, it is surrounded by 4 S²⁻ ions, also giving it a coordination number of 4.

7. **Conclusion**:
- Therefore, the coordination number of both the cation (Zn²⁺) and the anion (S²⁻) in the zinc blende structure is 4. The correct statement is that the coordination number of each cation and anion is 4.

### Final Answer:
The correct statement in the zinc-blende-type structure of an ionic compound is that the coordination number of each cation and anion is 4.

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