Which is /are correct statement about zinc blende structure ?
(a) The number of first neighbours of `S^(2-)` is 4
(b) The maximum distance `Zn^(2+)` is `asqrt(3)/(2)` , where 'a' = egde length of unit cell
(c) If all tetrahedral voids are occupied by `Zn^(2+)` then C.N. of `S ^(2-)` is 8
(d) If all tetrahedral voids are occupied by `Zn^(2+)` then C.N. change from 4:4 to 8:8.

Options

A. The number of first neighbours of `S^(2-)` is 4
B. The maximum distance `Zn^(2+)` is `asqrt(3)/(2)` , where 'a' = egde length of unit cell
C. If all tetrahedral voids are occupied by `Zn^(2+)` then C.N. of `S ^(2-)` is 8
D. If all tetrahedral voids are occupied by `Zn^(2+)` then C.N. change from 4: 4 to 8: 8.

Answer

To determine which statements about the zinc blende structure (ZnS) are correct, we will analyze each statement one by one based on the properties of the zinc blende structure.

### Step-by-Step Solution:

1. **Understanding the Zinc Blende Structure:**
- The zinc blende structure consists of Zn²⁺ ions and S²⁻ ions. In this structure, S²⁻ ions occupy the face-centered cubic (FCC) lattice, while Zn²⁺ ions occupy half of the tetrahedral voids.

2. **Analyzing Statement (a):**
- **Statement:** The number of first neighbors of S²⁻ is 4.
- **Explanation:** In the zinc blende structure, each S²⁻ ion is surrounded by 4 Zn²⁺ ions, which are located at the corners of a tetrahedron. Therefore, this statement is **correct**.

3. **Analyzing Statement (b):**
- **Statement:** The maximum distance Zn²⁺ is \( \frac{a \sqrt{3}}{2} \), where 'a' is the edge length of the unit cell.
- **Explanation:** In the FCC structure, the maximum distance between two ions can be calculated. The distance between the centers of two corner atoms (Zn²⁺) in the tetrahedral arrangement can be derived as \( \frac{a \sqrt{3}}{2} \). Thus, this statement is also **correct**.

4. **Analyzing Statement (c):**
- **Statement:** If all tetrahedral voids are occupied by Zn²⁺, then the coordination number of S²⁻ is 8.
- **Explanation:** If all tetrahedral voids are occupied by Zn²⁺ ions, each S²⁻ ion will be surrounded by 8 Zn²⁺ ions. This means the coordination number of S²⁻ would indeed be 8. Therefore, this statement is **correct**.

5. **Analyzing Statement (d):**
- **Statement:** If all tetrahedral voids are occupied by Zn²⁺, then the coordination number changes from 4:4 to 8:8.
- **Explanation:** While the coordination number of S²⁻ does change to 8 when all tetrahedral voids are filled, the statement implies a change in the ratio from 4:4 to 8:8. However, the coordination number for Zn²⁺ does not change; it remains 4. Thus, this statement is **incorrect**.

### Conclusion:
The correct statements about the zinc blende structure are:
- (a) The number of first neighbors of S²⁻ is 4.
- (b) The maximum distance Zn²⁺ is \( \frac{a \sqrt{3}}{2} \).
- (c) If all tetrahedral voids are occupied by Zn²⁺, then the coordination number of S²⁻ is 8.

### Final Answer:
Correct statements are (a), (b), and (c).

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