Assertion (A) : Zinc blende and wurtzite both have `fcc` arrangement of `S^(2-)` ions.
Reason (R ) : A unit cell of both has four formula units of `ZnS`.

Options

A. If both `(A)` and `(R)` are correct, and `(R)` is the correct explanation of `(A)`
B. If both `(A)` and `(R)` are correct, but `(R)` is not the correct explanation of `(A)`
C. If `(A)` is correct, but `(R)` is incorrect.
D. If both `(A)` and `(R)` are incorrect.

Explanation

To solve the given question, we need to analyze both the assertion (A) and the reason (R) provided in the question.

### Step 1: Understand the Assertion (A)
The assertion states that "Zinc blende and wurtzite both have `fcc` arrangement of `S^(2-)` ions."

- **Zinc Blende (ZnS)**: In the zinc blende structure, the sulfide ions (S²⁻) are arranged in a face-centered cubic (FCC) lattice. This means that the S²⁻ ions occupy the lattice points of the FCC structure.

- **Wurtzite (ZnS)**: In the wurtzite structure, the sulfide ions (S²⁻) also form a hexagonal close-packed (hcp) arrangement, but it is important to note that the assertion specifically mentions the FCC arrangement, which is not correct for wurtzite.

### Step 2: Understand the Reason (R)
The reason states that "A unit cell of both has four formula units of `ZnS`."

- In the zinc blende structure, the unit cell indeed contains four formula units of ZnS. This is calculated based on the arrangement of ions in the FCC lattice:
- There are 8 corner atoms contributing \( \frac{1}{8} \) each, and 6 face-centered atoms contributing \( \frac{1}{2} \) each.
- Thus, the total number of S²⁻ ions in the unit cell = \( 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \).

- For wurtzite, the unit cell also contains four formula units of ZnS, but the arrangement is not FCC.

### Step 3: Conclusion
- The assertion (A) is **incorrect** because wurtzite does not have an FCC arrangement of S²⁻ ions.
- The reason (R) is **correct** because both structures indeed have four formula units of ZnS in their unit cells.

### Final Answer
Based on the analysis:
- **Assertion (A)** is incorrect.
- **Reason (R)** is correct.
- Therefore, the correct option is: **C) A is incorrect but R is correct.**