Statement-1:For a CsCl unit cell `r_(Cs)^+ + r_(Cl)^(-)=sqrt3/2 a` where a is edge-length
Statement-2: CsCl structure has FCC type unit-cell

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To solve the question, we need to analyze both statements regarding the CsCl unit cell.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- The statement claims that for a CsCl unit cell, the relationship between the radii of the cation (Cs⁺) and the anion (Cl⁻) is given by:
\[ r_{Cs}^+ + r_{Cl}^- = \frac{\sqrt{3}}{2} a \]
- Here, \(a\) is the edge length of the unit cell.

2. **Analyzing the CsCl Structure**:
- CsCl crystallizes in a body-centered cubic (BCC) structure.
- In a BCC structure, the body diagonal of the cube can be calculated using the formula:
\[ \text{Body diagonal} = a\sqrt{3} \]
- The body diagonal connects two opposite corners of the cube and passes through the center atom.

3. **Relating the Radii to the Body Diagonal**:
- In the case of CsCl, the body diagonal is equal to the sum of the radii of the cation and anion:
\[ r_{Cs} + r_{Cl} = \frac{1}{2} \times \text{Body diagonal} = \frac{1}{2} \times a\sqrt{3} \]
- Rearranging gives:
\[ r_{Cs} + r_{Cl} = \frac{\sqrt{3}}{2} a \]
- Therefore, Statement 1 is **true**.

4. **Understanding Statement 2**:
- The second statement claims that CsCl has a face-centered cubic (FCC) type unit cell.
- However, as established earlier, CsCl actually has a body-centered cubic (BCC) structure.

5. **Conclusion**:
- Statement 1 is true, while Statement 2 is false.
- Therefore, the correct answer is that Statement 1 is true and Statement 2 is false.

### Final Answer:
- Statement 1: True
- Statement 2: False