If the radious of `Cs^(o+) = 1.69 Å` and `Br^(Θ) = 1.95 Å`, then which of the following is//are correct statement?

Options

A. The edge length of unit cell is `4.2 Å`.
B. The coordination number for `Cs^(o+)` is `6`.
C. `CsBr` has bcc-type structure.
D. `Br^(Θ)` ions touch each other along the edge.

Explanation

To solve the problem, we need to analyze the given ionic radii of Cs⁺ and Br⁻ and determine the correct statements based on their coordination and structural arrangement.

### Step-by-step Solution:

1. **Identify the Ionic Radii**:
- The radius of Cs⁺ (Cesium ion) = 1.69 Å
- The radius of Br⁻ (Bromide ion) = 1.95 Å

2. **Calculate the Radius Ratio**:
- Radius ratio = \( \frac{r_{Cs^+}}{r_{Br^-}} = \frac{1.69}{1.95} \)
- Performing the calculation:
\[ \frac{1.69}{1.95} \approx 0.867 \]

3. **Determine the Structure Type**:
- A radius ratio of approximately 0.867 suggests a body-centered cubic (BCC) structure.
- In a BCC structure, the cation (Cs⁺) occupies the body center, while the anions (Br⁻) are located at the corners of the cube.

4. **Find the Coordination Number**:
- In a BCC structure, the coordination number of the cation (Cs⁺) is 8. This means each Cs⁺ ion is surrounded by 8 Br⁻ ions.

5. **Calculate the Edge Length (a)**:
- For a BCC structure, the relationship between the edge length (a) and the ionic radii is given by:
\[ \sqrt{3}a = 2r_{Cs^+} + 2r_{Br^-} \]
- Substituting the values:
\[ \sqrt{3}a = 2(1.69) + 2(1.95) \]
\[ = 3.38 + 3.90 = 7.28 \]
- Therefore:
\[ a = \frac{7.28}{\sqrt{3}} \approx 4.20 \, \text{Å} \]

6. **Evaluate the Statements**:
- **Statement 1**: "Edge length is 4.2 Å" - **Correct** (as calculated).
- **Statement 2**: "Coordination number of Cs⁺ is 6" - **Incorrect** (it is 8).
- **Statement 3**: "Br⁻ ions touch each other along the edge" - **Incorrect** (the cation is present between them).
- **Statement 4**: "Coordination number of Br⁻ is 4" - **Correct** (Br⁻ ions are at the corners, and each corner shares with adjacent cubes).

### Conclusion:
The correct statements are:
- Edge length is 4.2 Å.
- Coordination number of Br⁻ is 4.