The ratio of cationic radius to anionic radius in an ionic crystal is greater than `0.732` its coordination number is

Options

A. 6
B. 8
C. 1
D. 4

Answer

To determine the coordination number of an ionic crystal based on the ratio of cationic radius to anionic radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Radius Ratio**:
- The radius ratio (R) is defined as the radius of the cation (R+) divided by the radius of the anion (R-).
- Mathematically, it is expressed as:
\[ R = \frac{R^+}{R^-} \]

2. **Given Information**:
- The problem states that the radius ratio is greater than 0.732:
\[ R > 0.732 \]

3. **Radius Ratio Ranges**:
- We need to refer to the standard ranges of radius ratios and their corresponding coordination numbers:
- \( R < 0.155 \) → Coordination number = 3
- \( 0.155 < R < 0.255 \) → Coordination number = 4
- \( 0.255 < R < 0.414 \) → Coordination number = 6
- \( 0.414 < R < 0.732 \) → Coordination number = 8
- \( R > 0.732 \) → Coordination number = 8 or higher

4. **Determining Coordination Number**:
- Since the radius ratio is greater than 0.732, we can conclude that the coordination number must be 8 or higher.
- The coordination number of 8 corresponds to a cubic arrangement.

5. **Conclusion**:
- Therefore, the coordination number of the ionic crystal, given that the ratio of cationic radius to anionic radius is greater than 0.732, is:
\[ \text{Coordination Number} = 8 \]

### Final Answer:
The coordination number is **8**.

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