An ionic compound is expected to have octahedral structure if `r_(c)//r_(a)(r_(c) lt r_(a))` lies in the range of:

Options

A. 0.414 to 0.732
B. 0.732 to 0.82
C. 0.225 to 0.414
D. 0.155 to 0.225

Answer

To determine the range of the radius ratio \( \frac{r_c}{r_a} \) (where \( r_c \) is the radius of the cation and \( r_a \) is the radius of the anion) for an ionic compound to exhibit an octahedral structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Radius Ratio**:
- The radius ratio \( \frac{r_c}{r_a} \) is defined as the ratio of the radius of the cation to the radius of the anion.
- In this case, we are given that \( r_c < r_a \), which means the cation is smaller than the anion.

2. **Identifying Structure Ranges**:
- Different ionic structures correspond to specific ranges of the radius ratio:
- **Triangular planar**: \( 0.155 < \frac{r_c}{r_a} < 0.225 \)
- **Tetrahedral**: \( 0.225 < \frac{r_c}{r_a} < 0.414 \)
- **Octahedral**: \( 0.414 < \frac{r_c}{r_a} < 0.732 \)
- **Cubic**: \( 0.732 < \frac{r_c}{r_a} < 1 \)

3. **Finding the Required Range**:
- Since we are looking for the range where the ionic compound exhibits an octahedral structure, we focus on the octahedral range.
- According to the information, for an octahedral structure, the radius ratio must lie between \( 0.414 \) and \( 0.732 \).

4. **Conclusion**:
- Therefore, the ionic compound is expected to have an octahedral structure if the ratio \( \frac{r_c}{r_a} \) lies in the range of **\( 0.414 \) to \( 0.732 \)**.

### Final Answer:
The range of \( \frac{r_c}{r_a} \) for an octahedral structure is **\( 0.414 < \frac{r_c}{r_a} < 0.732 \)**.

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