If the value of ionic radius ratio `((r_(c ))/(r_(a)))` is `0.52` in an ionic compound , the geometrical of ions in crystal is

Options

A. Tetrahedral
B. Planar
C. Octahedral
D. Pyramidal

Answer

To determine the geometry of ions in a crystal based on the ionic radius ratio \((\frac{r_c}{r_a})\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ionic Radius Ratio**:
The ionic radius ratio \((\frac{r_c}{r_a})\) is the ratio of the radius of the cation (\(r_c\)) to the radius of the anion (\(r_a\)). This ratio helps in determining the coordination number and the geometrical arrangement of ions in the crystal lattice.

2. **Identify the Given Ratio**:
In this case, the given ionic radius ratio is \(0.52\).

3. **Refer to the Radius Ratio Rule**:
The radius ratio can be used to determine the coordination number and the corresponding geometry. The following ranges are typically used:
- \(0.155 < \frac{r_c}{r_a} < 0.225\): Coordination number = 2 (Linear)
- \(0.225 < \frac{r_c}{r_a} < 0.414\): Coordination number = 3 (Trigonal planar)
- \(0.414 < \frac{r_c}{r_a} < 0.732\): Coordination number = 4 (Tetrahedral)
- \(0.732 < \frac{r_c}{r_a} < 1.0\): Coordination number = 6 (Octahedral)

4. **Determine the Coordination Number**:
Since \(0.52\) falls within the range \(0.414 < \frac{r_c}{r_a} < 0.732\), we conclude that the coordination number is \(6\).

5. **Identify the Geometrical Arrangement**:
A coordination number of \(6\) corresponds to an octahedral arrangement of ions in the crystal lattice.

6. **Conclusion**:
Therefore, the geometry of ions in the crystal with an ionic radius ratio of \(0.52\) is octahedral.

### Final Answer:
The geometrical arrangement of ions in the crystal is **octahedral**.

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