If `r_(o+)//r_(ɵ)` for a crystal is `0.50`, it has ……….. structure.

Answer

To determine the structure of a crystal based on the radius ratio \( \frac{r_{o+}}{r_{\theta}} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Ratio**:
We are given the radius ratio \( \frac{r_{o+}}{r_{\theta}} = 0.50 \). Here, \( r_{o+} \) is the radius of the cation (positively charged ion) and \( r_{\theta} \) is the radius of the anion (negatively charged ion).

2. **Identify the Range for Radius Ratios**:
We need to compare the given ratio with known ranges for different types of voids in crystal structures. The ranges are as follows:
- Linear void: \( \frac{r_{o+}}{r_{\theta}} < 0.155 \)
- Triangular void: \( 0.155 \leq \frac{r_{o+}}{r_{\theta}} < 0.225 \)
- Tetrahedral void: \( 0.225 \leq \frac{r_{o+}}{r_{\theta}} < 0.414 \)
- Octahedral void: \( 0.414 \leq \frac{r_{o+}}{r_{\theta}} < 0.732 \)
- Cubical void: \( \frac{r_{o+}}{r_{\theta}} \geq 0.732 \)

3. **Determine the Type of Void**:
Since \( 0.50 \) lies within the range \( 0.414 \leq \frac{r_{o+}}{r_{\theta}} < 0.732 \), we can conclude that the type of void present in the structure is octahedral.

4. **Conclude the Structure**:
Given that the crystal has octahedral voids, we can say that the structure of the crystal is an octahedral structure.

### Final Answer:
The crystal has an **octahedral structure**.