An ionic crystal lattice has `(r^(+))/(r^(-))` radius ratio of 0.320, its co-ordination number is :

Options

A. 3
B. 4
C. 6
D. 8

Answer

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

### Step-by-Step Solution:

1. **Understand the Radius Ratio**: The radius ratio is given as \( \frac{r^+}{r^-} = 0.320 \), where \( r^+ \) is the radius of the cation and \( r^- \) is the radius of the anion.

2. **Identify the Coordination Number**: The coordination number (CN) can be determined based on the radius ratio. The general ranges for coordination numbers based on radius ratios are:
- \( \frac{r^+}{r^-} < 0.225 \) → CN = 4 (Tetrahedral)
- \( 0.225 < \frac{r^+}{r^-} < 0.414 \) → CN = 6 (Octahedral)
- \( 0.414 < \frac{r^+}{r^-} < 0.732 \) → CN = 8 (Cubic)
- \( 0.732 < \frac{r^+}{r^-} < 1 \) → CN = 12 (Cubic)

3. **Analyze the Given Ratio**: Since \( 0.320 \) falls within the range \( 0.225 < \frac{r^+}{r^-} < 0.414 \), we can conclude that the coordination number is 6.

4. **Final Answer**: Therefore, the coordination number of the ionic crystal lattice is **6**.