An ionic crystal lattice has `r+//r-` radius ratio of `0.524`, its coordination number is

Options

A. 2
B. 4
C. 6
D. 8

Answer

To determine the coordination number of an ionic crystal lattice based on the radius ratio \( \frac{r^+}{r^-} \), we can follow these steps:

### Step 1: Understand the Radius Ratio
The radius ratio \( \frac{r^+}{r^-} \) is the ratio of the cation radius (\( r^+ \)) to the anion radius (\( r^- \)). This ratio helps in predicting the coordination number of the cation in the crystal lattice.

### Step 2: Identify the Given Radius Ratio
In this case, the given radius ratio is \( \frac{r^+}{r^-} = 0.524 \).

### Step 3: Use the Radius Ratio to Determine Coordination Number
According to the radius ratio rule, different ranges of \( \frac{r^+}{r^-} \) correspond to specific coordination numbers. The ranges are generally as follows:
- \( \frac{r^+}{r^-} < 0.225 \): Coordination number = 4
- \( 0.225 < \frac{r^+}{r^-} < 0.414 \): Coordination number = 4
- \( 0.414 < \frac{r^+}{r^-} < 0.732 \): Coordination number = 6
- \( 0.732 < \frac{r^+}{r^-} < 1.0 \): Coordination number = 8

### Step 4: Determine the Coordination Number for \( 0.524 \)
Since \( 0.414 < 0.524 < 0.732 \), we can conclude that the coordination number for this radius ratio is 6.

### Step 5: Conclusion
Therefore, the coordination number of the ionic crystal lattice with a radius ratio of \( 0.524 \) is **6**.