Calculate the radius ratio `(r_(+)//r_(-))` and coordination number of `Li^(+)` and `F^(-)` ion in LiF crystal structure from the following data : `r_(Li^(+))` = 60 pm , `r_(F^(-))` = 136 pm

Explanation

To solve the problem of calculating the radius ratio and coordination number of \( Li^+ \) and \( F^- \) ions in the LiF crystal structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data:**
- Radius of \( Li^+ \) ion, \( r_{Li^+} = 60 \) pm
- Radius of \( F^- \) ion, \( r_{F^-} = 136 \) pm

2. **Calculate the radius ratio \( \left( \frac{r_{Li^+}}{r_{F^-}} \right) \):**
\[ \text{Radius Ratio} = \frac{r_{Li^+}}{r_{F^-}} = \frac{60 \, \text{pm}}{136 \, \text{pm}} \]
\[ \text{Radius Ratio} = \frac{60}{136} \approx 0.441 \]

3. **Determine the coordination number based on the radius ratio:**
- The coordination number can be determined by the radius ratio. The ranges for coordination numbers based on radius ratios are as follows:
- If \( 0.225 < \text{Radius Ratio} < 0.414 \), coordination number = 4
- If \( 0.414 < \text{Radius Ratio} < 0.732 \), coordination number = 6
- If \( 0.732 < \text{Radius Ratio} < 1.0 \), coordination number = 8
- Since our calculated radius ratio \( 0.441 \) falls between \( 0.414 \) and \( 0.732 \), the coordination number is:
\[ \text{Coordination Number} = 6 \]

### Final Results:
- **Radius Ratio**: \( 0.441 \)
- **Coordination Number**: \( 6 \)