What is the coordination number of `Rb^(+)` in RbBr unit cell if ionic radii of `Rb^(+)` and `Br^(-)` ions being 148 and 195 respectively ?

Options

A. 6
B. 4
C. 8
D. 12

Answer

To find the coordination number of `Rb^(+)` in the RbBr unit cell, we will use the Radius Ratio Rule. Here is a step-by-step solution:

### Step 1: Identify the ionic radii
- The ionic radius of `Rb^(+)` is given as 148 pm (picometers).
- The ionic radius of `Br^(-)` is given as 195 pm.

### Step 2: Calculate the radius ratio
- The radius ratio \( r \) is calculated using the formula:
\[ r = \frac{r_{positive}}{r_{negative}} \]
- Substituting the values:
\[ r = \frac{148}{195} \]

### Step 3: Perform the division
- Now, calculate the value of \( r \):
\[ r \approx 0.758 \]

### Step 4: Determine the coordination number using the Radius Ratio Rule
- According to the Radius Ratio Rule, we compare the calculated ratio \( r \) with the following ranges:
- \( 0.155 \) to \( 0.225 \): Coordination number = 3
- \( 0.225 \) to \( 0.414 \): Coordination number = 4
- \( 0.414 \) to \( 0.732 \): Coordination number = 6
- \( 0.732 \) to \( 1 \): Coordination number = 8

### Step 5: Identify the appropriate coordination number
- Since \( 0.758 \) falls in the range of \( 0.732 \) to \( 1 \), the coordination number of `Rb^(+)` in the RbBr unit cell is:
\[ \text{Coordination number} = 8 \]

### Final Answer
The coordination number of `Rb^(+)` in the RbBr unit cell is **8**.

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