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 determine the coordination number of \( Rb^+ \) in the RbBr unit cell, we will follow these steps:

### Step 1: Identify the ionic radii
We are given the ionic radii of \( Rb^+ \) and \( Br^- \):
- Ionic radius of \( Rb^+ \) = 148 pm
- Ionic radius of \( Br^- \) = 195 pm

### Step 2: Calculate the radius ratio
The radius ratio is calculated by dividing the radius of the cation by the radius of the anion:
\[ \text{Radius Ratio} = \frac{\text{Radius of } Rb^+}{\text{Radius of } Br^-} = \frac{148 \, \text{pm}}{195 \, \text{pm}} \]
Calculating this gives:
\[ \text{Radius Ratio} = \frac{148}{195} \approx 0.76 \]

### Step 3: Determine the coordination number from the radius ratio
We use the radius ratio to find the coordination number. The ranges for coordination numbers based on the radius ratio are as follows:
- \( 0.155 - 0.225 \): Coordination number = 3 (triangular void)
- \( 0.225 - 0.414 \): Coordination number = 4 (tetrahedral void)
- \( 0.414 - 0.732 \): Coordination number = 6 (octahedral void)
- \( 0.732 - 1.0 \): Coordination number = 8 (cubic void)

Since our calculated radius ratio is approximately \( 0.76 \), it falls within the range of \( 0.732 - 1.0 \), indicating a cubic void with a coordination number of 8.

### Conclusion
Thus, the coordination number of \( Rb^+ \) in the RbBr unit cell is **8**.

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