In the crystalline solids the smallest repeating part in the lattice is known as unit cell. The unit cells are described as simple (points at all corners), body centred (points at all the corners and it the centre), face centred (points at all the corners and centre of all faces), and end centred (points at all hte corners and centres of two opposite and faces) unit cells. In two common tyupes of packing ccp and hcp, 26% of space is left unoccupied in the form of interstitial sites. For the stable ionic crystalline structures, there is difinite radius ratio limit for a cation to fit perfectly in the lattice of anions, called radius ratio rule. This also defines the coordination number of an ion, which is the number of nearest neighbours of opposite charges. This depeds upon the ratio of radii of two types of ions, `r_(+)//r_(-)`. This ratio for coordination numbers 3,4,6,and 8 is respectively 0.155 - 0.225, 0.225 - 0.414, 0.414 - 0.732 and 0.732 - 1 respectively.
The ionic radii of `K^(+), Rb^(+) and Br^(-)` are 137, 148 and 195 pm. The coordination number of cation in RbBr and KBr structures are respectively

Options

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

Explanation

To determine the coordination number of cations in RbBr and KBr structures, we will follow these steps:

### Step 1: Identify the ionic radii
Given the ionic radii:
- \( r_{K^+} = 137 \, \text{pm} \)
- \( r_{Rb^+} = 148 \, \text{pm} \)
- \( r_{Br^-} = 195 \, \text{pm} \)

### Step 2: Calculate the radius ratio for RbBr
For RbBr, the radius ratio \( \frac{r_{Rb^+}}{r_{Br^-}} \) can be calculated as follows:
\[ \text{Radius ratio for RbBr} = \frac{r_{Rb^+}}{r_{Br^-}} = \frac{148}{195} \]

Calculating this gives:
\[ \frac{148}{195} \approx 0.76 \]

### Step 3: Determine the coordination number for RbBr
Using the radius ratio rule:
- The range for coordination number 8 is \( 0.732 - 1 \).
- Since \( 0.76 \) falls within this range, the coordination number for RbBr is **8**.

### Step 4: Calculate the radius ratio for KBr
For KBr, the radius ratio \( \frac{r_{K^+}}{r_{Br^-}} \) can be calculated as follows:
\[ \text{Radius ratio for KBr} = \frac{r_{K^+}}{r_{Br^-}} = \frac{137}{195} \]

Calculating this gives:
\[ \frac{137}{195} \approx 0.702 \]

### Step 5: Determine the coordination number for KBr
Using the radius ratio rule:
- The range for coordination number 6 is \( 0.414 - 0.732 \).
- Since \( 0.702 \) falls within this range, the coordination number for KBr is **6**.

### Final Answer
- Coordination number of cation in RbBr: **8**
- Coordination number of cation in KBr: **6**

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