The ratio of anion radius to cation radius of a crystal is 10:9,3. then , the coordination number of the cation in the crystal is

Options

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

Answer

To determine the coordination number of the cation in the crystal given the ratio of the anion radius to cation radius as 10:9.3, we can follow these steps:

### Step 1: Understand the Given Ratio
The ratio of the anion radius (r⁻) to the cation radius (r⁺) is given as:
\[ \frac{r^-}{r^+} = \frac{10}{9.3} \]

### Step 2: Calculate the Reciprocal Ratio
To find the ratio of the cation radius to the anion radius, we take the reciprocal:
\[ \frac{r^+}{r^-} = \frac{9.3}{10} = 0.93 \]

### Step 3: Identify the Type of Void
We need to compare this ratio to known ratios for different types of voids in crystal structures. The relevant ratios are:
- **Triangular void**: \( \frac{r^+}{r^-} = 0.155 : 0.225 \)
- **Tetrahedral void**: \( \frac{r^+}{r^-} = 0.225 : 0.41 \)
- **Octahedral void**: \( \frac{r^+}{r^-} = 0.414 : 0.732 \)
- **Cubic void**: \( \frac{r^+}{r^-} = 0.732 : 1.00 \)

### Step 4: Compare the Ratio
The calculated ratio \( 0.93 \) falls within the range of the octahedral void ratio \( (0.414 : 0.732) \) and the cubic void ratio \( (0.732 : 1.00) \). This indicates that the cation is likely coordinated in an octahedral arrangement.

### Step 5: Determine the Coordination Number
In an octahedral arrangement, the coordination number of the cation is 6, as it is surrounded by 6 anions.

### Conclusion
Thus, the coordination number of the cation in the crystal is:
\[ \text{Coordination Number} = 6 \]

### Final Answer
The coordination number of the cation in the crystal is **6**.

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