Given : Radius of `A^(2+)=100 pm` : Radius of `C^(+)` = 240 "pm" `, Radius of `B^(200 " pm"` ,Radius of `D^(-) =480 `"pm" . Which is/are correct statement ?

Options

A. Coordination number of `A^(2+)` in comp AB is 4
B. Coordination number of `A^(2+)` in comp AB is 6.
C. Coordination number of `C^(+)` in comp CD is 6.
D. Coordination number of `C^(+)` in comp AB is 8.

Answer

To solve the problem, we need to analyze the given ionic radii and determine the coordination numbers based on the radius ratio rule. Let's go through the steps systematically.

### Step 1: Understand the given data
We have the following ionic radii:
- Radius of A²⁺ = 100 pm
- Radius of C⁺ = 240 pm
- Radius of B²⁻ = 200 pm
- Radius of D⁻ = 480 pm

### Step 2: Identify the compounds and their coordination numbers
We need to determine the coordination numbers for the following compounds:
1. Compound AB (A²⁺ and B²⁻)
2. Compound A (A²⁺)
3. Compound CD (C⁺ and D⁻)
4. Compound AB with C⁺

### Step 3: Calculate the radius ratios for each compound
1. **For compound AB (A²⁺ and B²⁻)**:
\[ \text{Radius ratio} = \frac{\text{Radius of A²⁺}}{\text{Radius of B²⁻}} = \frac{100 \text{ pm}}{200 \text{ pm}} = 0.5 \]
According to the radius ratio rule, a ratio of 0.5 corresponds to a coordination number of 6. The statement claims it is 4, which is incorrect.

2. **For compound A (A²⁺)**:
Since there is no anion mentioned, we cannot calculate a coordination number here. However, it is stated that the coordination number is 6. This can be assumed to be correct based on the previous calculation.

3. **For compound CD (C⁺ and D⁻)**:
\[ \text{Radius ratio} = \frac{\text{Radius of C⁺}}{\text{Radius of D⁻}} = \frac{240 \text{ pm}}{480 \text{ pm}} = 0.5 \]
Again, a ratio of 0.5 corresponds to a coordination number of 6. The statement claims it is 6, which is correct.

4. **For compound AB with C⁺**:
We need to determine the coordination number of C⁺ in compound AB. However, since there is no direct calculation provided in the question, we can assume that the statement claiming the coordination number is 10 is incorrect based on the previous ratios.

### Step 4: Summarize the findings
- The coordination number of A²⁺ in compound AB is incorrectly stated as 4 (it should be 6).
- The coordination number of A²⁺ in compound A is stated as 6 (assumed correct).
- The coordination number of C⁺ in compound CD is correctly stated as 6.
- The coordination number of C⁺ in compound AB is incorrectly stated as 10.

### Conclusion
The correct statements are:
- The coordination number of A²⁺ in compound A is 6.
- The coordination number of C⁺ in compound CD is 6.

### Final Answer
The correct statements are B and C.

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