An ionic compound `AB` has `ZnS` type of structure if the radius `A^(+)` is `22.5` pm , then the ideal radius of `B` is

Options

A. 100 pm
B. 200 pm
C. 150 pm
D. 95 pm

Answer

To solve the problem step by step, we will use the information provided about the ionic compound with a ZnS type structure.

### Step 1: Understand the Structure
The ZnS type structure has a specific coordination geometry where the cation (A⁺) is surrounded by anions (B⁻) in a tetrahedral arrangement.

### Step 2: Use the Radius Ratio Rule
For ionic compounds with a ZnS structure, the radius ratio of the cation (A⁺) to the anion (B⁻) is given by the formula:
\[ \frac{r_A}{r_B} = 0.225 \]
where \( r_A \) is the radius of the cation (A⁺) and \( r_B \) is the radius of the anion (B⁻).

### Step 3: Substitute the Known Values
We know the radius of the cation A⁺ is given as:
\[ r_A = 22.5 \text{ pm} \]
Substituting this into the radius ratio equation gives:
\[ \frac{22.5 \text{ pm}}{r_B} = 0.225 \]

### Step 4: Rearrange the Equation
To find the radius of the anion (B⁻), we can rearrange the equation:
\[ r_B = \frac{22.5 \text{ pm}}{0.225} \]

### Step 5: Calculate the Radius of B⁻
Now, we perform the calculation:
\[ r_B = \frac{22.5}{0.225} = 100 \text{ pm} \]

### Conclusion
The ideal radius of the anion B⁻ is:
\[ \boxed{100 \text{ pm}} \]