A solid AB has NaCl type structure. If the radius of the cation A is 100 pm, then the maximum possible radius of the anion B will be

Options

A. 241 pm
B. 414 pm
C. 225 pm
D. 44.4 pm

Answer

To find the maximum possible radius of the anion B in a solid AB with an NaCl type structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure**:
- The NaCl structure has a face-centered cubic (FCC) arrangement where each cation (A) is surrounded by six anions (B) in an octahedral coordination.

2. **Identify the Coordination Number**:
- In this structure, the coordination number for both cations and anions is 6.

3. **Use the Radius Ratio**:
- The radius ratio (r) is defined as the ratio of the radius of the cation (r_A) to the radius of the anion (r_B):
\[ r = \frac{r_A}{r_B} \]
- For NaCl type structures, the radius ratio must be between 0.414 and 0.732. For the maximum radius of the anion, we will use the minimum value of the radius ratio, which is 0.414.

4. **Given Data**:
- The radius of cation A is given as \( r_A = 100 \) pm.

5. **Set Up the Equation**:
- Using the radius ratio for the maximum possible radius of the anion:
\[ 0.414 = \frac{100 \text{ pm}}{r_B} \]

6. **Rearranging the Equation**:
- Rearranging the equation to solve for \( r_B \):
\[ r_B = \frac{100 \text{ pm}}{0.414} \]

7. **Calculate the Radius of Anion**:
- Performing the calculation:
\[ r_B = \frac{100}{0.414} \approx 241 \text{ pm} \]

8. **Conclusion**:
- The maximum possible radius of the anion B is approximately **241 pm**.

### Final Answer:
The maximum possible radius of the anion B is **241 pm**.

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