NaCl is a AB type of solid . Its crystalline structure is known as rock salt structure in which `r_"Na"^+` and `r_"Cl"^-` are 95 and 181 pm respectively , where `Cl^-` is present at the lattice point of face centered cubic unit cell `Na^+` ions are located in void and those compounds which have same crystalline structure also have same coordination system in which `Na^+` and `Cl^-` ions are surrounded by certain number of opposite ions respectively. Under high pressure coordination number changes to 8 :8 type from 6 :6 type.
In rock salt type structure of AB solid , what would be the maximum radius of 'X' that can displace `A^+` if radius of `B^-` is 100 pm ?

Options

A. 41.4 pm
B. 73.2 Å
C. 41.4 Å
D. 73.2 pm

Answer

To solve the problem, we need to determine the maximum radius of the ion 'X' that can replace the cation 'A^+' (which is Na^+ in this case) in the rock salt structure, given that the radius of the anion 'B^-' (which is Cl^-) is 100 pm.

### Step-by-Step Solution:

1. **Understand the Structure**:
- In the rock salt structure (NaCl), the cation (Na^+) occupies the octahedral voids of the face-centered cubic (FCC) lattice formed by the anion (Cl^-).
- The coordination number for Na^+ and Cl^- in this structure is 6:6.

2. **Use the Radius Ratio**:
- The stability of the rock salt structure is determined by the radius ratio of the cations and anions. For octahedral voids, the radius ratio (r_A^+/r_B^-) should be approximately 0.414 to 0.732.
- The maximum radius ratio for stable octahedral coordination is given by:
\[ \frac{r_A^+}{r_B^-} = 0.732 \]

3. **Calculate the Radius of A^+**:
- Given that the radius of B^- (Cl^-) is 100 pm, we can find the maximum radius of A^+ (Na^+) using the radius ratio:
\[ r_A^+ = 0.732 \times r_B^- = 0.732 \times 100 \text{ pm} = 73.2 \text{ pm} \]

4. **Determine the Maximum Radius of X**:
- The maximum radius of the ion 'X' that can replace A^+ in the octahedral voids must be equal to or less than the radius of A^+ calculated above.
- Therefore, the maximum radius of X that can replace Na^+ is:
\[ r_X \leq 73.2 \text{ pm} \]

### Conclusion:
The maximum radius of 'X' that can displace A^+ in the rock salt structure is **73.2 pm**.