A solid AB has NaCl type structure. if the radius of cation is 220 pm, calculate the maximum possible value of the anion ?

Options

A. `190.2 "pm"`
B. `540.13 "pm"`
C. `525 "pm"`
D. `531.50 "pm"`

Explanation

To solve the problem, we need to calculate the maximum possible value of the anion radius (R-) given the radius of the cation (R+) and the type of structure (NaCl type structure). Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Structure
The solid AB has a NaCl type structure, which means it has a face-centered cubic (FCC) arrangement of ions. In this structure, the coordination number is 6 for both the cation and the anion.

### Step 2: Identify the Radius Ratio
For a NaCl type structure, the radius ratio (R+/R-) must lie between 0.414 and 0.732. Since we are looking for the maximum possible value of the anion radius, we will use the minimum radius ratio of 0.414 for our calculation.

### Step 3: Given Data
- Radius of cation (R+) = 220 pm (picometers)
- Minimum radius ratio for coordination number 6 = 0.414

### Step 4: Set Up the Equation
Using the radius ratio, we can express the relationship between the cation radius and the anion radius as follows:
\[ \frac{R+}{R-} = 0.414 \]
This can be rearranged to find R-:
\[ R- = \frac{R+}{0.414} \]

### Step 5: Substitute the Values
Substituting the value of R+ into the equation:
\[ R- = \frac{220 \text{ pm}}{0.414} \]

### Step 6: Calculate R-
Now, performing the calculation:
\[ R- = \frac{220}{0.414} \approx 531.4 \text{ pm} \]

### Step 7: Conclusion
The maximum possible value of the anion radius (R-) is approximately 531.4 pm.

### Final Answer
Thus, the maximum possible value of the anion radius is **531.4 pm**.

---