If the close packed cations in an AB type solid with NaCl structure have a radius of 75 pm, what would be the maximum and mimimum sizes of the anions filling the voids ?

Explanation

To determine the maximum and minimum sizes of the anions filling the voids in an AB type solid with NaCl structure, we can follow these steps:

### Step 1: Understand the NaCl Structure
In the NaCl structure, the cations and anions are arranged in a face-centered cubic (FCC) lattice. Each cation is surrounded by six anions, and the coordination number is 6 for both cations and anions.

### Step 2: Identify the Radius of Cation
Given that the radius of the cation (let's denote it as \( r_{c} \)) is 75 pm (picometers).

### Step 3: Calculate the Radius of Anion
In an NaCl structure, the ratio of the radius of the cation to the radius of the anion is given by the formula:

\[ \frac{r_{c}}{r_{a}} = 0.414 \]

Where \( r_{a} \) is the radius of the anion. Rearranging this formula to find \( r_{a} \):

\[ r_{a} = \frac{r_{c}}{0.414} \]

### Step 4: Substitute the Value of Cation Radius
Now, substituting the value of \( r_{c} \):

\[ r_{a} = \frac{75 \, \text{pm}}{0.414} \approx 181.15 \, \text{pm} \]

### Step 5: Determine Maximum and Minimum Sizes of Anion
- **Maximum Size of Anion**: In the NaCl structure, the maximum size of the anion occurs when the cation and anion are in contact. Therefore, the maximum size of the anion is approximately 181.15 pm.

- **Minimum Size of Anion**: The minimum size of the anion can be determined by considering the limit where the anion is still able to fit into the voids without overlapping with the cations. This is typically a smaller ratio, often around 0.225 for the minimum coordination. Thus, we can use:

\[ \frac{r_{c}}{r_{a}} = 0.225 \]

Rearranging gives:

\[ r_{a} = \frac{r_{c}}{0.225} \]

Substituting the value of \( r_{c} \):

\[ r_{a} = \frac{75 \, \text{pm}}{0.225} \approx 333.33 \, \text{pm} \]

### Summary of Results
- Maximum size of anion: 181.15 pm
- Minimum size of anion: 333.33 pm