In a simple cubic lattice of anions, the side length of the unit cell is `2.88 Å`. The diameter of the void in the body centre is

Options

A. `1.934 Å`
B. `0.461Å`
C. `2.108Å`
D. `4.988Å`

Answer

To find the diameter of the void in the body center of a simple cubic lattice of anions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The side length (edge length) of the unit cell, \( a = 2.88 \, \text{Å} \).

2. **Understand the Relationship:**
- In a simple cubic lattice, the relationship between the radius of the void in the body center (let's denote it as \( r \)) and the edge length \( a \) is given by:
\[ a = r + \sqrt{3} \cdot r \]
- This can be simplified to:
\[ a = r(1 + \sqrt{3}) \]

3. **Rearranging the Equation:**
- To find the radius \( r \), we can rearrange the equation:
\[ r = \frac{a}{1 + \sqrt{3}} \]

4. **Substituting the Values:**
- Now, substitute the value of \( a \):
\[ r = \frac{2.88 \, \text{Å}}{1 + \sqrt{3}} \]
- We know that \( \sqrt{3} \approx 1.732 \), thus:
\[ r = \frac{2.88 \, \text{Å}}{1 + 1.732} = \frac{2.88 \, \text{Å}}{2.732} \]

5. **Calculating the Radius:**
- Performing the calculation:
\[ r \approx \frac{2.88}{2.732} \approx 1.0549 \, \text{Å} \]

6. **Finding the Diameter:**
- The diameter \( D \) of the void is twice the radius:
\[ D = 2r = 2 \times 1.0549 \, \text{Å} \approx 2.1098 \, \text{Å} \]

7. **Final Answer:**
- The diameter of the void in the body center is approximately \( 2.11 \, \text{Å} \).