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. **Understanding the Simple Cubic Lattice**:
- In a simple cubic lattice, the anions are located at each corner of the cube. The body center of the cube is empty in a simple cubic structure.

2. **Identifying the Unit Cell Dimensions**:
- The side length of the unit cell is given as \( a = 2.88 \, \text{Å} \).

3. **Determining the Radius of the Anion**:
- In a simple cubic lattice, the anions touch each other along the edges of the cube. Therefore, the relationship between the side length \( a \) and the radius \( r \) of the anion is given by:
\[ a = 2r \]
- Rearranging this equation gives:
\[ r = \frac{a}{2} = \frac{2.88 \, \text{Å}}{2} = 1.44 \, \text{Å} \]

4. **Finding the Diameter of the Void**:
- The void in the body center of a simple cubic lattice is spherical and its diameter is equal to the distance between the centers of the anions located at the corners of the cube.
- The distance between the centers of the anions at opposite corners of the cube can be calculated using the diagonal of the face of the cube:
\[ \text{Diagonal of face} = a\sqrt{2} \]
- The diameter of the void can be calculated as:
\[ \text{Diameter of void} = \text{Diagonal of face} - 2r \]
- Substituting the values:
\[ \text{Diameter of void} = a\sqrt{2} - 2r = 2.88\sqrt{2} - 2(1.44) \]
- Calculating \( 2.88\sqrt{2} \):
\[ 2.88 \times 1.414 \approx 4.07 \, \text{Å} \]
- Now substituting back:
\[ \text{Diameter of void} = 4.07 - 2.88 \approx 1.19 \, \text{Å} \]

### Final Answer:
The diameter of the void in the body center is approximately \( 1.19 \, \text{Å} \).