`AB` crystallizes in a body centred cubic lattice with edge length `a` equal to `387p m` .The distance between two oppositely charged ions in the lattice is :

Options

A. 335 pm
B. 250 pm
C. 200 pm
D. 300 pm

Explanation

To find the distance between two oppositely charged ions in a body-centered cubic (BCC) lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of BCC Lattice**:
In a body-centered cubic lattice, there are atoms located at the eight corners of the cube and one atom at the center of the cube.

2. **Calculate the Number of Atoms in the Unit Cell**:
- Each corner atom is shared by 8 unit cells, so the contribution from the 8 corner atoms is \( \frac{1}{8} \times 8 = 1 \) atom.
- There is 1 atom at the body center.
- Therefore, the total number of atoms in a BCC unit cell is \( 1 + 1 = 2 \).

3. **Identify the Edge Length**:
- The edge length \( a \) is given as \( 387 \) picometers.

4. **Determine the Nearest Neighbor Distance**:
- In a BCC lattice, the nearest neighbor distance \( d \) can be calculated using the formula:
\[ d = \frac{\sqrt{3}}{2} a \]
- Substitute the value of \( a \) into the formula:
\[ d = \frac{\sqrt{3}}{2} \times 387 \, \text{pm} \]

5. **Calculate the Value**:
- First, calculate \( \sqrt{3} \approx 1.732 \).
- Now, calculate \( d \):
\[ d = \frac{1.732}{2} \times 387 \approx 0.866 \times 387 \approx 335.14 \, \text{pm} \]

6. **Round the Result**:
- Rounding \( 335.14 \) picometers gives us \( 335 \) picometers.

7. **Conclusion**:
- The distance between the two oppositely charged ions in the BCC lattice is \( 335 \) picometers.

### Final Answer:
The distance between two oppositely charged ions in the lattice is **335 picometers**.