`AB` crystallizes in a body centred cubic lattice with edge length `a` equal to `365p m` .The distance between two oppositely charged ions in the lattice is :

Options

A. 335 pm
B. 316 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 1: Understand the BCC Structure
In a body-centered cubic lattice, there are atoms located at each corner of the cube and one atom at the center of the cube.

### Step 2: Identify the Body Diagonal
The body diagonal of the cube connects two opposite corners of the cube and passes through the center atom. The length of the body diagonal can be calculated using the formula:
\[ \text{Length of body diagonal} = a \sqrt{3} \]
where \( a \) is the edge length of the cube.

### Step 3: Calculate the Length of the Body Diagonal
Given that the edge length \( a = 365 \) picometers, we can calculate the body diagonal:
\[ \text{Length of body diagonal} = 365 \sqrt{3} \text{ pm} \]

### Step 4: Find the Distance Between Oppositely Charged Ions
The distance between the two oppositely charged ions (one at a corner and one at the body center) is half the length of the body diagonal:
\[ \text{Distance} = \frac{\text{Length of body diagonal}}{2} = \frac{a \sqrt{3}}{2} \]

### Step 5: Substitute the Value of \( a \)
Now, substituting the value of \( a \):
\[ \text{Distance} = \frac{365 \sqrt{3}}{2} \text{ pm} \]

### Step 6: Calculate the Numerical Value
Now, we can calculate the numerical value:
\[ \sqrt{3} \approx 1.732 \]
Thus,
\[ \text{Distance} = \frac{365 \times 1.732}{2} \text{ pm} \approx \frac{632.58}{2} \text{ pm} \approx 316.29 \text{ pm} \]

### Step 7: Round Off the Value
Rounding off, we get:
\[ \text{Distance} \approx 316 \text{ pm} \]

### Conclusion
The distance between the two oppositely charged ions in the BCC lattice is approximately **316 picometers**.

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