Question

The nearest neighbor distance in case of BCC structure is

• A. \( \frac{a\sqrt{3}}{2} \)
• B. \( \frac{2a}{\sqrt{3}} \)
• C. \( \frac{a}{\sqrt{2}} \)
• D. \( a \)

Hint:

For BCC structures, the nearest neighbor distance can be derived using the body diagonal, but note that atoms at the corners and the center share space, which leads to a slightly shorter distance than half the body diagonal.

Answer 1

The Correct Option is B

In a body-centered cubic (BCC) structure, atoms are located at the corners and the center of the unit cell. The body diagonal of the cube connects two nearest atoms through the center atom. The body diagonal of a cube with edge length \( a \) is given by: \[ \text{Body diagonal} = a\sqrt{3} \] Since the atoms at the ends of the body diagonal are nearest neighbors in a BCC structure, the nearest neighbor distance would ideally be half of the body diagonal: \[ \text{Nearest neighbor distance} = \frac{a\sqrt{3}}{2} \] However, in a BCC structure, atoms at the center and corners share space, which alters the actual nearest neighbor distance. The correct nearest neighbor distance is: \[ \frac{2a}{\sqrt{3}}. \]