Question

In a BCC (Body-Centered Cubic) structure, the radius of the atoms is:

• A. \( \frac{a}{2} \)
• B. \( \frac{a}{4} \)
• C. \( \frac{\sqrt{3}}{4} a \)
• D. \( \frac{\sqrt{2}}{4} a \)

Hint:

For a BCC structure, the diagonal of the cube is equal to four times the radius of the atoms. Use this to derive the relationship between atomic radius and edge length.

Answer 1

The Correct Option is C

In a BCC structure, the atoms at the corners are in contact with the atom at the center. The relationship between the atomic radius \( r \) and the edge length \( a \) of the unit cell for a BCC structure is given by: \[ 4r = \sqrt{3}a \quad \Rightarrow \quad r = \frac{\sqrt{3}}{4}a. \] Thus, the atomic radius is \( \frac{\sqrt{3}}{4}a \).