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

For a BCC structure, atoms at the corners touch the central atom. The atomic radius \( r \) and unit cell edge length \( a \) are related by: \[4r = \sqrt{3}a \quad \Rightarrow \quad r = \frac{\sqrt{3}}{4}a.\]The atomic radius is therefore \( \frac{\sqrt{3}}{4}a \).