In a body-centered cubic lattice, the lattice parameter a relates to the atomic radius R by which expression?

• A. a = 2R
• B. a = 4R/√2
• C. a = 4R/√3
• D. a = 2√3 R

Answer: (C)

In a body-centered cubic lattice, the closest atoms touch along the body diagonal. The center of a corner atom and the center atom are in contact, so their center-to-center distance is 2R. The distance between these two centers lies along the body diagonal and is half of that diagonal: (a√3)/2. Setting this equal to 2R gives (a√3)/2 = 2R, so a = 4R/√3.

This specific relation comes from the geometry of the BCC arrangement, where the nearest-neighbor direction is the body diagonal, not along an edge or a face. The other expressions correspond to different packing directions or lattice types (for example, a = 4R/√2 is the FCC case, where atoms touch along the face diagonal).