In a body-centered cubic lattice, the edge length a is related to the atomic radius R by which expression?

• A. a = 2R sqrt(3)
• B. a = 4R / sqrt(3)
• C. a = R sqrt(2)
• D. a = 2R

Answer: (B)

In a body-centered cubic lattice, atoms touch along the body diagonal. The body diagonal length is √3 times the edge length a. The centers of the corner atom and the center atom lie on this diagonal and are separated by 2R when they touch. That center-to-center distance is half the body diagonal, (√3/2) a. Setting (√3/2) a = 2R gives a = 4R/√3. This is why that expression is the correct relation. Other options would correspond to atoms touching along edges or face diagonals, which isn’t the case for BCC.