What is the length of the diagonal (in atomic radii)along the face of a face-centered cubic unit cell?
B) 2 × r
C) 4 × r
E) r

Question

What is the length of the diagonal (in atomic radii)along the face of a face-centered cubic unit cell?
B) 2 × r 
C) 4 × r 
E) r

Quizplus · Accepted Answer

In a face-centered cubic unit cell, there are four atoms at the corners of the unit cell and one atom at the center of each face. If we consider the diagonal joining two opposite corners of a face, it passes through one face-centered atom and goes up to the center of another face. This diagonal passes through two edges of the unit cell and hence has a length equal to the diagonal of a square face of the unit cell. In a square face, the diagonal is √2 times the length of the edge. Therefore, the diagonal of the face-centered cubic unit cell is 2√2 times the length of the edge. But the edge length of a face-centered cubic unit cell (in terms of the atomic radius, r) is 4r/√3. Therefore, the diagonal length is 2√2 times this value, which simplifies to 4r. Hence, the answer is C.

What Is the Length of the Diagonal (In Atomic Radii)along