X-ray diffraction measurements revealed that Ag crystallizes in a face-centered cubic lattice in which the unit cell edge length is 408.6 picometers. Calculate the atomic radius of the Ag atoms in this crystal, based on the usual assumption that the atoms are tightly packed in the unit cell.

Question

Quizplus · Accepted Answer

In a face-centered cubic (FCC) lattice, the atomic radius (r) is related to the edge length (a) by the formula: a = 2√2r. Solving for r gives r = a/(2√2). Substituting a = 408.6 pm, we get r = 408.6/(2√2) = 144.5 pm.

X-Ray Diffraction Measurements Revealed That Ag Crystallizes in a Face-Centered