X-ray diffraction measurements revealed that Cu crystallizes in a face-centered cubic lattice in which the unit cell edge length is 361.5 picometers. Calculate the atomic radius of the Cu atoms in this crystal, based on the assumption that the atoms are tightly packed in the unit cell.Hint: Find the length of the cell face diagonal using the Pythagorean theorem.

Question

Quizplus · Accepted Answer

In a face-centered cubic lattice, the face diagonal is equal to 4 times the atomic radius. Using the Pythagorean theorem, the face diagonal is √2 times the edge length. Therefore, 4r = 361.5√2, solving for r gives approximately 127.8 pm.

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