A metallic element crystallizes in a face-centered cubic array of atoms, for which the length of the cube edge is 351 pm. What is the atomic radius of the metal, in pm?

Question

Quizplus · Accepted Answer

In a face-centered cubic array, the diagonal of the face of the cube is equal to four times the atomic radius. Therefore, the atomic radius is equal to one-fourth of the diagonal of the face of the cube. The diagonal of the face of the cube is equal to the square root of 2 times the length of the cube edge. Therefore, the atomic radius is equal to one-fourth of the square root of 2 times the length of the cube edge. Substituting the given value of the length of the cube edge, we get:atomic radius = (1/4) * sqrt(2) * 351 pm = 124 pm

A Metallic Element Crystallizes in a Face-Centered Cubic Array of Atoms