A metal crystallizes with a face-centered cubic lattice.The edge of the unit cell is 395 pm.The diameter of the metal atom is:
A)140 pm
B)198 pm
C)279 pm
D)395 pm
E)none of these

Question

Quizplus · Accepted Answer

In a face-centered cubic (FCC) lattice, the atoms touch along the face diagonal. The face diagonal is equal to 4 times the atomic radius (r), and it can also be expressed in terms of the edge length (a) as √2 * a. Therefore, 4r = √2 * a. Solving for the diameter (2r), we get 2r = (√2 * a) / 2 = (√2 * 395 pm) / 2 ≈ 279 pm.

A Metal Crystallizes with a Face-Centered Cubic Lattice