Exhibit 11-4 Consider Aluminum metal that crystallizes in a face centered cubic cell to answer the following problem(s). The atomic radius of an aluminum atom is 1.43 . One face of this unit cell is shown in the diagram below.
-Refer to Exhibit 11-4. How many aluminum atoms are present in a single face centered unit cell?

Question

Exhibit 11-4 Consider Aluminum metal that crystallizes in a face centered cubic cell to answer the following problem(s). The atomic radius of an aluminum atom is 1.43 . One face of this unit cell is shown in the diagram below. 
-Refer to Exhibit 11-4. How many aluminum atoms are present in a single face centered unit cell?

Quizplus · Accepted Answer

In a face centered cubic cell, there are atoms at the corners and atoms in the center of each face. The number of atoms at the corners is 8, but each corner atom is shared between eight adjacent unit cells. Therefore, each corner atom contributes only 1/8 of an atom to the unit cell. The number of atoms at the centers of the faces is 6, and each face center atom is shared between two adjacent unit cells. Therefore, each face center atom contributes 1/2 of an atom to the unit cell. Thus, the total number of atoms in a single face centered unit cell is: 8 corners x 1/8 atom per corner + 6 face centers x 1/2 atom per face center = 4 atoms. Therefore, the correct answer is C) 4 Al atoms.

Exhibit 11-4 Consider Aluminum Metal That Crystallizes in a Face