Aluminum metal crystallizes in a face centered cubic cell . One face of this unit cell is shown in the diagram that follows. The length along one edge equals 4.04 . What is the atomic radius of an aluminum atom?

Question

Aluminum metal crystallizes in a face centered cubic cell . One face of this unit cell is shown in the diagram that follows. The length along one edge equals 4.04 .  What is the atomic radius of an aluminum atom?

Quizplus · Accepted Answer

In a face centered cubic unit cell, there are atoms at each of the corners and the center of each face. This means there are a total of four atoms within the unit cell.

If we consider the diagonal of the face diagonal in the unit cell, we can see that it passes through the center of the aluminum atom and has a length of:

√2a = √2(4.04 Å) ≈ 5.72 Å

Therefore, the atomic radius of aluminum is approximately half of this value:

r = 5.72 Å/2 ≈ 2.86 Å

So, the correct answer is choice A).

Aluminum Metal Crystallizes in a Face Centered Cubic Cell