What is the edge length of a face-centered cubic unit cell made up of atoms having a radius of 200 pm?
A)71 pm
B)566 pm
C)20 pm
D)110 pm

Question

Quizplus · Accepted Answer

In a face-centered cubic unit cell, there are atoms at each of the 8 corners of the cube, and an additional atom at the center of each face of the cube. This gives a total of 4 atoms per unit cell. 
To determine the edge length, we can use the formula:

2r = √8a

where r is the atomic radius, and a is the edge length of the unit cell.

Plugging in the values, we get:

2(200 pm) = √8a

400 pm = √8a

(400 pm)^2 = 8a

a = 400 pm x √2 = 566 pm

Therefore, the edge length of the face-centered cubic unit cell made up of atoms with a radius of 200 pm is 566 pm.

What Is the Edge Length of a Face-Centered Cubic Unit