Question

A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 417 pm. The diameter of the metal atom is:_______

a. 417 pm
b. 295 pm
c. 209 pm
d. 147 pm
e. none of these

Answer 1

b. 295 pm

Step-by-step explanation:

To answer this question we need to use the equation of a face-centered cubic laticce:

Edge length = √8 R

Where R is radius of the atom.

Replacing:

417pm = √8 R

R = 147.4pm is the radius of the atom

As diameter = 2 radius.

Diameter of the metal atom is:

147.4pm* 2 =

295pm

Right answer is:

b. 295 pm