The unit cell of crystalline iron is body-centered cubic, and the atomic radius of iron is 124.1 pm. Determine the length of a unit cell of iron.

would you do this, because I keep getting the wrong answer

c^2=a^2+b^2

(4r)^2=l^2+l^2

16r^2=2l^2

l^2=8r^2

l=r sqrt8

124.1 x sqrt 8= 351.0 pm

The answer should be 286.6 pm

## Answers (1)

No, for a body-centered cubic cell the 4r corresponds to the diagonal passing through the atom in the middle of the cell. This distance corresponds to [sqrt(3)]L, where sqrt means square-root and L is the length of the cube. Therefore, the length of the unit cell of Fe is:

L = (4r/3)[sqrt(3)] = (4/3)(124.1 pm)[sqrt(3)] = 286.6 pm