Iron (Fe) crystallizes as a body-centered unit cell and has an atomic radius of 126 pm. What is the edge length for the unit cell of iron?

Question

Quizplus · Accepted Answer

In a body-centered cubic (BCC) structure, the body diagonal is equal to 4 times the atomic radius. The body diagonal can also be calculated using the edge length (a) of the cube by the formula: $\sqrt{3}a$. Given the atomic radius (r) is 126 pm, the body diagonal is $4r = 4 \times 126 = 504$ pm. Setting this equal to $\sqrt{3}a$, we solve for $a$: $a = \frac{504}{\sqrt{3}} \approx 291$ pm.

Iron (Fe) Crystallizes as a Body-Centered Unit Cell and Has