X-ray diffraction measurements revealed that $\alpha$-Fe crystallizes in a face-centered cubic lattice in which the unit cell edge length is 286.6 picometers. Calculate the atomic radius of the Fe atoms in this crystal, based on the assumption that the atoms are tightly packed in the unit cell.Hint: Find the length of the cell face diagonal using the Pythagorean theorem.

Question

Quizplus · Accepted Answer

In a face-centered cubic (FCC) lattice, the face diagonal is equal to 4 times the atomic radius. Using the Pythagorean theorem, the face diagonal is $\sqrt{2} \times 286.6$ pm. Solving for the atomic radius: $4r = \sqrt{2} \times 286.6$, so $r = \frac{\sqrt{2} \times 286.6}{4} \approx 101.3$ pm.

X-Ray Diffraction Measurements Revealed That α\alphaα -Fe Crystallizes in a Face-Centered Cubic Lattice in Which the Face-Centered

X-Ray Diffraction Measurements Revealed That $\alpha$ -Fe Crystallizes in a Face-Centered Cubic Lattice in Which the Face-Centered