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

Multiple Choice

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.

A) 71.7 pm
B) 101.3 pm
C) 124.1 pm
D) 143.3 pm
E) 248.2 pm