What is the radius of the largest sphere that can be placed at the center of a face-centered cubic unit cell of a cubic closest-packed array of spheres if the spheres have diameters of 4.00 × 10² pm? A) 2.0 × 10² pm B) 41.5 pm C) 83.0 pm D) 4.0 × 10² pm E) none of these

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Quizplus · Accepted Answer

In a face-centered cubic (FCC) structure, the largest sphere that can fit in the octahedral hole at the center of the unit cell has a radius of 0.414 times the radius of the spheres forming the FCC lattice. Given the diameter of the spheres is 400 pm, the radius is 200 pm. Thus, the radius of the largest sphere that can fit is 0.414 × 200 pm = 83.0 pm.

What Is the Radius of the Largest Sphere That Can