Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form nearly spherical molecules of 60 atoms each. In the pure compound, the spheres pack in a cubic close-packed array.

(a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere.

(b) The compound K₃C₆₀ is a superconductor at low temperatures. In this compound the K⁺ ions lie in holes in the C₆₀^3– face-centered cubic lattice. Considering the radius of the K⁺ ion and assuming that the radius of C₆₀^3– is the same as for the C₆₀ molecule, predict in what type of holes the K⁺ ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled.