Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 carbons each. In a pure compound the spheres pack in a cubic close packed array. The length of the side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm.
a. 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 the holes in the C60- face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of C60- 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 percentages of these holes are filled.