Silicon (Si) has a diamond crystal structure which has
a lattice spacing of
*
a
*
= 0.542 nm.

(a) Calculate the density of Si atoms per cm
^{
2
}
on {100} planes.

(b) Treat atoms as rigid spheres with radii equal to one-half of the distance between nearest neighbors. Calculate the percentage of volume occupied by the Si atoms, i.e., its packing fraction.