The simplest fullerene is C$60,$ a molecule which can be described as a

hollow spherical cage of diameter $0\mathrm{.}71$ nm$.$ At room temperature, crystalline

C$60$ is face centred cubic with a cell edge a $=1\mathrm{.}417$ nm$.$

a$)$ Calculate the average separation between two closest C$60$ molecules at

room temperature.

b$)$ Calculate the density of C$60$ at room temperature.