$($Planar Density$)$ Find the answers for gold $($Au$),$ which has a FCC $($face centered$-$cubic$)$ structure. Lattice parameter of gold is $0\mathrm{.}408nm.)=({10}^{-9}(m).$ Lattice parameter is the edge length of unit cell.

a$.$ Write the equation for planar density.

b$.$ How many atoms are centered on the $(100)$ plane?

c$.$ What is the area of the $(100)$ plane?

d$.$ Calculate the planar density for the $(100)$ plane

e$.$ How many atoms are centered on the $(111)$ plane?

f$.$ What is the area of the $(111)$ plane.

g$.$ Calculate the planar density of the $(111)$ plane

h$.$ Which plane is the closed packed plane?