$($Linear 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 linear density

b$.$ How many atoms are centered on the $[100]$ direction?

c$.$ What is the length of the $[100]$ direction?

d$.$ Calculate the linear density for the $[100]$ direction

e$.$ How many atoms are centered on the $[110]$ direction?

f$.$ What is the length of the $[110]$ direction.

g$.$ Catculate the linear density of the $[110]$ direction

h$.$ Which direction is the closed pack direction?