Germanium has the same crystal structure $($diamond$)$ as $Si,$ with a lattice constant of $a=0\mathrm{.}564nm.(20pts$

$($a$)$ How many atoms are contained within a unit cell of a Ge crystal? $(5p{t}_4)$

$($b$)$ Find the spacing $($distance$)$ between $"1$ earest$-$neighbor"$\text{'}$ atoms in Ge$.$ is $(3)$

pts$)$

$nm={10}^{-9}m={10}^{-7}cm$

$($c$)$ Calculate the surface density of Ge atoms per $m^2$ on $\{110\}$ planes. $(5$ pts$)$

$($d$)$ If the observed interplanar spacing is $0\mathrm{.}327nm$ for $Ge,$ please estimate

the possible corresponding $(h,k,l)$ plane. SHOW your work! $(5$ pts$)$