data below to answer the questions:

$a=\sqrt[\phantom{2}]{8}R$

Avogadro's Number $=6\mathrm{.}023**{10}^{23}$ atoms $\frac{?}{\text{m}\text{o}\text{l}\text{e}}$

Atomic Number $=79$

Atomic Mass $=197\mathrm{.}00\frac{g}{m}$ole

Atomic radius $=0\mathrm{.}144nm$

$($a$)$ What is the lattice constant of gold?

$a=\sqrt[\phantom{2}]{8}(\mathrm{.}144mm)=0\mathrm{.}407nm$

$($b$)$ What is the linear density in the $\left[\begin{array}{ccc}1& 0& 1\end{array}\right]$ direction?

$\frac{?}{{?}_D}$

$($c$)$ What is the planar density of the $(($:$[1,1,1]\}$ plane?