For a face$-$centered $c^{-}$

$($a$)$ What is the coordination number? $(15$ points$)$

$($b$)$ What are the close$-$packed planes and close$-$packed directions? $(20$ points$)$

$($c$)$ How many atoms are there in the unit cell? $(15$ points$)$

$($d$)$ What is the relationship between the atomic radius $(R)$ and the unit cell edge $($a$)?(20$ points$)$

$($e$)$ Calculate the atomic packing factor $($AFP $=$ total volume of atoms in unit cell $/$ total volume

of unit cell$).(30$ points$)$