$2.($a$)$ Calculate the Atomic Packing Factor $($APF$)$ of the materials shown below:

$($i$)$ Po $($Polonium$)\backslash (/2\backslash )$

$($ii$)\backslash (\backslash$mathrm$\{$Ni$\}(\backslash )$ Nickel $\backslash ()/2\backslash )$

$($iii$)$ W $($Tungsten$)\backslash (/2\backslash )$

$($iv$)$ Au $($Gold$)\backslash (/2\backslash )$

$($v$)\backslash (\backslash$alpha $\backslash )-$Fe $($alpha$-$iron$)\backslash (/2\backslash )$

$($b$)$ A group of atoms associated with each lattice point is called basis or motif, i$.$e$.$ the repeating pattern. Give the number of atoms per unit cell of the BCC and FCC$,$ and represent the atomic positions of the basis comprising the unit cell. Use simple cubic lattice to determine basis positions of the BCC and FCC$./4$