Aluminium metal has a density of $2.72 \ g \ cm^{-3}$ and crystallizes in a cubic lattice with an edge length of $404 \ pm$. Which of the following is correct?

$A$ metal with an atomic radius of $141.4 \, pm$ crystallises in the face-centred cubic structure. The volume of the unit cell in $pm^3$ is $.... . \times 10^7$.

Copper crystallises in a $ccp$ arrangement and the accepted value of the metal ion radius was found to be $1.28 \ \mathring{A}$. Calculate the density of copper in grams per cubic centimetre. (Atomic weight of copper is $63.5 \ g/mol$, $N_A = 6.022 \times 10^{23} \ mol^{-1}$) (in $g/cm^3$)

Calculate the interplanar spacing between the $111$ planes in a $Ca$ crystal (in $nm$). Given that the edge length of the $Ca$ unit cell is $0.556 \ nm$.

What is the molar mass of a metal having a density of $8.57 \ g \ cm^{-3}$ and an edge length of $3.3 \ \mathring{A}$? (Packing efficiency $= 68 \%$)

In an orthorhombic crystal system,the values of $a$,$b$,and $c$ are $4.2 \, \mathring{A}$,$8.6 \, \mathring{A}$,and $8.3 \, \mathring{A}$ respectively. Given the molar mass of the solute is $155 \, g \, mol^{-1}$ and the density is $3.3 \, g \, cm^{-3}$,calculate the number of formula units $(Z)$ per unit cell.