Calculate the edge length of a simple cubic unit cell if the radius of an atom is $167.3 \ pm$. (in $pm$)

$A$ metal $M$ crystallizes into two lattices: face-centered cubic $(fcc)$ and body-centered cubic $(bcc)$ with unit cell edge lengths of $2.0 \ \mathring{A}$ and $2.5 \ \mathring{A}$ respectively. The ratio of densities of the $fcc$ lattice to the $bcc$ lattice for the metal $M$ is $...........$ (Nearest integer).

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.

Derive the expression to calculate the density of a unit cell.

Calculate the density of a metal having molar mass $197 \ g \ mol^{-1}$ if it forms $fcc$ structure. $\left[a^3 \times N_{A}=40 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

Calculate the volume of the unit cell of an element having a molar mass of $27 \ g \ mol^{-1}$ that forms an $fcc$ unit cell. Given: $\rho \cdot N_{A} = 16.0 \times 10^{23} \ g \ cm^{-3} \ mol^{-1}$.