Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

An element crystallises in $fcc$ type of unit cell. The volume of one unit cell is $24.99 \times 10^{-24} \ cm^{3}$ and density of the element is $7.2 \ g \ cm^{-3}$. Calculate the number of unit cells in $36 \ g$ of a pure sample of the element.

Lithium has a body-centered cubic $(BCC)$ structure. If the edge length of its unit cell is $351 \ pm$, what is the atomic radius of lithium in $pm$?

Silver crystallises in $fcc$ structure. If the edge length of the unit cell is $316.5 \text{ pm}$, what is the radius of the silver atom (in $\text{pm}$)?

$A$ metal crystallises in a face-centred cubic $(FCC)$ structure with a metallic radius of $\sqrt{2} \ \mathring{A}$. The volume of the unit cell (in $m^{3}$) is:

Calculate the volume of the unit cell of an element having a molar mass of $63.5 \ g \ mol^{-1}$ that forms an $fcc$ structure $\left[\varrho \times N_{A} = 5.5 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.