An element has $2.03 \times 10^{24}$ atoms in $135 \ g$. If the element crystallizes in a face-centered cubic $(FCC)$ lattice structure with an edge length of $150 \ pm$, then the density of the element is ............... $g \ cm^{-3}$.

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length $405 \ pm$. If its density is $2.7 \times 10^{3} \ kg \ m^{-3},$ the radius of the element is approximately......... $\times 10^{-12} \ m$ (to the nearest integer).

Niobium crystallizes in a $bcc$ structure. If its density is $8.55 \, g/cm^3$, calculate the atomic radius of niobium. [Atomic mass of $Nb = 93 \, u$] (in $pm$)

Sodium metal crystallizes in a $bcc$ lattice with a unit cell edge length of $a = 4.29 \ \mathring{A}$. What is the radius of the sodium atom in $\mathring{A}$?

Aluminium crystallises in a face-centred cubic structure, its atomic radius is $125 \text{ pm}$. What is the edge length of the unit cell (in $\text{pm}$)?

The inter-planar spacing between the $(2, 2, 1)$ planes of a cubic lattice of length $450 \, pm$ is $.... \, pm$