An element crystallizes in an $f.c.c.$ structure with a unit cell edge length of $200 \, pm$. If $200 \, g$ of this element contains $24 \times 10^{23}$ atoms,calculate its density in $\text{g cm}^{-3}$.

Niobium crystallises in a body-centred cubic $(bcc)$ structure. If the density is $8.55 \ g \ cm^{-3}$, then the atomic radius of niobium is (atomic mass of niobium $= 93 \ u$) (in $pm$)

Calculate the radius of an atom of metal if it forms a simple cubic unit cell with an edge length of $380 \ pm$. (in $pm$)

Calculate the number of unit cells in $1 \ cm^3$ volume of an element if unit cell edge length is $4.0 \times 10^{-8} \ cm$.

$A$ diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of $300 \ pm$. The density of the molecule is $6.17 \ g \ cm^{-3}$. The number of molecules present in $200 \ g$ of $X_2$ is (Avogadro constant $N_A = 6 \times 10^{23} \ mol^{-1}$) (in $N_A$)

What is the edge length of the unit cell of a body-centred cubic $(BCC)$ crystal of an element whose atomic radius is $75 \ pm$ (in $pm$)?