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).

Calculate the edge length of a $bcc$ unit cell if the radius of the metal atom is $227 \ pm$.

$A$ certain element crystallises in a $bcc$ lattice of unit cell edge length $27 \mathring{A}$. If the same element under the same conditions crystallises in the $fcc$ lattice,the edge length of the unit cell in $\mathring{A}$ will be .........
(Round off to the Nearest Integer).
[Assume each lattice point has a single atom]
[Assume $\sqrt{3}=1.73, \sqrt{2}=1.41$]

An element (atomic mass $= 100 \ g/mol$) having $bcc$ structure has a unit cell edge of $400 \ pm$. The density of the element is ................. $g/cm^3$.

An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

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