At $T \ K$, copper (atomic mass $= 63.5 \ u$) has $fcc$ structure with an edge length of $x \ \mathring{A}$. The density of copper (in $g \ cm^{-3}$) at that temperature is approximately $(N_A = 6.0 \times 10^{23} \ mol^{-1})$

An element has a crystalline structure where the unit cell is a cube with one atom at each corner and two atoms on its body diagonal. If the volume of this unit cell is $24 \times 10^{-24} \, cm^3$ and the density of the element is $7.2 \, g \, cm^{-3}$,then the number of atoms present in $200 \, g$ of the element is:

Calculate the distance between two parallel $(220)$ planes in a crystal with an edge length of $450 \, pm$. (in $pm$)

Ionic radii of cation $A^{+}$ and anion $B^{-}$ are $102 \ pm$ and $181 \ pm$ respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for $B^{-}$ and $A^{+}$ is present in all octahedral voids. The edge length of the unit cell of the crystal $AB$ is $pm$.

$A$ 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 $N_A$)

An element crystallizes in a $bcc$ lattice. The atomic radius of the element is $2.598 \ \mathring{A}$. What is the volume (in $cm^3$) of one unit cell?