Salt $AB$ has a zinc blende structure. The radii of $A^{2+}$ and $B^{2-}$ ions are $0.7 \ \mathring{A}$ and $1.8 \ \mathring{A}$ respectively. The edge length of the $AB$ unit cell is ........... $\mathring{A}$.

$A$ 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 $N_A$)

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

The density of chromium metal is $7.2 \, g \, cm^{-3}$. If the edge length of the unit cell is $289 \, pm$, determine the type of unit cell (Simple Cubic, Body-Centered Cubic, or Face-Centered Cubic). [Atomic mass of $Cr = 52 \, a.m.u.$, $N_A = 6.02 \times 10^{23} \, mol^{-1}$]

Calculate the density of a metal with molar mass $56 \ g \ mol^{-1}$ that crystallises in a $bcc$ structure with an edge length of $288 \ pm$. (in $g \ cm^{-3}$)

If $M$ is the atomic mass of an element and $a$ is the edge length of the unit cell,then the formula to calculate the density $\rho$ is: