Silver has an atomic radius of $144 \ pm$ and the density of silver is $10.6 \ g \ cm^{-3}$. Based on this information, identify the correct statement.

The cubic unit cell structure of a compound containing cation $M$ and anion $X$ is shown below. When compared to the anion,the cation has a smaller ionic radius. Choose the correct statement$(s)$:
$(A)$ The empirical formula of the compound is $MX$.
$(B)$ The cation $M$ and anion $X$ have different coordination geometries.
$(C)$ The ratio of $M-X$ bond length to the cubic unit cell edge length is $0.866$.
$(D)$ The ratio of the ionic radii of cation $M$ to anion $X$ is $0.414$.

An element crystallizes in a body-centred cubic $(BCC)$ structure with an edge length of $400 \ pm$. Calculate the interatomic distance in the crystal. Additionally, if an atom has a radius of $300 \ pm$ and crystallizes in a face-centred cubic $(FCC)$ lattice, calculate the distance between the nearest neighbours.

Calculate the number of atoms present in $1.625 \text{ g}$ of a metal that forms a $bcc$ unit cell structure. Given: $[\rho \times a^3 = 3.25 \times 10^{-22} \text{ g}]$.

$CCP$ lattice of a solid made up of $B^{-}$ ions has an edge length of $3 \ \mathring{A}$ and a density of $5 \ g/cm^3$. If in this lattice $A^{+}$ ions are placed at alternate tetrahedral voids,then the percentage increase in density will be $............. \ \%$. [Molar mass of $A^{+} = 30 \ g/mol$,$N_A = 6 \times 10^{23}$]

The only $INCORRECT$ statement for cubic metallic crystal is