Silver metal crystallizes in a $ccp$ lattice. If the edge length of the unit cell is $407 \ pm$, the radius of the silver atom is ............. $pm$.

Gold (edge length $0.144 \ nm$) crystallizes in a face-centered cubic unit cell. What is the radius $(r)$ of the gold atom 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 $Cr = 52 \, a.m.u.$, $N_A = 6.02 \times 10^{23} \, mol^{-1}$]

An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?

Derive the formula to determine the density of a unit cell.

What is the volume of one particle in $BCC$ structure if '$a$' is edge length?