The cubic unit cell of aluminium (Molar mass $27.0 \ g \ mol^{-1}$) has an edge length of $405 \ pm$. Its density is $2.70 \ g \ cm^{-3}$. The type of unit cell is

$A$ metal has a $fcc$ structure. If the edge length of the unit cell is $200 \text{ pm}$, calculate the volume occupied by the particles in a unit cell.

Calculate the edge length of a unit cell for a metal with an atomic radius of $128 \ pm$ that forms an $fcc$ unit cell structure.

An element (atomic weight $= 250 \ u$) crystallises in a simple cubic lattice. If the density of the unit cell is $7.2 \ g \ cm^{-3}$,what is the radius (in $\mathring{A}$) of the atom of the element? $(N_A = 6.02 \times 10^{23} \ mol^{-1})$

If the radii of $Na^{+}$ and $Cl^{-}$ are $95 \, pm$ and $181 \, pm$ respectively, then the edge length of the $NaCl$ unit cell is equal to ...... $pm$.

Calculate the number of atoms in $100 \, g$ of a crystal that crystallizes in an $fcc$ structure, given that its density is $10 \, g/cm^3$ and the edge length is $200 \, pm$.