In an $fcc$ lattice,the edge length of a silver unit cell is $4.077 \times 10^{-8} \ cm$ and the density is $10.5 \ g \ cm^{-3}$. Calculate the atomic mass of silver.

If the atomic radius of an element is $75 \, pm$ and it crystallizes in a body-centered cubic $(BCC)$ lattice,what is the edge length of the unit cell in $pm$?

What is the atomic radius of an element if it crystallises in a $BCC$ structure with an edge length of unit cell $287 \ pm$ (in $pm$)?

Calculate the number of atoms per unit cell of an element having a molar mass of $92.0 \ g \ mol^{-1}$ and a density of $8.6 \ g \ cm^{-3}$ forming a cubic unit cell structure. Given $[a^3 \times N_{A} = 21.5 \ cm^3 \ mol^{-1}]$.

$A$ metal crystallizes in a $bcc$ unit cell having unit cell volume $2.5 \times 10^{-23} \text{ cm}^3$. Find the number of unit cells in $18 \text{ g}$ of the metal if the density of the metal is $7.2 \text{ g cm}^{-3}$.

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$