An element has a $bcc$ structure with an atomic mass of $50$. If the edge length of the unit cell is $290 \ pm$, calculate the density of the unit cell in $\text{g/cm}^{-3}$.

Calculate the number of unit cells in $0.9 \ g$ of a metal if it forms a $bcc$ structure. Given: $\rho \times a^3 = 3 \times 10^{-22} \ g$.

How many atoms of niobium are present in $2.43 \ g$ if it forms $bcc$ structure with density $9 \ g \ cm^{-3}$ and volume of unit cell $2.7 \times 10^{-23} \ cm^3$?

Copper crystallizes in an $fcc$ lattice with an edge length of $3.61 \times 10^{-8} \, cm$. If the measured density is $8.92 \, g \, cm^{-3}$,calculate the theoretical density of the crystal in $g \, cm^{-3}$. (Atomic mass of $Cu = 63.5 \, g \, mol^{-1}$)

The crystal of $CsBr$ has an edge length of $437 \ pm$. If the density of the crystal is $4.24 \ g \ cm^{-3}$, determine the type of crystal structure of $CsBr$ (Atomic mass of $Cs = 133, Br = 80$).

$A$ metal $(X)$ of atomic weight $M \ g \ mol^{-1}$ crystallizes in a $bcc$ lattice. Its density is $d \ g \ cm^{-3}$. What is the equation for the unit cell edge length $(a)$? ($N=$ Avogadro number)