Calculate the number of atoms present in $90 \text{ g}$ of a metal that forms a $bcc$ structure. Given: $[\rho \times a^3 = 1.8 \times 10^{-22} \text{ g}]$, where $\rho$ is density and $a$ is the edge length of the unit cell.

Niobium crystallizes in a body-centered cubic $(BCC)$ structure. If the density is $8.55 \ g \ cm^{-3}$,calculate the atomic radius of niobium. (Atomic mass of niobium $M_w = 93 \ g \ mol^{-1}$)

In an ionic compound with a $bcc$ structure, the distance between the two nearest ions is $173 \, pm$. What is the edge length of the unit cell in $pm$?

$A$ copper complex crystallising in a $CCP$ lattice with a cell edge of $0.4518 \ nm$ has been revealed by employing $X$-ray diffraction studies. The density of the copper complex is found to be $7.62 \ g \ cm^{-3}$. The molar mass of the copper complex is $..... \ g \ mol^{-1}$. (Nearest integer)
[Given : $N_{A} = 6.022 \times 10^{23} \ mol^{-1}$]

An element has a $BCC$ structure. The edge length of the unit cell is $288 \, pm$. If the density of the crystal is $7.2 \, g \, cm^{-3}$, what is the atomic mass of the element?

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