Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

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 $M_w = 93 \ g \ mol^{-1}$)

The unit cell of copper corresponds to a face-centered cubic $(FCC)$ lattice with an edge length of $3.596 \, \mathring{A}$. The calculated density of copper in $kg / m^{3}$ is ....... .
[Molar mass of $Cu = 63.54 \, g/mol$; Avogadro Number $= 6.022 \times 10^{23} \, mol^{-1}$]

Nickel crystallises in a $fcc$ type of unit cell,with edge length $0.3524 \ nm$. Calculate the radius of nickel atom. (in $nm$)

What is the relationship between the edge length $(a)$ and the radius of the atom $(r)$ in a simple cubic unit cell?

Xenon crystallizes in $fcc$ lattice and the edge length of unit cell is $620 \ pm$. What is the radius of $Xe$ atom (in $pm$)?