If the crystal structure of $KCl$ is the same as that of $NaCl$,and the radius ratios are $r_{Na^+}/r_{Cl^-} = 0.55$ and $r_{K^+}/r_{Cl^-} = 0.74$,calculate the ratio of the edge lengths of the unit cells of $KCl$ and $NaCl$.

$A$ 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.

Radius of cation and anion are $2.5 \ \mathring{A}$ and $2.6 \ \mathring{A}$ respectively. If a cubic crystal system is prepared by combination of above cation and anion then edge length of unit cell is ................ $\mathring{A}$ (Take $\sqrt{3} = 1.7$)

What is the number of unit cells present in a cubic crystal lattice having $4$ atoms per unit cell and weighing $0.60 \ g$ (molar mass $60 \ g \ mol^{-1}$)?

Niobium crystallises in a body-centred cubic $(bcc)$ structure. If the density is $8.55 \, g \, cm^{-3}$,calculate the atomic radius of niobium using its atomic mass $93 \, u$.

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 $3.2 \times 10^{-22} \ g$.