The edge length of the unit cell of a metal $(M_w = 24 \ g \ mol^{-1})$ having a cubic structure is $4.53 \ \mathring{A}$. If the density of the metal is $1.74 \ g \ cm^{-3}$, the radius of the metal atom is ............... $pm$ $(N_A = 6 \times 10^{23} \ mol^{-1})$

In a cubic unit cell of an ionic compound, the eight corners are occupied by anions and cations are at the center of the cube. Calculate the volume of the unit cell if the density of the unit cell is $4 \text{ g cm}^{-3}$. [Molar mass of compound $= 168.6 \text{ g mol}^{-1}$ and $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$]

Calculate the number of atoms present in a unit cell for an element having a molar mass of $23 \ g \ mol^{-1}$ and a density of $0.96 \ g \ cm^{-3}$. Given that $a^3 \cdot N_{A} = 48 \ cm^3 \ mol^{-1}$.

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.52 \ \mathring{A}$. Its atomic weight is $39$. Its density (in $kg \ m^{-3}$) will be:

In an orthorhombic crystal system,the values of $a$,$b$,and $c$ are $4.2 \, \mathring{A}$,$8.6 \, \mathring{A}$,and $8.3 \, \mathring{A}$ respectively. Given the molar mass of the solute is $155 \, g \, mol^{-1}$ and the density is $3.3 \, g \, cm^{-3}$,calculate the number of formula units $(Z)$ per unit cell.

$A$ compound has $fcc$ structure. If the density of the unit cell is $3.4 \text{ g cm}^{-3}$,what is the edge length of the unit cell? (Molar mass $= 98.99 \text{ g mol}^{-1}$)