Calculate the molar mass of an element having density $7.8 \ g \ cm^{-3}$ that forms a $bcc$ unit cell. $\left[a^3 \cdot N_{A} = 16.2 \ cm^3 \ mol^{-1}\right]$

$CsBr$ has $b.c.c.$ structure with edge length $4.3 \ \mathring{A}$. The shortest inter-ionic distance between $Cs^{+}$ and $Br^{-}$ is ........... $\mathring{A}$.

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 $a^3 \cdot N_{A} = 48 \ cm^3 \ mol^{-1}$.

Calculate the number of atoms present in a unit cell of an element having molar mass $190 \ g \ mol^{-1}$ and density $20 \ g \ cm^{-3}$. Given that $[a^3 \cdot N_A = 38 \ cm^3 \ mol^{-1}]$.

The volume occupied by a single $CsCl$ ion pair in a crystal is $7.014 \times 10^{-23} \ cm^{3}$. The smallest $Cs^{+}-Cs^{+}$ inter-nuclear distance is equal to the length of the side of the cube corresponding to the volume of one $CsCl$ ion pair. The smallest $Cs^{+}-Cs^{+}$ inter-nuclear distance is nearly:

$NaCl$ has $4$ formula units per unit cell. If the edge length of the unit cell is $0.564 \, nm$,then the density of the crystal is ............ $\text{g/cm}^3$. $(NaCl = 58.5 \, \text{g/mol})$