$A$ metal with an atomic radius of $141.4 \, pm$ crystallises in the face-centred cubic structure. The volume of the unit cell in $pm^3$ is $.... . \times 10^7$.

Calculate the molar mass of an element having density $5.6 \ g \ cm^{-3}$ that forms a $bcc$ structure. $\left[a^3 \times N_{A}=75 \ cm^3 \ mol^{-1}\right]$

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

$A$ diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of $300 \ pm$. The density of the molecule is $6.17 \ g \ cm^{-3}$. The number of molecules present in $200 \ g$ of $X_2$ is (Avogadro constant $N_A = 6 \times 10^{23} \ mol^{-1}$) (in $N_A$)

$A$ metal has a $fcc$ lattice. The edge length of the unit cell is $404 \, pm$. The density of the metal is $2.72 \, g \, cm^{-3}$. The molar mass of the metal is :- ............ $g \, mol^{-1}$ ( $N_A$ Avogadro constant $= 6.02 \times 10^{23} \, mol^{-1}$ )

Calculate the number of unit cells in $10 \, g$ of $CsCl$ which crystallizes in a $bcc$ structure. $(CsCl = 168.5 \, amu)$