An element with a molar mass $27 \text{ g mol}^{-1}$ forms a cubic unit cell. Calculate the number of atoms present in a unit cell if the density of the metal is $2.7 \text{ g cm}^{-3}$. Given: $[a^3 \times N_A = 40 \text{ cm}^3 \text{ mol}^{-1}]$

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$

$Fe$ crystallizes in a $bcc$ lattice. If the edge length is $286.65 \,pm$ and the density is $7.874 \,g/cm^3$, calculate the Avogadro number. $(Fe = 55.845 \,u)$

The edge length of a cube is $300 \ pm$. Its body diagonal would be: (in $pm$)

In an $NaCl$ crystal, the radii of $Na^{+}$ and $Cl^{-}$ ions are $95 \, pm$ and $180 \, pm$ respectively. The edge length of its unit cell is ........... $pm$.

An element $A$ has a face-centred cubic $(fcc)$ structure with an edge length equal to $361 \ pm$. The radius of atom $A$ is ............... $pm$.