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: $[a^3 \times N_A = 40 \text{ cm}^3 \text{ mol}^{-1}]$

Niobium crystallizes in a $bcc$ structure. If its density is $8.55 \, g/cm^3$, calculate the atomic radius of niobium. [Atomic mass of $Nb = 93 \, u$] (in $pm$)

Lithium forms a body-centred cubic $(BCC)$ structure. The length of the side of its unit cell is $351 \ pm$. The atomic radius of lithium will be: ............. $pm$

Element $X$ crystallizes in a $12$ coordination face-centered cubic $(fcc)$ lattice. On applying high temperature,it changes to an $8$ coordination body-centered cubic $(bcc)$ lattice. Find the ratio of the density of the crystal lattice before and after applying high temperature. The atomic radius of $X$ is the same in both crystals.

What is the edge length of a simple cubic unit cell if the radius of the atom is $174 \ pm$ (in $pm$)?

$KCl$ has the same structure as $NaCl$. If ${r_{Na^+}}/{r_{Cl^-}} = 0.55$ and ${r_{Na^+}}/{r_{K^+}} = 0.74$,then the ratio of the edge lengths of $KCl$ and $NaCl$ is: