Calculate the density of a metal having molar mass $197 \ g \ mol^{-1}$ if it forms $fcc$ structure. $\left[a^3 \times N_{A}=40 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

An element has a body-centered cubic $(bcc)$ structure with a cell edge of $288 \ pm$. The atomic radius is $...... \ pm$.

The inter-planar spacing between the $(2, 2, 1)$ planes of a cubic lattice of length $450 \, pm$ is $.... \, pm$

Find the molar mass of an element that crystallizes forming a unit cell structure having an edge length of $4 \times 10^{-8} \ cm$ and containing $4$ particles. (Density $\rho = 19.7 \ g \ cm^{-3}$)

$A$ crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400 \ pm$. If the density of the substance in the crystal is $8 \ g \ cm^{-3}$, then the number of atoms present in $256 \ g$ of the crystal is $N \times 10^{24}$. The value of $N$ is

Derive the expression for the density $(d)$ of a unit cell: $d = \frac{zM}{a^3 N_A}$.