When sodium is heated above $1000 \ K$,its crystal structure changes from $bcc$ to $fcc$. Assuming the metallic radius of the atom remains unchanged,the ratio of the fraction of volume occupied by atoms in $bcc$ and $fcc$ structures will be .......

$A$ metal crystallises in a face-centred cubic $(fcc)$ structure. If the edge length of its unit cell is $a$,the closest approach between two atoms in the metallic crystal will be:

Which of the following metals crystallizes in a hexagonal close-packed $(hcp)$ structure?

In a compound $AB_2O_4$,the oxide ions form a cubic close-packed $(CCP)$ lattice. The molar ratio of trivalent cations to bivalent cations is $2:1$. If all the bivalent ions occupy octahedral voids and trivalent ions occupy both tetrahedral and octahedral voids in equal numbers,then the fraction of octahedral voids that remain unoccupied is:

The percentage of unoccupied volume in a simple cubic cell is (in $\%$)

Calculate the volume occupied by a particle in $bcc$ unit cell if the volume of unit cell is $8.2 \times 10^{-23} \ cm^3$.