Calculate the interplanar spacing between the $111$ planes in a $Ca$ crystal (in $nm$). Given that the edge length of the $Ca$ unit cell is $0.556 \ nm$.

$A$ metal has a $fcc$ structure. If the edge length of the unit cell is $200 \text{ pm}$, calculate the volume occupied by the particles in a unit cell.

Copper crystallizes in an $fcc$ lattice with a unit cell edge length of $361 \ pm$. What is the radius of the copper atom in $pm$?

How many unit cells are present in $100 \ g$ of an element with $fcc$ crystal structure having density $10 \ g/cm^{3}$ and edge length $100 \ pm$?

Calculate the number of atoms present in a unit cell of an element having molar mass $190 \ g \ mol^{-1}$ and density $20 \ g \ cm^{-3}$. Given that $[a^3 \cdot N_A = 38 \ cm^3 \ mol^{-1}]$.

Iron exhibits $bcc$ structure at room temperature. Above $900^{\circ}C$,it transforms to $fcc$ structure. The ratio of density of iron at room temperature to that at $900^{\circ}C$ (assuming molar mass and atomic radii of iron remains constant with temperature) is