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 $0.556 \ nm$.

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

For a simple cubic system,find the ratio of the interplanar distances between the $(100)$,$(110)$,and $(111)$ planes.

Calculate the number of unit cells in $10.8 \ g$ of metal,given that $\rho a^3 = 7.2 \times 10^{-22} \ g$.

Calculate the molar mass of an element having density $5.6 \ g \ cm^{-3}$ that forms a $bcc$ structure. $\left[a^3 \times N_{A}=75 \ cm^3 \ mol^{-1}\right]$

The density of $\beta-Fe$ is $7.6 \ g \ cm^{-3}$. It crystallizes in a cubic lattice with $a = 290 \ pm$. What is the value of $Z$? $(Fe = 56 \ g \ mol^{-1}; N_{A} = 6.022 \times 10^{23} \ mol^{-1})$