$A$ metal crystallizes in two cubic phases,$fcc$ and $bcc$,whose unit cell edge lengths are $3.5 \ \mathring{A}$ and $3.0 \ \mathring{A}$ respectively. Calculate the ratio of the densities of $fcc$ and $bcc$ phases.

When an electron in an excited atom jumps from the $L$ shell to the $K$ shell,$X$-rays are emitted. These $X$-rays undergo first-order diffraction at an angle of $7.75^{\circ}$ by a crystal with an interplanar spacing of $2.64 \ \mathring{A}$. Calculate the energy difference between the $K$ shell and the $L$ shell. $(\sin \ 7.75^{\circ} = 0.1349)$

$A$ binary compound $(A^{+} B^{-})$ has a rock salt structure. If the edge length is $400 \, pm$ and the radius of the cation $(A^{+})$ is $75 \, pm$, what is the radius of the anion $(B^{-})$ in $pm$?

At $T \ K$, copper (atomic mass $= 63.5 \ u$) has $fcc$ structure with an edge length of $x \ \mathring{A}$. The density of copper (in $g \ cm^{-3}$) at that temperature is approximately $(N_A = 6.0 \times 10^{23} \ mol^{-1})$

$NaCl$ has a face-centered cubic structure. The edge length of the unit cell is $0.564 \ nm$. What is the density of sodium chloride? $.............. \ g/cm^3$ [$1 \ nm = 10^{-7} \ cm$]

$A$ metal has a $fcc$ lattice. The edge length of the unit cell is $404 \, pm$. The density of the metal is $2.72 \, g \, cm^{-3}$. The molar mass of the metal is ................. $g \, mol^{-1}$.
($N_A$ Avogadro's constant $= 6.02 \times 10^{23} \, mol^{-1}$)