$A$ metal crystallises in a body-centred cubic $(BCC)$ lattice with the metallic radius $\sqrt{3} \ \mathring{A}$. The volume of the unit cell in $m^3$ is:

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 $(N_A = 6.0 \times 10^{23} \ mol^{-1})$

Lithium has a $bcc$ structure. Its density is $530 \ kg \ m^{-3}$ and its atomic mass is $6.94 \ g \ mol^{-1}$. Calculate the edge length of a unit cell of lithium metal in $pm$ $(N_A = 6.02 \times 10^{23} \ mol^{-1})$.

Xenon crystallizes in $fcc$ lattice and the edge length of unit cell is $620 \ pm$. What is the radius of $Xe$ atom (in $pm$)?

An element crystallises in a $bcc$ lattice with a cell edge of $500 \ pm$. The density of the element is $7.5 \ g \ cm^{-3}$. How many atoms are present in $300 \ g$ of the metal?

$CsCl$ crystallises in a cubic structure that has $Cl^{-}$ at each corner and $Cs^{+}$ at the centre of the unit cell. If $r_{Cs^{+}} = 1.69 \ \mathring{A}$ and $r_{Cl^{-}} = 1.81 \ \mathring{A}$,what is the value of the edge length of the cube in $\mathring{A}$?