Calculate the molar mass of a metal having a density of $9.3 \ g \ cm^{-3}$ that forms a simple cubic unit cell. $[a^3 \cdot N_A = 22.6 \ cm^3 \ mol^{-1}]$

$A$ metal $(X)$ of atomic weight $M \ g \ mol^{-1}$ crystallizes in a $bcc$ lattice. Its density is $d \ g \ cm^{-3}$. What is the equation for the unit cell edge length $(a)$? ($N=$ Avogadro number)

$A$ metal crystallises in a face-centred cubic $(FCC)$ structure with a metallic radius of $\sqrt{2} \ \mathring{A}$. The volume of the unit cell (in $m^{3}$) is:

An element (atomic mass $= 100 \ g/mol$) having $bcc$ structure has a unit cell edge of $400 \ pm$. The density of the element is ................. $g/cm^3$.

The atomic radius of strontium $(Sr)$ is $215 \, pm$ and it crystallises in a cubic closed packed $(ccp)$ structure. The edge length of the cube is .............. $pm$.

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$