Metal $M$ crystallizes in $fcc$ lattice. If the edge length of the unit cell is $4.077 \times 10^{-8} \ cm$ and the density is $10.5 \ g \ cm^{-3}$,the atomic mass of the metal is:

Calculate the molar mass of a metal with density $1 \ g \ cm^{-3}$ forming a $bcc$ structure with an edge length of $420 \ pm$.

Calculate the edge length of a unit cell for a metal with an atomic radius of $128 \ pm$ that forms an $fcc$ unit cell structure.

If the crystal structure of $KCl$ is the same as that of $NaCl$,and the radius ratios are $r_{Na^+}/r_{Cl^-} = 0.55$ and $r_{K^+}/r_{Cl^-} = 0.74$,calculate the ratio of the edge lengths of the unit cells of $KCl$ and $NaCl$.

$A$ solid has a $bcc$ structure. If the distance of nearest approach between two atoms is $1.73 \, \mathring{A}$, the edge length of the cell is ........... $pm$.

An element has $2.03 \times 10^{24}$ atoms in $135 \ g$. If the element crystallizes in a face-centered cubic $(FCC)$ lattice structure with an edge length of $150 \ pm$, then the density of the element is ............... $g \ cm^{-3}$.