Metal $M$ crystallises in $fcc$ lattice. If the unit cell has an edge length of $4.077 \ \mathring{A}$ and the density is $10.5 \ g \ cm^{-3}$,then the atomic weight of the metal is:

Nickel crystallises in a $fcc$ type of unit cell,with edge length $0.3524 \ nm$. Calculate the radius of nickel atom. (in $nm$)

The crystal of $CsBr$ has an edge length of $437 \ pm$. If the density of the crystal is $4.24 \ g \ cm^{-3}$, determine the type of crystal structure of $CsBr$ (Atomic mass of $Cs = 133, Br = 80$).

Calculate the edge length of a simple cubic unit cell if the radius of an atom is $167.3 \ pm$. (in $pm$)

$A$ solid having density of $9 \times 10^3 \ kg \ m^{-3}$ forms face-centred cubic crystals of edge length $200 \sqrt{2} \ pm$. What is the molar mass of the solid? [Avogadro constant $\cong 6 \times 10^{23} \ mol^{-1}$,$\pi \cong 3$]

The edge length of a body-centered cubic $(BCC)$ unit cell is $390 \ pm$. If the radius of the cation is $150 \ pm$, what is the radius of the anion? (in $pm$)