Question

A metal has an fcc lattice. The edge length of the unit cell is $400 \,pm$. The density of the metal is $2.8 \,g \, cm ^{-3}$. The molar mass of the metal is ____$g \, mol ^{-1}$.
(Avogadro's constant $=6.00 \times 10^{23} \, mol ^{-1}$ )

Answer 1

Metal has $fcc$ lattice,
$\therefore Z=4$
$ d =\frac{Z \times M }{ a ^{3} \times N _{ A }} $
$\therefore 2.8=\frac{4 \times M }{\left(4.00 \times 10^{-8}\right)^{3} \times 6.00 \times 10^{23}} $
$\therefore M =\frac{2.8 \times(4.00)^{3} \times 6.00 \times 10^{-1}}{4}$
$=26.88\,g \,mol ^{-1}$