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Q.
A metal has a $fcc$ lattice. The edge length of the unit cell is $404\, pm$. The density of the metal is $2.72\,g$ $cm^{-3}$. The molar mass of the metal is :
Given, cell is $fcc$. So, $Z=4$
Edge length, $a=404\, pm =4.04 \times 10^{-8} cm$
Density of metal, $d=2.72\, g / cm ^{3}$
$N_{A}=6.02 \times 10^{23} mol ^{-1}$
Molar mass of the metal, $M=$ ?
We know that density,
$d =\frac{Z \times M}{a^{3} \cdot N_{A}}$
$\Rightarrow M=\frac{d \cdot a^{3} N_{A}}{Z}$
$=\frac{2.72 \times\left(4.04 \times 10^{-8}\right)^{3} \times 6.02 \times 10^{23}}{4}$
$=27\, g / mol$
$\therefore$ Atomic mass of copper $(Cu)=63.1\, u$.