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Q.
An element crystallises in a structure having a $fcc$ unit cell of an edge $200\,pm$. If $200\,g$ of this element contains $24 \times 10^{23}$ atoms then its density is
The Solid State
Solution:
Molar mass of the element
$=\frac{200}{24\times10^{23}}\times6.023\times10^{23}$
$=50.19\,g\,mol^{-1}$
For $fcc, Z=4$,
$V=a^{3}=\left(200\times10^{-10}\right)^{3}$
$d=\frac{Z\times M}{N_{A}\,\times V}$
$=\frac{4\times50.19}{6.023\times10^{23}\times\left(200\times10^{-10}\right)^{3}}$
$=41.66\,g\,cm^{-3}$