Question

An element crystallizes in a structure having an fcc unit cell of an edge $200pm$. Calculate its density if $200g$ of this element contains $24\times {10}^{23}atoms$.

Answer 1

Molar mass $=\frac{200}{24\times {10}^{23}}\times 6.023\times {10}^{23}=50.19gmo{l}^{-1}$
For $fcc,Z=4,V=a^3=(200\times {10}^{-10}{)}^3$
density $=\frac{ZM}{N_0\times V}$

$=\frac{4\times 50.19}{6.023\times {10}^{23}\times 8\times {10}^{-24}}$=$4.166gc{m}^{-3}$