Question

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

Answer 1

For fcc,

$z=4$

$N=24\times {10}^{23}$ atoms

$a=200$ pm

$=200\times {10}^{-10}$pm

$=2\times {10}^{-8}$ cm

$d=\frac{z\times M}{a^3\times N}$

$=\frac{4\times 200}{8\times {10}^{-24}\times 24\times {10}^{23}}$

$=\frac{1000}{24}$

$=41.67gc{m}^{-3}$