Question

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

Answer 1

For Fcc

$Z=4$

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

$a=200$ $pm$

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

$d=\frac{2\times M}{a^3\times N}=\frac{4\times 200}{8\times {10}^{-24}\times 24\times {10}^{23}}$

$=41.67$ $g/c{m}^3$

The density of $200$ $g$ of this element is $=41.67$ $g/c{m}^3$