Question

 Xenon crystallizes in a FCC unit cell. If we assume xenon has a radius of 186.9 pm, what is the density of xenon in g/cm³ ?

Answer 1

Number of atoms present in a FCC unit are four.

Density of face-centered cubic unit cell=$\frac{4\times M}{A3\times Na}$

$M=molar\space mass \space of \space xenon=131.293g$

$A=$ edge of unit cell$=2\sqrt{2r}=2\times \sqrt{2\times 186.9\times 10^{-12}}=3.8668\times 10^{-3}cm$

$Na=$ Avogadro's number$=6.02\times 10^{23}$

In this case, density of xenon$=\frac{4\times 131.293g}{(3.8668\times 10^{-3})^3 \times 6.02\times 10^{23}cm^3}=\frac{525.172g}{(3.4806\times 10^{16}cm^3)}=1.5089\times 10^{-14}g/cm^3$