Respuesta :
Answer:
The estimated radius is 2.734*10^(-10) m.
Explanation:
If we assume the van der Waals constant b for Xenon divided by Avogadro's number gives the volume of a single Xenon, we have
[tex]V=\frac{b}{N}=\frac{0.05156 l/mol}{6.02214076*10x^{23}} =8.56*10^{-26}litres\\[/tex]
We can express this volume in other units, more suitable for the size of an atom:
[tex]V=8.56*10^{-26}litres*\frac{1m3}{10^{3}litres }*(\frac{10^{9} nm}{1m } )^{3}\\\\V=8.56*10^{-26}litres*\frac{1m3}{10^{3}litres }*\frac{10^{27} nm3}{1m3 } \\\\ V=0.0856 \, nm^{3}[/tex]
The volume of the sphere is
[tex]V=\frac{4\pi}{3}*r^{3}[/tex]
Then we can rearrange to clear r
[tex]r=\sqrt[3]{\frac{3V}{4\pi} }= \sqrt[3]{\frac{3*0.0856nm^{3}}{4\pi} }=\sqrt[3]{0.0204 nm^{3} }=0.2734nm[/tex]
The estimated radius is 0.2734 nm. As the problem ask for the radius to be in meters (1 nm = 10^(-9) m), we can multiply it by 10^(-9) and determine that the radius is 2.734*10^(-10) m.
