Question

A sample of gaseous neon atoms at atmospheric pressure and 0 °c contains 2.69 * 1022 atoms per liter. the atomic radius of neon is 69 pm. what fraction of the space do the atoms occupy? what does this reveal about the separation between atoms in the gaseous phase?

Answer 1

Explanation

Radius of neon atom : 69 pm = $69\times 10^{-12} m$

Volume occupied by the one atom:$\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times 3.14\times(69\times 10^{-12} m)^3=1.37\times 10^{-30} m^3$

given that $2.69\times 10^{22}$ atoms are present in 1L

1 L = 0.001 $m^3$

The volume occupied by the $2.69\times 10^{22}$ neon atoms

$2.69\times 10^{22}\times 1.37\times 10^{-30} m^3=3.68\times 10^{-8} m^3$

Fraction of volume occupied by the neon atom:

$=\frac{3.68\times 10^{-8} m^3}{0.001 m^3}=3.68\times 10^{-11} m^3$

$3.68\times 10^{-11} m^3$

The fraction of of volume occupied by the neon atom is very less than the 1 L which indicates the presence of large amount of empty space between the atoms of the gas.