Question

a sample of gaseous neon atoms at atmospheric pressure and 0 dregees C contains 2.69*10^22 atoms per liter. the atomic radius of neon is 69 pm

what fraction of the space is occupied by the atoms themselves

Answer 1

Radius of each neon atom = 69 pm = (69 pm)*(1 m)/(1.0*10¹² pm)

= 6.9*10^-11 m (1 m = 1.0*10¹² pm)

Assume that the neon atoms are spherical. Hence, the volume of each neon atom

= 4/3*π*(radius)³

= 4/3*22/7*(6.9*10^-11 m)³

= 1.3766*10^-30 m³

= (1.3766*10^-30 m³)*(1000 L)/(1 m³)

= 1.3766*10^-27 L (1 m³ = 1000 L).

The gas contains 2.69*10²² neon atoms.

Therefore, volume occupied by 2.69*10²² neon atoms =

(2.69*10²² atoms)*(1.3766*10^-27 L/atom)

= 3.7030*10^-5 L.

The volume occupied by the gas is 1 L.

Therefore, the fraction of volume occupied by the gas atoms

= (volume occupied by the neon atoms)/(volume occupied by the gas)

= (3.7030*10^-3 L)/(1 L)

= 3.7030*10^-5

≈ 3.7*10^-5 (ans, correct to 2 sig. figs).