Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 Å.
Given:
Diameter of an oxygen molecule (D) = 3 Å
∴ the radius of an oxygen molecule (r) = 1.5 Å (∵ r = D/2)
Fraction = ?
Explanation: We know that the volume occupied by 1 mole of oxygen gas at STP = 22.4 litres. The molecular volume occupied 1 mole of oxygen molecules can be found by multiplying the volume of a single oxygen molecule (considering it to be a sphere) with the
Avogadro's constant. Then dividing the latter by the former the required result is obtained.
Volume of 1 mole of oxygen gas at S.T.P(Vmolecular)
Vmolecular = 
πr3 × NA ---(1)
The actual volume occupied by oxygen gas at STP (Vactual)
Vactual = 22.4 litres = 0.0224 m3
Vactual = 0.0224 m3 ---(2)
(Where NA = 6.02214086 × 1023 mol-1 is Avogadro's constant.)
Substituting for ‘r’ and ‘NA’ in equation (1) we get
Vmolecular = 
πr3 × NA = 
π(1.5 × 10-10)3 × ( 6.02214086 × 1023)
= 0.000008513≈ 8.51 × 10-6 m3
(∵ 1 Å = 1 × 10-10 m)
∴ Vmolecular = 8.52 × 10-6 m3 ---(3)
Fraction = 
= 
= 0.00038007 ≈ 3.8 × 10-4
Fraction = 3.8 × 10-4
The required ratio/fraction is 3.8 × 10-4.