Question
The oxygen molecule has a mass of 5.30 × 10–26 kg and a moment of inertia of 1.94×10–46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.
Solution
Mass of an oxygen molecule, m = 5.30 × 10–26 kg
Moment of inertia, I = 1.94 × 10–46 kg m2 Velocity of the oxygen molecule, v = 500 m/s
The separation between the two atoms of the oxygen molecule = 2r
Mass of each oxygen atom =
Hence, moment of inertia I, is calculated as
(
)r2 + (
)r2 = mr2 r =
= 0.60 × 10-10 m It is given that,
KErot =
KEtrans 
I ω2 = 
×
× mv2 mr2ω2 =
mv2 ω =
=
= 6.80 × 1012 rad/s.
