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.

Answer 1

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 = m/2

Hence, moment of inertia I, is calculated as: