The oxygen molecule has a mass of `5.30 xx 10^(-26) kg` and a moment of inertia of `1.94 xx 10^(-46) kg m^(2)` about an axis through its centre perpendicular to the line 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.

Explanation

To solve the problem, we need to find the average angular velocity of the oxygen molecule given its mass, moment of inertia, mean speed, and the relationship between its rotational and translational kinetic energies.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of the oxygen molecule, \( m = 5.30 \times 10^{-26} \, \text{kg} \)
- Moment of inertia, \( I = 1.94 \times 10^{-46} \, \text{kg m}^2 \)
- Mean speed, \( v = 500 \, \text{m/s} \)
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