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

Given , m = 5.30 × 10^-26kg,

I = 1.94 × 10^-26 kgm² and

V = 500 m/s

KE (translation) = \(\frac{1}{2}\)mv²

= \(\frac{1}{2}\)× (5.30 × 10^-26) (500)²

= 6.625 × 10^-21J

given that,

KE (rotation) =(\(\frac{2}{3}\)) KE (translation)

= 6.748 × 10¹² rad/sec.