A diatomic molecule is rotating about its center of mass with an angular speed of 2.50 ✕ 1012 rad/s. Determine the rotational kinetic energy (in J) of one molecule, if the gas is fluorine which has a bond length of 0.919 Å and a molecular molar mass of 38.0 g/mole.

Answer: kinetic energy Ke = 4.16 * 10^-22J

Explanation:

Moment of inertia I = 2mr^2

m = (38 * 10^-3 kg/mol) / (2 * 6.02 * 10^23)

Atomic mass m = 3.16 * 10^-26 kg

r = bond length/2 = 0.919Å/2 = 0.4595Å

Bond radius r = 0.4595 * 10^-10m

I = 2 * 3.16*10^-26 * (0.4595 * 10^-10) ^2

I = 1.33 * 10^-46 kgm^2

Kinetic energy Ke = 1/2 (I * w^2)

Angular speed w = 2.50 ✕ 10^12 rad/s

Ke = 1/2 (1.33 * 10^-46 kgm^2 * (2.5 * 10^ 12rad/s) ^2)

Ke = 4.16 * 10^-22J