Question

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 1

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

Step-by-step 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