Question

Consider the diatomic oxygen molecule, O_2, which is rotating in the xy plane about the z axis passing through its center, perpendicular to its length. At room temperature, the "average" separation between the two oxygen atoms is 1.21 times 10^-10 m (the atoms are treated as point masses, each with 2.66 times 10^-26 kg.) (a) Calculate the moment of inertia of the molecule about the z-axis. (b) If the angular velocity of the molecule about the z axis is 2.0 times 10^12 rad/s, what is its rotational kinetic energy?

Answer 1

Given :-

r = 1.21 x 10^-10 / 2 = 6.05 x 10^-11 m

w = 2 x 10^12 rad/s

m = 2.66 x 10^-26 kg

a)

I = 2*m*r^2

I = (2 x 2.66 x 10^-26 x (6.05 x 10^-11)^2)

I = 1.9473 x 10^-46 kg-m^2

b)

KE = (1/2)*I*w^2

KE = 3.8946 x 10^-22 J