An oxygen molecule has a moment of inertia of 5 × 10−⁴⁶ kg ⋅ m². Calculate the bond length (in nm). Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−²⁷ kg). A) 0.3 B) 0.1 C) 0.2 D) 0.4 E) 0.5

Question

Quizplus · Accepted Answer

The moment of inertia, I, is related to the bond length, r, and the reduced mass, µ, by the equation:

I = µr^2

Rearranging this equation to solve for r, we get:

r = sqrt(I/µ)

The reduced mass is given by:

µ = (m1 * m2)/(m1 + m2)

For an oxygen molecule, m1 = m2 = 16 u, so:

µ = (16 u * 16 u)/(16 u + 16 u) = 8 u = 1.33 × 10^-25 kg

Substituting this and the given moment of inertia into the equation for r, we get:

r = sqrt((5 × 10^-41 kg⋅m^2)/(1.33 × 10^-25 kg)) = 0.197 nm

Therefore, the answer is choice C: 0.2, in nanometers.

An Oxygen Molecule Has a Moment of Inertia of 5