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) of an oxygen molecule can be related to its bond length (r) using the formula:
I = µr^2
where µ is the reduced mass of the molecule, given by:
µ = m/2
where m is the atomic mass of oxygen.

Substituting the given values, we have:
I = 5.46 x 10^-46 kg m^2
µ = (16/2) x 1.66 x 10^-27 kg = 1.328 x 10^-26 kg

Rearranging the first equation, we get:
r = sqrt(I / µ) = sqrt(5.46 x 10^-46 kg m^2 / 1.328 x 10^-26 kg) = 0.21 nm (approx.)

Therefore, the closest answer choice is C) 0.2.

An Oxygen Molecule Has a Moment of Inertia of 5