Question

An oxygen molecule consists of two oxygen atoms whose total mass is 5.3 x 10-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.82 × 10-46 kg·m2. From these data, estimate the effective distance between the atoms.

Answer 1

For each atom, more than 99.9% of the mass is in the nucleus, which can be treated as a point, when compared to the internuclear separation, d. Let M be the total mass of the molecule.

The moment of inertia of the O2 molecule, though an axis that passes midway between the atoms, is

I = 2*(M/2)*(d/2)^2 = M*d^2/4
= 1.82*10^-46 kg*m^2

d^2 = 7.28^10^-46/5.3*10^-26
= 13.74*10^-21 m^2
d = 1.172*10^-10 m = 1.172*10^-8 cm
= 1.172 Angstroms

The actual value is somewhat higher (1.21 Angstroms), but this is what the formula says.