Question

A diatomic molecule has two atoms connected by electronic bonds. These atoms aren’t fixed, so they oscillate...meaning they’re a good time to apply the har- monic oscillator knowledge we have.
”Bond Energy” is not strictly defined this way, but it’s the energy of the system when the atoms are at their average bond length. Each particle has 1/2 the total energy, and can be thought of as attached by an idealized spring to a non-moving central anchor point.

For an Oxygen-Oxygen bond, the average separation (distance between the two nuclei) is 120.7 picometers, and the bond energy is 494 kilojoules per mole. Find the frequency of oscillation in hertz.

Answer 1

The energy corresponding to a single molecule will be

Half of this energy will be KE hence

The reduced mass of the system can be given as

Then the frequency of the oscillation can be given as

and

therefore frequency will be