Editing Diatomic molecule (section)

=== Rotational energies ===
Classically, the kinetic energy of rotation is
<math display="block">E_\text{rot} = \frac{L^2}{2 I} </math>
where
* <math>L \,</math> is the [[angular momentum]]
* <math>I \,</math> is the [[moment of inertia]] of the molecule

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by
<math display="block">L^2 = \ell(\ell+1) \hbar^2 </math>
where <math>\ell</math> is a non-negative integer and <math>\hbar</math> is the [[reduced Planck constant]].

Also, for a diatomic molecule the moment of inertia is
<math display="block">I = \mu r_0^2 </math>
where
* <math>\mu \,</math> is the [[reduced mass]] of the molecule and
* <math>r_0 \,</math> is the average distance between the centers of the two atoms in the molecule.

So, substituting the angular momentum and moment of inertia into {{math|''E''<sub>rot</sub>}}, the rotational energy levels of a diatomic molecule are given by:
<math style="" display="block">E_\text{rot} = \frac{\ell (\ell + 1) \hbar^2}{2 \mu r_0^2}, \quad \ell = 0, 1, 2, \dots</math>