Rotational Energy Levels For A Rigid-Rotor Diatomic Molecule

The rotational energy levels (in cm^{-1}) for the rigid-rotor diatomic are given by the formula:

J is the rotational quantum number and be zero or any positive integer (0, 1, 2, 3, 4, 5...). B is the rotational constant and is inversely proportional to the moment of inertia of the molecule, I:

where h is Planck's constant (6.626 x 10^{-34} J s) and c is the speed of light (2.998 x 10^{-10} cm s^{-1}). The moment of inertia for a diatomic molecule is simply related to the length of the bond (r) and the masses of the two atoms (m_{1} and m_{2}):

where m is the reduced mass, given by

Input values into the calculator below for the bond length and atomic masses and press "calculate" to work out the energy levels. Alternatively, just enter a value of B to work out the energy levels or B and either the atomic or reduced mass to work out the bond length.