rotational energy level

In the gas phase, molecules can rotate, and this rotation is quantized, meaning it can only occur at specific energy levels. For a diatomic molecule, the rotational energy is described by the formula (E_J = J(J + 1)(h^2/8\pi^2I)), where (I) is the moment of inertia and (J) is the rotational quantum number ((J = 0, 1, 2, \dots)). Molecular rotational spectra arise when a molecule transitions between these energy levels, absorbing or emitting radiation. For a transition to occur, the molecule must have a permanent dipole moment, and the change in the rotational quantum number must be (\Delta J = \pm 1). The frequency of the absorbed or emitted radiation is related to the energy difference between these levels. Real molecules also vibrate, and these vibrations affect their rotational energy levels.12