Molecular spectra
 

It may be noted that molecules also provide spectral features and patterns that allow their identification. A simple diatomic molecule such as CO, for example, suffers vibration such that the axial distance between the components oscillates. Again the molecules have spin with components normal to and around the axis. The energies associated with the vibration and rotation are also quantized so that radiation at specific wavelengths is emitted or absorbed by a molecule according to the change of its energy state.
For example, the rotational energy, E, of a molecule depends on its moment of inertia, I, and the spin rate, ω, so that
E = Iω²/2
and, for a simple diatomic molecule,
I = μr ²
where r is the separation of the component atoms of mass M₁ and M₂ with μ the reduced mass of the molecule given by
μ = M₁M₂/M₁ + M₂.
By applying the quantization principle, the angular momentum can only have integer (J ) values such that
Iω = h/2π  J.
The energy levels corresponding to the possible states of J may be written as

From knowledge of the structure of the molecule, i.e. the masses of the component atoms and their separation, the wavelength positions of spectral lines are readily calculated. The photon energies associated with the transitions are normally less than those generated by the electron jumps within atoms this being reflected by the fact that spectral features associated with molecules are likely to be more apparent in the infrared and millimetre region rather than at optical wavelengths. Many of the spectral features of identifiable molecules from the interstellar medium do, in fact, appear in the

millimetre region. For example, one of the strong features associated with the CO molecule is the rotational line corresponding to J → 2 to 1 at ∼230·5 GHz or ∼1.3 mm and this has been used to advantage to map out the distribution of this common compound in the molecular clouds within the interstellar medium.
An important adjunct to molecular spectroscopy is the possibility of undertaking measurements of isotope abundances. For the case of a diatomic molecule, if one of the component atoms, say M₁, has two isotopes, two possible moments of inertia ensue so generating spectral lines at differingwavelength positions. Hence, lines associated with ¹²C¹⁶O and ¹³C¹⁶O will differ in wavelength position in the ratio of the reduced masses of their associated molecules, i.e.