Fig 14.18.

Rotational energy levels for two diatomic molecules, CO and CS.The states are designated by the rotational quantum number J.The differences between the two molecules arise from the differences in rotational inertias resulting from different masses for O and S, and different bond lengths for the two molecules.

major difference between I(CO) and I(CS) are from the difference in the masses of the O and S. In addition, the bond lengths are slightly different in the two molecules. Note that the closest spacing is for the first two energy levels (J = 0 and J = 1). As we go to higher values of J, the energy levels are farther apart. This means that at low temperatures only a few of the lowest energy levels are populated. For example, the 2.6 mm transition in which CO is most commonly observed is the J = 1 s 0. The values of rotational inertia for many simple molecules are such that the lowest transitions lie in the millimeter part of the radio spectrum. That is why so many molecules were discovered at millimeter wavelengths.

Adding more atoms to a molecule can complicate the spectra. If we still have a linear molecule (for example, in HCN the three atoms are in a line), then the energy levels are essentially the same as the diatomic case, with the appropriate value for I. If molecules are not linear, then the spectra are more complicated, since we have to allow for rotation about more than one axis, but there are similarities to the linear case.

If we want to look at a new interstellar molecule, we need to know the wavelengths at which it can emit. For the most part, we rely on accurate laboratory measurements of molecular spectra. Once the wavelengths of a few transitions have been measured, those of other transitions can be calculated very accurately (using expressions such as equation (14.23)). There are some molecules that have been found in interstellar space without prior laboratory study. These were found accidentally, in the course of searches for other molecules. In some cases the interstellar medium provides us with a unique opportunity to study molecules that are not stable in the laboratory.

The most important feature of interstellar molecules is that they provide us with a way of obtaining information about the physical conditions in the molecular clouds. If we take the energy corresponding to the 2.6 mm photon, and divide by k, we find an equivalent temperature of 5.5 K. This means that rotational transitions in molecules are excited even at low temperatures. Also, the factor e " E/kT in the Boltzmann equation is most sensitive to changes in temperature and density when E is of the order of kT.

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