Rotational energy levels are much more closely spaced than vibrational levels. For example, for HCl the spacing between the lowest two rotational energy levels(J=0 and J=1) is about 20 cm-1, whereas the gap between the lowest vibrational level (v = 0,ground state) and the next highest one (v = 1, first vibrational excited state) is about 2900 cm-1. The arrangement of rotational and vibrational levels is shown schematically in Figure 13.1 in your textbook.

Because we wish to examine transitions between different vibrational-rotational levels, the spectrometer must be able to resolve the rotational "fine structure" in the vibrational spectrum. The absorption spectrum involving the lowest energy vibrational transition, v = 0 to v = 1, called the fundamental, is observed in the infrared region at about 2900 cm -1, or 3400 nm, [The wavelength of a transition is the reciprocal of its energy in cm-1 ; the nm (10-9m) is a common wavelength unit.] Infrared spectrophotometers that are based on dispersive optics, i.e., a grating or a prism used to separate the radiation into narrow wavelength "bands", generally do not possess the required resolution for this experiment. Fourier transform (FT)instruments, however, which operate on a different principle are routinely capable of providing resolution of around 1 cm -1, which is satisfactory for this experiment. The fundamental relation in spectroscopy is derived by equating the photon energy with the difference in state energies involved in the transition. For the case where radiation of frequency v is absorbed, the energy of the transition (ergs) is

E = h ν=h c̃ν= Ev’,J’– Ev”,J”

where ̃ νis the photon “frequency” in cm-1 and v',J' and v",J" are, respectively, the vibrational/rotational quantum numbers of the upper and lower