The absorption spectrum of real gases

We will now take a close look at the absorption properties of CO2, in order to introduce some general ideas about the nature of the absorption of infrared radiation by molecules in a gas. Continuing to use CO2 as an example, these ideas will be developed in Sections 4.4.3,4.4.4 and

4.4.6 into a computationally efficient means of calculating infrared fluxes in a real-gas atmosphere. A survey of the spectral characteristics of selected other greenhouse gases will be given in Sections

Figure 4.7 shows the absorption coefficient of CO2 as a function of wavenumber, for pure CO2 gas at a pressure of 1bar and a temperature of 296K. In some spectral regions, e.g. 17001800 cm-1, CO2 at this temperature and pressure is essentially transparent. This is a window region through which infrared can easily escape to space if no other greenhouse gas intervenes. For a 285K blackbody, 60W/m2 can be lost through this window. There are two major bands in which absorption occurs. For Earthlike temperatures, the lower wavenumber band, from about

450 to 1100 cm-1 is by far the most important. At 285K the blackbody emission in this band is 218W/m2 out of a total of 374W/m2, so the absorption in this band is well tuned to intercept terrestrial infrared and to thus reduce OLR. The blackbody emission in the higher wavenumber band, from 1800 to 2500 cm-1, is only 6W/m2. This band has a minor effect on OLR for Earth, but it can become important for much hotter planets like Venus, and even for Earth is important for the absorption of solar near-infrared. Within either band, the absorption coefficient varies by more than eight orders of magnitude.

The absorption does not vary randomly. It is arrange around six peaks (three in each major band), with the overall envelope of the absorption declining approximately exponentially with distance from the peak. However, there is a great deal of fine-scale variation within the overall envelope. Zooming in on a typical region in the inset to Figure 4.7 we see that the absorption can vary by an order of magnitude over a wavenumber range of only a few tenths of a cm-1. Most significantly, the absorption peaks sharply at a discrete set of frequencies.

Why does the absorption peak at preferred frequencies? In essence, molecules are like little radio receivers, tuned to listen to light only at certain specific frequencies. Since energy is conserved, the absorption or emission of a photon must be accompanied by a change in the internal energy state of the molecule. It is a consequence of quantum mechanics that the internal energy of a molecule can only take on values drawn from a finite set of possible energy states, the distribution of which is determined by the structure of the molecule. If there are N state, there are N(N — 1)/2 possible transitions, and each one leads to a possible absorption/emission line as illustrated in Figure 4.8. Transitions between different energy states of a molecule's electron configuration do not significantly contribute to infrared absorption in most planetary situations. The energy states involved in infrared absorption and emission are connected with displacement of the nuclei in the molecule, and take the form of vibrations or rotations. Every molecule has an equilibrium configuration, in which each nucleus is placed so that the sum of the electromagnetic forces from the other nuclei and from the electron cloud sum up to zero. A displacement of the nuclear positions will result in a restoring force that brings the system back toward equilibrium, leading to vibrations. The nucleii can be thought of as being connected with quantum-mechanical springs (one between each pair of nucleii) of different spring constants, and the vibrations can be thought of as arising from a set of coupled quantum-mechanical oscillators. Rigid molecules, held together by rigid rods rather than springs, would have rotational states but not vibrational states. The fact that molecules are not rigid causes the rotational states to couple to the vibrational states, through the coriolis and centrifugal forces.

Noble gases (He, Ar, etc.) are monatomic, have only electron transitions, and are not active in the infrared. A diatomic molecule (Fig. 4.9) has a set of energy levels associated with the oscillation caused by pulling the nuclei apart and allowing them to spring back; it also has a set of energy levels associated with rotation about either of the axes perpendicular to the line joining the nuclei. Centrifugal force couples the stretching to the rotation. Triatomic molecules (Fig. 4.10) have an even richer set of vibrations and rotations, especially if their equilibrium state is bent rather than linear (Fig. 4.11). Polyatomic molecules like CH4, NH3, and the chlorofluorcarbons (e.g. CFC-12, which is CCl2F2) have yet more complex modes of vibration and rotation. As the set of energy states becomes richer and more complex, the set of differences between states fills in more and more of the spectrum, making the molecule a better infrared absorber.

For a molecule to be a good infrared absorber and emitter, it is not enough that it have transitions whose energy corresponds to the infrared spectrum. In order for a photon to be absorbed or emitted, the associated molecular motions must also couple strongly to the electromagnetic field. Although the quantum nature of radiation is crucial for many purposes, when it comes to the interaction of infrared or longer wavelength radiation with molecules, one can productively

Wavenumber (cm )

200 600 1000 1400 1800 2200 2600 3000 !,r,i,"i'"i",iMri"li,l,r,li'Mi"li',li,r,r,li",,i

200 600 1000 1400 1800 2200 2600 3000 !,r,i,"i'"i",iMri"li,l,r,li'Mi"li',li,r,r,li",,i

Figure 4.7: The absorption coefficient vs. wavenumber for pure CO2 at a temperature of 293K and pressure of 105Pa. This graph is not the result of a measurement by a single instrument, but is synthesized from absorption data from a large number of laboratory measurements of spectral features, supplemented by theoretical calculations. The inset shows the detailed wavenumber dependence in a selected spectral region.

Ji E

Figure 4.8: Schematic of emission of a photon by transition from a higher energy state to a lower energy state

Figure 4.9: Vibration and rotation modes of a diatomic molecule made of a pair of identical atmos, with associated charge distributions
Figure 4.10: Vibration and rotation modes of a linear symmetric triatomic molecule (like CO2), with associated charge distributions

Was this article helpful?

0 0

Post a comment