Molecules and Particles Similarities and Differences

As far as absorption (or scattering) is concerned a molecule is a particle of zero dimensions. Although molecules do indeed have extension in space they are fuzzy. In any interaction of electromagnetic radiation with matter, the relevant measuring stick is the wavelength, against which molecules are quite small, even for wavelengths well into the ultraviolet. The separate parts of molecules therefore radiate in unison. A corollary of this is that absorption by molecules and by small (compared with the wavelength) particles ought to be similar. And indeed they are, with some notable exceptions. The absorption spectrum of water vapor at infrared frequencies exhibits many narrow, closely spaced rotational lines (Fig. 2.12), whereas these lines vanish completely in bulk water, which we interpreted as collisional broadening taken to its extreme, and hence vanish from the absorption spectra of water droplets of all sizes. Although vibrational bands are broadened and shifted in going from vapor to the condensed phases (liquid and ice), they still are prominent in the infrared absorption spectrum of water (Fig. 2.25) and hence in the absorption spectra of small water droplets. Where molecules and particles go their separate ways is when particles become comparable with or greater than the wavelength. This additional degree of freedom (size) results in particle absorption spectra that may bear no resemblance to that of individual molecules or even the condensed phases of these molecules. A single particle larger than the wavelength and weakly absorbing can exhibit a series of narrow, closely spaced lines in its absorption spectrum, reminiscent of rotational bands in molecular spectra but arising from a completely different cause: interference.

Another difference between molecules and particles is that we have a hope of calculating the energy levels of molecules, and hence the frequency dependence of molecular cross sections, by quantum mechanics. Difficult, yes, but not impossible. Calculating the cross sections of particles, aggregations of many closely-packed interacting molecules, by quantum mechanics is essentially impossible. This would be like trying to forecast the weather using quantum mechanics - in principle not impossible, but in practice not advisable. To calculate absorption cross sections of particles we must use classical electromagnetic theory and obtain the electromagnetic properties of the materials of which they are composed from measurements. This is how the volumetric absorption cross sections for water droplets shown in Figs. 2.25 and 2.26 were obtained.

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