Absorption of Light

The rather simple example just presented can be used to point out one of the basic principles of photochemistry (the Grotthus-Draper law, first formulated early in the nineteenth century): for light to be effective in producing photochemical transformations, not only must the photon possess sufficient energy to initiate the reaction, it must also be absorbed. Thus, even though we see from equation (4-5) that a 243-nm photon possesses enough energy to break the oxygen bond, in fact oxygen is not dissociated to any measurable extent when exposed to light of this wavelength because it is not absorbed.

A second important principle of photochemistry, which follows directly from quantum theory, is that absorption of radiation is a one-photon process: absorption of one photon excites one atom or molecule in the primary or initiating step, and all subsequent physical and chemical reactions follow from this excited species.3 This principle is not strictly obeyed with the extremely high intensities possible from high-energy artificial light sources such as flash lamps or pulsed lasers. When such high-intensity radiation is used, the simultaneous absorption of two photons is possible. However, only single-photon absorption occurs in all environmental situations involving solar radiation.

In principle, electromagnetic radiation can extend essentially over an almost infinite range of wavelengths, from the very long wavelengths of thousands of miles and low energies [the relationship between the two given by equation (4-3)] to the very short wavelengths of 10~12 m, which is on the order of magnitude of nuclear dimensions. It is convenient to divide this electromagnetic spectrum into regions, as given in Table 4-2.

3As shown later, however, the overall effect from secondary reactions may be much greater than simply one molecule reacting per photon absorbed (see Section 4.4).


The Electromagnetic Spectrum


The Electromagnetic Spectrum

Spectral region

Wavelength range

Energy range

Radio waves

> 10 cm

< 1.2 J/einstein


10 cm-1 cm

1.2-12 J/einstein

Far infrared (IR)

1 cm-0.01 cm

12-1200 J (1.2 kJ) /einstein

Near IR

0.01 cm-700 nm

1.2-170 kJ/einstein


700 nm-400 nm

170-300 kJ/einstein

Near ultraviolet (UV)

400 nm-200 nm

300-600 kJ/einstein

Far (vacuum) UV

200 nm-100 nm

600-1200 kJ/einstein

X-rays and 7-rays

< 100 nm

> 1200 kJ/einstein

Photochemistry is generally limited to absorption in the visible, near-ultraviolet, and far-ultraviolet spectral regions, corresponding primarily to electronic excitation and (at sufficiently high energies) atomic or molecular ionization. Absorption in different spectral regions may lead to different electronic states of the absorbing molecule and electronically different intermediate species, as well as to different products of the photochemical reaction. It is therefore important to understand the designations of electronic states of atoms and molecules insofar as they relate to or indicate possible electronic transitions and transition probabilities. A summary of the recipes used in arriving at atomic and molecular state descriptions is given in Appendix A; the mathematical formulations of these principles are given in standard textbooks of quantum mechanics and spectroscopy, some of which are given in the Additional Reading for Appendix A.

Absorption in the low-energy radio, microwave, or infrared spectral regions results in no direct photochemistry unless very high-intensity laser radiation is used, the excitation for the most part only increasing the rotational and vibrational energies of the molecule and eventually being dissipated as heat. Some deleterious physiological effects do result from overexposure to microwave and infrared radiation (e.g., at radar installations or with improperly controlled microwave ovens), but these presumably are due to excessive localized heating. The chemical effects following illumination with very high-energy radiation (x-rays and 7-rays) are considered in Chapters 13 and 14.

It is worth noting that there is concern about the health effects of electric and magnetic fields (EMFs), primarily in two categories: ELF-EMFs, or extremely low frequencies (mainly 60 Hz) from power lines, household appliances, electric blankets, etc., and RF-EMFs, or radio frequencies transmitted by cellular phone antennas (800-1900 MHz, the frequency range between UHF radio/TV and microwave ovens). Although ELF-EMFs can have biological effects at very high intensities, electric fields are so greatly reduced by the human body that they are negligible compared with the normal body background electric fields; even the largest magnetic field normally encountered (^3000 milligauss) will not induce an electric current density comparable to that normally in the human body. Nevertheless, over the years several epidemiological studies have suggested fairly weak associations between exposures to ELF-EMFs, at levels found in typical residential areas, and some types of human cancers, particularly childhood leukemia.4 On the other hand, there are other recent epidemiological studies that find no definitive link between typical ELF-EMF dosages and childhood leukemia.5 Reviews in recent years have also arrived at conflicting conclusions. For example, one review strongly states that "there is no conclusive and consistent evidence that ordinary exposure to ELF-EMFs causes cancer, neurobehavioral problems or reproductive and developmental disorders."6 However, an advisory panel to the National Institutes of Health concluded that although there is a "lack of positive findings in animals or in mechanistic studies," ELF-EMF is a "possible human carcinogen" and should be classified as such, and further strongly recommended that more research is needed.7

Many laboratory and epidemiological studies have also been carried out directed towards a possible link between RF-EMFs and brain cancer from handheld cellular phones where the antenna is placed near the head, even though they are operated at power levels (< 1W) well below which no known biological damage occurs. Most of these studies are controversial and inconclusive. However, the most recent (at the time of writing) reports—two case-control studies8 and one cohort study of almost half a million cell telephone subscribers9—clearly find no association between cell phone usage and cancers of the brain. All agree, however, that risks associated with long-term exposures and/or potentially long induction periods cannot be ruled out. It is

4For example, a highly cited reference is M. Feychting and A. Ahlbom, Magnetic fields and cancer in children residing near Swedish high-voltage power lines, Am. J. Epidemiol., 138, 467-481 (1993).

5Such as M. S. Linet et al., Residential exposure to magnetic fields and acute lymphoblastic leukemia in children, N. Engl. J. Med., 337, 1-7 (1997); M. L. McBride et al., Power frequency electric and magnetic fields and risk of childhood leukemia in Canada, Am. J. Epidemiol., 149, 831-842 (1999), and correction, 150, 223 (1999).

^National Research Council Committee on the Possible Effects of Electromagnetic Fields on Biologic Systems, Possible Health Effects of Exposure to Residential Electric and Magnetic Fields. National Academy Press, Washington, DC, 1997.

7NIEHS Report on Health Effects from Exposure to Power-Line Frequency Electric and Magnetic Fields, NIH Publication No. 99-4493. National Institutes of Health, Bethesda, MD, 1999.

8J. E. Muscat et al., Handheld cellular telephone use and risk of brain cancer, JAMA, 284, 3001-3007 (2000); P. D. Inskip et al., Cellular-telephone use and brain tumors, N. Engl. J. Med., 344, 79-86 (2001).

9C. Johansen, J. D. Boice, Jr., J. K. McLaughlin, and J. H. Olsen, Cellular telephones and cancer—A nationwide cohort study in Denmark, J. Natl. Cancer Inst., 93, 203-207 (2001).

evident that continued long-term research is called for on the biological and biophysical effects from low-dosage exposure to ELF-EMFs and to RF-EMFs.

Direct physiological and biochemical responses occur from exposure to ultraviolet light. Because of the characteristics of atmospheric ozone absorption (see Section 5.2.3) and the degrees of deleterious biological effects resulting from absorption in this spectral region, the near-ultraviolet region (400-200 nm) is often divided into three bands: UV-A (400-320 nm), UV-B (320-290 nm), and UV-C (290-200 nm). Generally speaking, the UV-C band is virtually totally absorbed by atmospheric ozone and the UV-A band, although transmitted by ozone, is not carcinogenic at reasonable exposure levels,10 so the UV-B band—partially transmitted by atmospheric ozone (see later: Figure 5-4) and directly absorbed by specific molecules, such as DNA or proteins—is for the most part the biologically active one.

The absorption of monochromatic electromagnetic radiation is given by the Beer-Lambert law, which says that the probability of light being absorbed by a single absorbing species is directly proportional to the number of molecules in the light path, which in turn is proportional to the concentration c (Beer's law) and the incremental thickness of the absorbing sample dx (Lambert's law)

^j- = probability of light of intensity I being absorbed in thickness dx

= fraction that the intensity I is reduced in thickness dx = —acdx (4-6)

where a is the proportionality constant. The negative sign is included to account for the fact that the intensity is reduced by absorption, and thus dI is negative. Assuming that c and a are constant, integration of —ac dx from the incident light intensity I0 at x = 0 to I at x r'di '-1

ho 1 Jlo J0

10Radiation in the UV-A and visible regions has been implicated in malignant melanoma, possibly through energy or free-radical transfer from the broadly absorbing melanin. See R. B. Setlow, E. Grist, K. Thompson, and A. D. Woodhead, Wavelengths effective in induction of malignant melanoma, Proc. Nat. Acad. Sci. USA, 90, 6666-6670 (1993).

The absorbance A is

where s ( = a/2.303) is the extinction coefficient.11 The fraction of light absorbed is given by k = 1 _ L = 1 _ io-scx (4-11)

Io Io which holds for all concentrations. For small fractions of light absorbed—for example, at low concentrations of absorbers in the atmosphere—the fraction is directly proportional to the concentration of the absorbing species since e_y s 1 _ y when y is much less than unity:

This relationship cannot hold at high concentrations as is shown by going to the extreme in the opposite direction, where 2.303scx is very large, so that essentially all the light is absorbed:

The light intensity I is normally expressed as the rate at which energy is transmitted through the cell or column of material, so that I0 is then the light energy incident at the cell face per unit time—that is, it is the rate at which photons pass through the cell face. For reasons that will be apparent later, it is often convenient in photochemical systems to express the light absorbed, la, as the concentration of photons absorbed per unit time (photons volume_1 time_1) or alternatively of einsteins absorbed per unit time (einsteins volume_1 time_1). In these cases, I0 is then the concentration of photons or einsteins passing through the cell face per unit time.

The units of a and s are (concentration^ length ), but obviously a variety of units may be used for concentration and length, leading to different values for a and s. If c is given in molarity M (mol/dm3) and x in centimeters, then a and s have the units M_1cm_1 and s is called the molar extinction coefficient, sM (sometimes referred to as the molar absorption coefficient or the absorptivity). Frequently, however, in gaseous systems such as the atmosphere it is convenient to express the concentration in pressure units. These are generally related to concentration units at low pressures by the ideal gas equation

11The constant a is also sometimes called the extinction coefficient. In usage here, however, we shall always refer to the extinction coefficient as the constant s in the Beer-Lambert law in the decadic (base 10) form, equation (4.10), and to a as the proportionality constant in equation (4-6).

P = (n/V)RT = cRT, and therefore the temperature must be specified. If the pressure is to be expressed in atmospheres, R = 0.08206 dm atm • K^mol"1.

If x is expressed in centimeters and the concentration of the absorbing species in molecules per cubic centimeter, as commonly used by atmospheric scientists, then the proportionality constant a in the base e form of the BeerLambert law, equation (4-8), has the units cm2/molecule. This is called the absorption cross section and given the symbol a. For very strongly absorbing species, at maximum absorption a is roughly the order of magnitude of physical cross sections of molecules. In most cases we will use this absorption cross section and the symbol a for expressing the absorption curves.

Table 4-3 summarizes and compares several of these Beer-Lambert law quantities for expressing the absorption of light by a single absorbing species.

As a comparison of these various ways of expressing the proportionality constants, consider a hypothetical gaseous species at a pressure of 1 matm (10"3 atm) and 25°C (298.15 K) that absorbs 40% of the incident light in 1 cm (i.e., is strongly absorbing). It follows from equations (4-9) and (4-12) that sM = 5.43 x 103M"1cm"1 = 222 atm^cm"1 a = 1.25 x 104M"1cm"1 = 511 atm^cm"1

and a = 2.1 x 10"17cm2/molecule

Strictly speaking, the Beer-Lambert law applies only to monochromatic radiation, since s is a function of wavelength. The extent to which use of nonmonochromatic light leads to significant error in the determination of concentration depends on the spectral characteristics of the absorbing and illuminating system. If the extinction coefficient and incident intensity are known as functions of wavelength, however, the total amount of light absorbed may be obtained by integrating over all wavelengths. Also, if there are i absorbing species or components present, the Beer-Lambert equation in base 10 form [equation (4-10)] becomes


Beer-Lambert Law Quantities






Proportionality constant Extinction coefficient Molar extinction coefficient Absorption cross section logio (V-T)


Concentration"1 length"1 Concentration"1 length"1 dm3mol"1cm"1 cm2/molecule t — \ EjCjx

to where the exponential part of the equation represents the sum of the scx terms for all the j absorbing species.

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