## Absorption Of Light

1. Basic Relationships

Light has both wave-like and particle-like properties. As a wave, it is a combination of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation (Fig. 3.f0). The distance between consecutive peaks is the wavelength, A, and the number of complete cycles passing a fixed point in 1 s is the frequency, v. They are inversely proportional through the relationship

where c is the speed of light in a vacuum, 2.9979 X 10 m s_l.

Considered as a particle, the energy of a quantum of light E is

where h is Planck's constant, 6.6262 X 10-34 J s per quantum, and the frequency v is in s-1. In the visible and ultraviolet regions of the spectrum, wavelength is commonly expressed in nanometer units, f nm = 10"9 m. In the older literature, units of angstroms, 1 A = 10"1(1 m, are also found.

In the infrared region both microns [1 micron = 1 micrometer (jum) = 10~6 m] and wavenumbers a> (in cm-1) are employed; o> is the reciprocal of the wave-

Direction of propagation

Direction of propagation

(Distance)

FIGURE 3.10 The instantaneous electric (Ev) and magnetic (Hz) field strength vectors of a plane-polarized light wave as a function of position along the axis of propagation (x) (from Calvert and Pitts, 1966).

(Distance)

FIGURE 3.10 The instantaneous electric (Ev) and magnetic (Hz) field strength vectors of a plane-polarized light wave as a function of position along the axis of propagation (x) (from Calvert and Pitts, 1966).

length A expressed in centimeters. It is directly related to energy through the Planck relationship,

and today is generally the unit of choice in infrared spectroscopy.

Since chemists often deal experimentally with moles rather than molecules, a convenient unit is a mole of quanta, defined as 1 einstein. The energy of 1 einstein of light of wavelength A in nm is

E = (6.02 x 1023)hv = 6.02 x 1023/zc/A, = 1.196 x 105/A kJ einstein"1, = 2.859 x 104/A kcal einstein"1. (M)

Another unit used in photochemistry to express the energy of a quantum of radiation is the electron volt; f eV = 96.49 kJ mol"1 = 23.06 kcal mol"1. Thus for A in nm

To put these energies and wavelengths in perspective, Table 3.2 gives some typical wavelengths, frequencies, wavenumbers, and energies of various regions of the electromagnetic spectrum. The region of most direct interest in tropospheric photochemistry ranges from the visible at ~ 700 nm to the near-ultraviolet at ~ 290 nm, the short-wavelength cutoff of the stratospheric ozone layer. The corresponding energies [Eq. (M)], 170.9 and 412.4 kJ einstein"1 (or 40.8 and 98.6

kcal einstein "1), are sufficient to break chemical bonds ranging from, for example, the weak 02 ā O bond in ozone, ~ 100 kJ mol"1 25 kcal mol"1), to the moderately strong CāH bond in formaldehyde, ~ 368 kJ mol"1 88 kcal mol"1).

Other spectral regions are also important because the detection and quantification of small concentrations of labile molecular, free radical, and atomic species of tropospheric interest both in laboratory studies and in ambient air are based on a variety of spectroscopic techniques that cover a wide range of the electromagnetic spectrum. For example, the relevant region for infrared spectroscopy of stable molecules is generally from - 500 to 4000 cm"1 (20-2.5 yum), whereas the detection of atoms and free radicals by resonance fluorescence employs radiation down to 121.6 nm, the Lyman a line of the H atom.

Table 3.3 gives some relationships between commonly used energy units. Today the SI system of units is in general use, although much of the data in the literature is in the older units. Thus we use both types of units for energy, that is calories or kilocalories and joules or kilojoules, where 1 cal = 4.184 J.

### 2. The Beer - Lambert Law

The basis for the measurement of the strength of light absorption by a molecule at various wavelengths is shown in Fig. 3.11. A parallel monochromatic light beam of wavelength A and power P() or intensity /ā, defined as the energy per second striking a unit area,

TABLE 3.2 Typical Wavelengths, Frequencies, Wavenumbers, and Energies of Various Regions of the Electromagnetic Spectrum

TABLE 3.2 Typical Wavelengths, Frequencies, Wavenumbers, and Energies of Various Regions of the Electromagnetic Spectrum

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