McKay, Donald. "Front matter" Multimedia Environmental Models ...

light. Sunburn and photosynthesis are examples of such reactions. This process is
primarily of interest when considering the fate of chemicals in solution in the
atmosphere and in water. The radiation that is most likely to effect chemical change
is high-energy, short-wavelength photons at the blue and near UV end of the spectrum,
i.e., shorter than 400 nm. The relationships between energy, wavelength, and
frequency are readily deduced using the fundamental constants of the speed of light
c (3.0 ¥ 10 8 m/s), Planck’s constant h (6.6 ¥ 10 –34 Js), and Avogadro’s Number N
(6.0 ¥ 10 23 ). The energy of a photon of wavelength l nm (frequency c/l Hz) is hc/l
J/molecule or hcN/l J/mol or Einsteins. A photon of wavelength 307 nm has a
frequency of 9.8 ¥ 10 14 Hz and energy of 387,000 J/mol or Einsteins. This is approximately
the dissociation energy of the tertiary C-H bond in isobutane (2 methyl
propane); thus, in principle, if the energy in such a photon could be applied to that
bond, dissociation would occur. Short-wavelength photons are more energetic and
are more likely to induce chemical reactions.
There are two general concerns. Will the photon be absorbed such that reaction
will occur? Will the quantity of photons be such that the reaction rate will be
significant?
To be absorbed directly, the molecule must have a chromophore that imparts
suitable absorption characteristics. These properties can be measured using a spectrophotometer.
As discussed later, there may be indirect absorption of the energy
from another species that absorbs the photon then passes on the energy to the
substance of interest.
The issue of quantity can be assessed by calculating the amount of energy
absorbed, recognizing that there are competitive absorbing substances such as natural
organic matter present in the environment. The extent of absorption can be calculated
from the Beer–Lambert Law such that
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log I = log I O – eCL = log I O – A
where I O is the incident radiation, I is the surviving radiation at distance L, concentration
C, extinction coefficient e, and absorbance A. The quantity of light
absorbed is (I O – I), and the fraction that is absorbed by the chemical can be deduced
by comparing A for the chemical with A for the natural organic matter. In neartransparent
or clear water when A is small, the quantity of light absorbed approaches
2.3I OeCL Einsteins/m 2 ·h. Note that (1 – 10 –x ) approaches 2.3x when x is small. If
each photon absorbed causes j molecules (the quantum yield) to react, then the
reaction rate will be 2.3jI OeCL mol/m 2 ·h and, in principle, the first-order rate
constant is 2.3jI Oe, I O having units of mol/m 2 h and e units of m 2 /mol. In practice,
I O and e are functions of wavelength. Not only is there direct absorption of sunlight
from the sun, but diffuse radiation from the sky also contributes. I O also depends
on latitude, time of day and year, and cloud cover. If e is known as a function of
wavelength, computer programs can be used to integrate over the solar spectrum to
give the total photolysis rate constant. The quantum yield may be quite small, e.g.,
0.1 or, in the case of chain reactions, it can be larger than 1.0. Computer programs
such as SOLAR are available to undertake these calculations. The reader is referred