Meteo 465/565 -- The Middle Atmosphere
Photochemistry and photolysis

1. Photochemical reactions

When molecules absorb light (called photolysis), several processes can occur:

   1.Dissociation: A + hn --> C, where A is the absorbing molecule,  hn is the typical symbol for light, and B and C are products of the dissociation.
   2.Reaction: A +  hn  --> A* + B --> C + D, where A* is an excited state molecule or atom.
   3.Fluorescence: A +  hn --> A +  hn'where  hn' may be different from  hn.
   4.Collisional deactivation: A +  hn --> A* + M --> A + M, with the energy going into heat.

2. Photolysis rates

The photochemical reactions written above can be described quantitatively using rate equations.  The rate equation for photolysis is:

                                                                   d[A]/dt = - J [A].

J is a first-order rate constant and is a special kind of rate coefficient that we call the photolysis rate coefficient. If this is the only
process happening to chemical species A, then in out usual fashion, we can find the change in [A] with time, and it is:

                                                                 [A] = [A]o exp ( - J t ).

What determines J for a given volume of air? It depends on the irradiance on that volume, the absorption cross section of A as a function of wavelength, and the quantum yield of the process, designated by . Thus,

                                                             J = integral [ F(n)T(n)s(n) j(n)dn ]

where the solar flux at the top of the atmosphere, F, has units of photons cm^-2 s^-1 nm^-1, the atmospheric transmission to the volume of air, T, is unitless, the absorption cross section, s, has units of cm² per molecule, and the quantum efficiency, j, is a fraction and thus unitless.  Notice how we use photons, not energy, when we talk about photolysis.  This switch makes sense if we think about light as being a "reactant" along with the molecules.  We can also do the integration over a wavelength range as well as a frequency range.  Also note that the photons can reach the volume of air not only directly from the sun, but also from reflections from clouds or the ground.  Photolysis has been observed to increase a factor of two or more for some situations where there are clouds below.

We can estimate the terms in the integral for J in order to determine the importance of a photochemical reaction. Consider the molecule NO₃, the nitrate radical by looking in the JPL kinetics book.  It absorbs mostly between 600 and 670 nm, and has a lumpy but about average absorption cross section of 5x10^-18 cm². The solar irradiance is in this wavelength range is about 5x10¹⁴ photons cm^-2 s^-1 nm^-1, or about 3.5x10¹⁶ photons cm^-2 s^-1. For the photodestruction of NO₃, j=1.

Thus,

                                                         J = 5x10¹⁴ 5x10^-18 1 70 = 0.18 s^-1

1/J is a characteristic time scale for the photodestruction of NO₃, often called a lifetime.

The correctly calculated photolysis rate coefficient is slightly more than 0.2 s^-1. So our estimate is close.