## [

which is just the lifetime of 03 against reaction 4 (above).

Now, let us obtain an estimate of the lifetime of 03 against reaction 4, x4. Shortly we will see that 03 concentrations at 30 and 40 km are about 3 x 1012 and 0.5 x 1012 molecules cm-3, respectively. Given these concentrations and the / estimates above, we find that z, km T, K £4, cm3 molecule-1 s-1 10/= 14), s

Whereas the photolytic lifetime of 03 at these altitudes is about lOmin, the overall lifetime of 03 is on the order of weeks to months, validating the assumption that cycling within the Ov family is rapid relative to loss of Ox. %ox varies from about 140 days at 20 km to about 12 days at 40 km. (Even though both jo , and  vary with altitude, it is the [M]2 dependence of xq, that dominates its behavior as a function of altitude.) At lower altitudes,

03 lifetime is sufficiently long for it to be transported intact. At high altitudes, ozone tends to be produced locally rather than imported.

Defining the chemical family [Ox] = [O] + [O3], and by adding (5.1) and (5.2), we obtain the rate equation governing odd oxygen:

Since O3 constitutes the vast majority of total Ox, a change in the abundance of Ox is usually just referred to as a change in 03. Two molecules of odd oxygen are formed on photolysis of 02, and two molecules of odd oxygen are consumed in reaction 4. Using (5.7) in (5.9), the reaction rate equation for odd oxygen becomes d\O, yo,[o!]-2t4oí|(¡|§L) (5.1»)

Since [Ox] = [O] + , and [O] < ,d[0x]/dt d/dt, so (5.10) becomes

After a sufficiently long time, the steady-state 03 concentration resulting from reactions 1-4 is

which can be rearranged as

An equivalent way to express the steady-state 03 concentration is

An equivalent way to express the steady-state 03 concentration is

The steady-state 03 concentration is sustained by the continual photolysis of 02.

The steady-state 03 concentration should be a maximum at the altitude where the product of the number density of air and the square root of the 02 photolysis rate is largest. Figure 4.14 shows jo2 as a function of altitude above 30 km. The photolysis rate of O 2,jo2  (molecules cm-3 s 1), peaks at about 29 km. This maximum results because even though jo2 continues to increase with z, the number density of 02,  = 0.21 [M], decreases with z. The product (/'o2 [O2])' '''2 [M] peaks at about 25 km. This is a key result—the peak in the stratospheric ozone layer occurs at ~ 25 km. In summary, at high altitudes the concentration of 03 decreases primarily as a result of a drop in the concentration of 02, the photolysis of which initiates the formation of 03. At low altitudes, the 03 concentration decreases because of a decrease in the flux of photons at the UV wavelengths at which 02 photodissociates.

An issue that we have not yet addressed is how long it takes to establish the steady-state 03 concentration at any particular altitude. To determine this we need to return to the rate equation for , namely, (5.11). If we let y = , this differential equation is of the form 