## Photolysis Rate As A Function Of Altitude

Photolysis reactions are central to atmospheric chemistry, since the source of energy that drives the entire system of atmospheric reactions is the Sun. The general expression for the first-order rate coefficient jA for photodissociation of a species A is given by (4.39). Because the rate of a photolysis reaction depends on the spectral actinic flux I and because photolysis rate as a function of altitude

the spectral actinic flux varies with altitude in the atmosphere, the rate of photolysis reactions depends in general on altitude. The altitude dependence of jA enters indirectly through the temperature dependence of the absorption cross section and directly through the altitude dependence of the spectral actinic flux, which can be written as I(z,X). We have already seen that the altitude dependence of the solar irradiance in the wavelength range below ~1 |im is essentially a result of absorption of solar radiation by 02 and 03. From the absorption cross sections for 02 and 03, it is possible to calculate I(z,X) at any altitude z, which can then be used in (4.39) to calculate the photolysis rate of any species A as a function of altitude.

The photolysis rate coefficient of a species A can be expressed as a function of altitude from (4.39) as jA{z) = t aa{T,X)§A(T,X)I(z,X)dX (4.47)

Assume that the attenuation of radiation is due solely to absorption by species A. From the Beer-Lambert Law, I(zX) can be expressed as

If we neglect the z dependence of temperature, then

To proceed further, consider the case in which the absorbing species A has a uniform mixing ratio, (e.g., 02); then, its concentration can be expressed in terms of the molecular air density as a function of altitude, nan (z):

The total number concentration of air as a function of altitude falls off approximately with the scale height H of atmospheric pressure:

Xa(ZA) = mnA{T,X)^An^{Q)He-zlH (4.52) Combing (4.47), (4.48), and (4.52), the photolysis rate coefficient is given by jA{z)= f 2 oa(T,X)§a(T,X)It0A(X) exp{—maA(T,X){,AnaiT(0)e~z/H}dX (4.53)

The photolysis rate at any altitude z is the product of j,\ (z.) and the number concentration of A, nA (z):

= -^A«air(0)e"z/H [ 2 aA(T, X)\$a(T, X)Ijoa(X) exp{—maA(r, X)i,An^t{0)e~^H}dX A,

= -^A«air(0) J oa{T,1)\$a(T,\) 7toa(X) exp|-^ - mcrA(T, X)^A«air(0)e~z/H}dX

As one descends toward the Earth's surface, the photolysis rate decreases because the overall actinic flux is decreasing due to increasing absorption in the layers above. As one ascends in the atmosphere, the concentration of the gas nA(z) simply decreases as the atmosphere's density thins out. These two competing effects combine to produce a maximum in the photolysis rate at a certain altitude. The altitude at which this rate is a maximum is the value of z at which

We find that the photolysis rate is a maximum at the altitude z at which maA ^A«air(0)// exp(-z/H) = 1 (4.56)

This is just the altitude z where x(zX) = 1.

The function in the integral of (4.54) is called a Chapman function in honor of Sydney Chapman, pioneer of stratospheric ozone chemistry. We will return to Chapman in the next chapter. The elegant analytical form of the Chapman function results when the mixing ratio of the absorbing gas A is constant throughout the atmosphere, so that nA(z) scales with altitude according to the scale height H of pressure. Molecular 02 is the prime example of such an absorbing gas. For a gas with a nonuniform mixing ratio with altitude, one can, of course, numerically evaluate (4.49) for the optical depth at any z on the basis of its actual profile nA(z).

Figure 4.14 shows the photodissociation rate coefficient for 02, namely,y'o,, as a function of altitude above 30 km. From 30 to 60 km, the Herzberg continuum provides the dominant contribution to jo2. At about 60 km, the contribution from the Schumann-Runge bands equals that from the Herzberg continuum; above 60 km, the Schumann-Runge bands predominate until about 80 km, where the Schumann-Runge continuum takes over. In the mid-to upper stratosphere, at solar zenith angle = 0°, an approximate value of jo2 is jo2 = 10 9 s 1.

4.9 PHOTODISSOCIATION OF 03 TO PRODUCE O AND O('D)

Ozone photodissociates to produce either ground-state atomic oxygen FIGURE 4.14 Photodissociation rate coefficient for 02,jo2, and 02 photolysis rate as a function of altitude at solar zenith angle 8q = 0°. (Courtesy Ross J. Salawitch, Jet Propulsion Laboratary.)

or the first electronically excited state of atomic oxygen, O('D):

Ozone always dissociates when it absorbs a visible or UV photon; therefore, the quantum yield for 03 dissociation is unity. Photodissociation of 03 in the visible region, the Chappuis band, is the major source of ground state O atoms in the stratosphere. (Since these O atoms just combine with 02 to reform 03 with the release of heat, this absorption of visible radiation by 03 merely converts light into heat.)

Figure 4.15 shows the photodissociation rate coefficients for 03 + hv —> O('D) + 02 [panels (a) and (b)] and for 03 + hv —> O + 02 [panels (c) and (d)]. Panels (a) and (c) show J03 —>o('d) and ./oi-^o, respectively, as a function of altitude at solar zenith angles 9 = 0° and 85°. Panels (b) and (d) show the two photolysis rate coefficients at 20 km as a function of solar zenith angle. The photodissociation of 03 at altitudes below about 30 km is governed mainly by absorption in the Chappuis bands, and this absorption is practically independent of altitude. Above ~30km, absorption in the Hartley bands dominates, the rate of which increases strongly with increasing altitude. In the troposphere, the photodissociation rate coefficients ./(>,—of D) and ./o, ,0 are virtually independent of altitude; at 9 = 0°: . ' ' ' ' \ '/

, , ■ 1 1 1

/

85°-»/

~ / 1 I

- 1 t 1

I -

1 1

1

1 1

i- SZA = 0°

— 1

1 1

1 15 30 45 60 75 Solar Zenith Angle, deg

FIGURE 4.15 Photodissociation rate coefficient for 03 as a function of altitude and solar zenith angle. Panels (a) and (b) are /0„0iiUj. Panels (c) and (d) are jo3^o- (Courtesy Ross J. Salawitch, Jet Propulsion Laboratory.)

Because of the importance of O('D) to the chemistry of the lower stratosphere and entire troposphere, a great deal of effort has gone into precisely determining its production from 03 photodissociation. Since solar radiation of wavelengths below ~ 290 nm does not reach the lower stratosphere and troposphere, the wavelength region just above 290 nm is critical for production of O('D). Table 4.4 gives the quantum yield for production of O('D) as a function of wavelength in this region. On the basis of heat of reaction data, the threshold energy for photodissociation of 03 to produce O('D) is estimated to be 390 kJ mol-1, which is equivalent to a wavelength of 305 nm. At wavelengths below 305 nm, the quantum yield for O('D) production is indeed close to unity. It is expected that the threshold is shifted to somewhat longer wavelengths (~310nm) because a fraction of the 03 molecules will have extra vibrational energy that can help overcome the barrier. Michelson et al. (1994) showed that the effect of vibrationally excited 03

 Wavelength, nm 298 K 253 K 203 K 306 0.884 0.875 0.872 307 0.862 0.844 0.836 308 0.793 0.760 0.744 309 0.671 0.616 0.585 310 0.523 0.443 0.396 311 0.394 0.298 0.241 312 0.310 0.208 0.152 313 0.265 0.162 0.112 314 0.246 0.143 0.095 315 0.239 0.136 0.090 316 0.233 0.133 0.088 317 0.222 0.129 0.087 318 0.206 0.123 0.086 319 0.187 0.116 0.085 320 0.166 0.109 0.083 321 0.146 0.101 0.082 322 0.128 0.095 0.080 323 0.113 0.089 0.079 324 0.101 0.085 0.078 325 0.092 0.082 0.078 326 0.086 0.080 0.077 327 0.082 0.079 0.077 328 0.080 0.078 0.077

Source: Matsumi et al. (2002).

Source: Matsumi et al. (2002).

leads to nonzero quantum yields that vary with temperature up to about 320 nm. Recent data, as reflected in Table 4.4, show that 0(1D) is produced well beyond the 310nm threshold, attributable to so-called spin-forbidden channels that may account for as much as 10% of the overall rate.

The critical role of wavelength in photolysis can be seen by comparing Figure 4.11 and Table 4.4. From X = 305 nm to 320 nm, the absorption cross section drops by a factor of ~ 10, and the quantum yield for 0(1D) formation drops from 0.9 to about 0.1. Since the ctc|) product changes rapidly with X, the actual rate of production of 0(1D) is critically dependent on how I(X) varies with X. At the surface of the Earth, the spectral actinic flux increases by about an order of magnitude between X — 300 nm and X = 320 nm (see Table 4.3).

### 4.10 PHOTODISSOCIATION OF N02

Since no solar radiation of wavelength shorter than about 290 nm reaches the troposphere, the absorbing species of interest from the point of view of tropospheric chemistry are those that absorb in the portion of the spectrum above 290 nm. Nitrogen dioxide is an extremely important molecule in the troposphere; it absorbs over the entire visible and ultraviolet range of the solar spectrum in the lower atmosphere (Figure 4.16). Between 300 and 370 nm over 90% of the N02 molecules absorbing will dissociate into NO and O (Figure 4.17). Above 370 nm this percentage drops off rapidly and above Wavelength, nm

FIGURE 4.16 Absorption cross section for N02 at 298 K. 0 0 ## How to Improve Your Memory

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### Responses

• Settimo
What is the photolysis rate?
9 years ago
• melissa
What is the function of photolysis ?
9 years ago
• Almaz
How to calculate photolysis reaction constant given temperature and SZA?
8 years ago
• thomas chavez
What is atmospheric photolysis?
4 years ago
• MAKDA
How to read photolysis rate coefficient?
3 years ago
• fatima
How to calculate photolysis rate?
2 months ago