with atomic oxygen in the ground state. This Herzberg dissociation continuum is weak, extends from 185 nm to 242 nm, and is the main source of O atoms for altitudes below 60 km in the Earth's atmosphere. The absorption cross-section of O2 as a function of wavelength for the Herzberg continuum is given in Fig. 7.4.
Intemuclear distance (Angstroms)
Intemuclear distance (Angstroms)
FlG. 7.3. Idealized potential energy curves for O2 and vibrational-rotational energy levels, with dissociation limits at 7.047 and 5.080 eV.
Bound-bound transitions from Xto B3£- involve nonradiative transitions to the unstable repulsive states 5n„, 3n„, 1n„ and 23S+ leading to pre-disocc-iation. This is the system of allowed strong Schumann-Runge bands with a sharp band structure from 175 to 200 nm that results in the dissociation channel with one of the oxygen atoms in the excited state O(1D). The absorption-cross-section has a detailed vibrational-rotational band structure. In Fig. 7.4 are given averaged values for the cross-section. Dissociation of O2 by absorption in the Schumann-Runge bands is dominant between 60 and 90 km.
Bound-continuum transitions from X3Sr to the dissociation continuum of B3£-also result in atomic oxygen products as for the Schumann-Runge bands. Such transitions result in the intense Schumann-Runge dissociation continuum between 137 and 175 nm. The cross-section peaks at 142.5 nm, as shown in Fig. 7.4, with three diffuse bands (interaction between discrete states and the continuum) at 129.4, 133.4, and 135.4 nm. Absorption in the Schumann-Runge continuum is the primary O2 dissociation process above 90 km.
Small portions of the two continua, Herzberg and Schumann-Runge, underlie the Schumann-Runge bands. Nicolet and Kennes (1986) give the formula for the
Schumann-Runge Continuum o
0.16 0.18 0.20 Wavelength (nm)
0.16 0.18 0.20 Wavelength (nm)
Flg. 7.4. The absorption cross-section of O2 at 273 K (band structure has been averaged out).
Herzberg continuum cross-section a(x) = 7.5 x 10 4xexp—50(lnx)2],
where x = 199/A, with A in nm, and recommended for use above 210 nm. The cross-section in the Schumann-Runge bands is highly variable with wavelength owing to the thousands of overlapping rotational lines that are broadened by predissociation and by Doppler broadening, resulting in Voigt rotational line profiles. The band cross-sections are temperature dependent as the temperature affects the populations in the vibrational and rotational levels of the ground electronic state and it also affects the broadening of the individual rotational lines. It is thus difficult to give average cross-sections over the wavelength intervals used to model atmospheric photochemistry. Photons that have wavelengths between band peaks can penetrate deeper into the atmosphere, as the cross-sections can vary by two orders of magnitude over an interval of 20 cm-1, or of the order of 10-5 nm. Murtagh (1988) used high spectral resolution cross-sections to derive average cross-sections in seventeen broad spectral intervals, from 175.4 to 205.8 nm, tabulated as functions of the O2 column number density (molecules cm-2). Allen and Frederick (1982) give temperature-dependent expressions for the cross-section in seventeen broad spectral intervals, for use in photochemical modelling studies.
Below 137 nm, the solar Lyman-a line becomes important for the photolysis of O2. The cross-section is temperature dependent and varies significantly, by almost one order of magnitude, over the Lyman-a line (Fig. 7.4). Lewis et al. (1983) tabulate the cross-section for the wavelength interval 121.40 to 121.90, in intervals of 0.01 nm, for the temperatures 84, 203, 288 and 366 K. We recall that the solar Lyman-a flux varies by a factor of 2 over the solar cycle.
The photoionization limit of O2 is 102.78 nm. Photoionization yield is unity below 60 nm and 0.65 at 102.57 nm, corresponding to Lyman-,3 . The cross-section between 137 and 105 is highly structured, varying between 10~20 and 10~17 cm2, while below 100 nm there is an ionization continuum. For photochemical modelling it is useful to have mean cross-sections over broad intervals and for this purpose Banks and Kockarts (1973) tabulate the absorption and photoionization cross-sections at 102.57, 97.7 (corresponding to the solar C(III) doubly ionized carbon line), and for seven spectral intervals from 91 to 8 nm. Below 71.9 nm, dissociative photoionization is possible where the second channel is possible below 60 nm. 7.6.4 O3 photolysis
Ozone absorbs strongly in the wavelength region between 200 and 300 nm. From 300 to 350 nm it absorbs in the relatively weak and temperature-dependent Hartley bands. It also absorbs in the visible region between 410 and 850 nm in the Chappuis bands. The photodissociation threshold of ozone is 1.14 ^m. Ozone is the main atmospheric absorber of solar ultraviolet and visible radiation above the cloud deck so that the variation of the enhancement factor fx, shown in Fig. 7.2, follows inversely the ozone absorption cross-section, shown in Fig. 7.5, between 0.3 and 0.75 ¡m. Below 0.3 ¡m the very strong absorption of the Hartley band results in no reflected radiation to space and so fx = 1. The minimum in fx at 0.6 ¡m corresponds to the peak in the absorption cross-section of the visible Chappuis bands of ozone. Ozone can photodissociate to different products depending on the photon wavelength (see Appendix B, Table B.3)
The quantum yield for the production of O(1D) is negligible for A > 330 nm but rises rapidly near 310 nm to 0.9 for A < 306 nm, independently of temperature (JPL 2006).
Absolute measurements in the Hartley band were reported by Hearn (1961) at wavelengths of several mercury lines 253.7, 289.4, 296.7 and 302.1 nm. In particular, the 253.65 nm cross-section of Hearn (1.147x10~17 cm2 molecule-1) is
O2(3Eg ) + hv ^ O+ + O(3P) + e, O2(3£-) + hv ^ O+ + O(XD) + e,
*fc FLy-a Hartley band
*fc FLy-a Hartley band
Flg. 7.5. The absorption cross-section of ozone from Lyman-a to the visible, at 273 K (band structure has been averaged out).
the primary standard for international agencies. These results have served as the basis for normalizing the relative measurements that cover the entire spectrum. Absorption cross-sections for the interval 175.4 to 362.5 nm are tabulated in JPL (2006) for 273 K. An expression for the temperature-dependent quantum yield for O(1D) production between 305 and 320 nm is also given. Bass and Paur (1981) measured the temperature dependence of the cross-section and found that it was significant for the region 263 to 350 nm, mainly corresponding to the Huggins bands. The original measurements for the Chappuis bands were made by Vigroux (1953) and later verified by Griggs (1968).
The absorption cross-section for water vapour is shown in Fig. 7.6. Water vapour can be photodissociated by photons with wavelength below 246 nm. There are three possible channels below 145 nm
H2O + hv — H2 + O(1D), H2O + hv — 2H + O, H2O + hv — H + OH,
Flg. 7.6. The absorption cross-section of H2O at 296 K.
where the branching ratio a = 0.11 for the first and second channels, and a = 0.78 for the third. These channels take place primarily by Lyman-a photons. The mean absorption cross-section over the Lyman-a interval 121.48-121.64 nm is 1.55x10~17 cm~2 for T = 292 K. Above 145 nm, water vapour photolyzes according to the third channel. The absorption cross-section of H2O at 296 K is shown in Fig. 7.6, based on the measurements of Yoshino et al. (1996) and Parkinson and Yoshino (2003).
In Fig. 7.7 we show the temperature-dependent absorption cross-section of CO2 from Lyman-a to about 0.2 ¡m based on the high-resolution (0.005 nm) measurements of Lewis and Carver (1983). The temperature dependence has also been demonstrated by Jensen et al. (1997), who give temperature-dependent absorption cross-sections at high temperatures (above 1000 K) in the spectral range 0.19 ¡m to 0.32 ¡m. Between 0.200 and 0.206 ¡m, Karaiskou et al. (2004) give absorption cross-section measurements at 295 K and at 373 K.
CO2 photodissociates below 0.2275 ¡m according to the two channels
CO2 + hv CO + O(3P) 0.2275 >A> 0.1672 ¡m, (7.60) CO2 + hv — CO + O(1D) A < 0.1672 ¡m. (7.61)
Fig. 7.7. The absorption cross-section of CO2 at 199 K, 294 K and 368 K (band structure at low temperature has been averaged out.
The quantum yield for the first channel is unity up to about 0.21 pm (Okabe 1978). The most important region is between 0.14-0.18 pm, which corresponds to the absorption region of the molecular oxygen Schumann-Runge bands and continuum.
7.6.7 CH4 photolysis
Methane absorbs strongly at wavelengths less than 145 nm, and photodissociates according to the following important channels
For Lyman-a, the branching ratio for the first channel is 0.24, for the second it is 0.25 and for the third it is 0.51. Above Lyman-a the branching ratio is unity for the third channel. In Fig. 7.8 is shown the absorption cross-section of methane taken from various sources. For the region 37.43-91.11 nm the data are from Samson et al. (1989), for 38.0-18.0 nm from Lee et al. (1977), at Lyman-a Brownsword et al. (1997) give a mean value of (2.0 ±0.1)x!0~17 cm~2, while
CH4 + hv ^ CH2 +H2, CH4 + hv ^ CH2 + 2H, CH4 + hv ^ CH3 + H.
Flg. 7.8. The absorption cross-section of CH4 at room temperature.
for 137-160 nm the data are from Mount et al. (1977). Further references for other cross-section data, photodissociation pathways and their corresponding branching ratios, are given in Lavvas et al. (2007).
In Appendix B, Tables B.1 to B.3, are given typical values for the total photodissociation and photoionization rates of atmospheric species for quiet-Sun irradi-ance in the ultraviolet and visible spectral regions at the top of the atmosphere, for mean global conditions. In Fig. 7.9 are shown the photodissociation rates of various molecules with altitude for global mean atmospheric conditions.
The photolysis rate of ozone with altitude is given for the two channels, for the mean global conditions mentioned earlier in relation to Fig. 7.2. The second channel is significant above 40 km with a photolysis rate of 7.1 x10~3 at TOA. The first channel is significant below 40 km and has a rate of 1.5x10~3 s_1 at TOA. In the upper atmosphere the CO2 second channel is important, while in the stratosphere the first channel is important. Due to the temperature dependence of the CO2 cross-section below 0.167 pm, the photolysis rate of the second channel increases to 7.45x10~7 s_1 at TOA. Water vapour is primarily dissociated by the solar Lyman-a line above 70 km altitude in the atmosphere and by photons of wavelength greater than Lyman-a below 70 km, as shown in
Flg. 7.9. Photolysis rate with altitude for various important molecules, for global mean atmospheric conditions.
7.7 Collisionally induced reactions
Let us consider a diatomic molecule consisting of two atoms A and B and that the molecule has been excited to some higher energy state, AB* by collisions. The molecule may then undergo spontaneous decomposition into its constituent atoms via the unimolecular reaction
The molecule AB may dissociate into its constituent atoms by collision with a second or catalytic molecule M via the bimolecular reaction
Alternatively, two atoms A and B can undergo an association reaction to form the molecule AB in a bimolecular reaction
A collision between the constituent atoms and a catalytic molecule M may result in the termolecular recombination reaction
Collisions involving four or more molecules are very infrequent.
For a bimolecular reaction driven by collisions, we can define a bimolecular collision rate between molecules per unit volume per second according to simple collision theory zab = ZoUAUB (7.69)
which has units of cm3 molecule-1 s-1, with the average molecular speed given by eqn (7.15), and ¿aB, is the mean diameter of the colliding molecules, as in eqn(7.16). The collision rate, Zab has units of molecules cm~3 s_1, for a population of colliding molecules. It varies as \/T, in disagreement with experiment. The reason is that the rate at which molecules react is much less than the rate at which they collide. For a reaction to proceed, the reactants, A and B, must form a transition state AB* that is at a higher potential energy than the reacting molecules or reactants, or the products, C and D, as in
For the reaction to proceed in the forward direction, the reactants require an activation energy, Er, to form the transition state. Similarly, the products require an activation energy, Ep, to form the transition state, for the backward reaction.
The rate of destruction of molecules A per cm3 per s is proportional to the product of the number densities of the reacting molecules. This is the Law of Mass Action, which can be written mathematically as the rate equation
dt where the constant of proportionality, kf in cm3 molecules-1 s-1, is the forward rate constant, with a similar equation for the destruction of molecule B. The forward rate constant of the reaction, and the rate constant for the backward reaction, kb, are related through the equilibrium constant, K, defined by
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