Environmental Engineering Reference
In-Depth Information
lar oxygen at altitudes from 100 to 120 km, and the number density of atomic oxy-
gen is compared with that of molecular nitrogen at altitudes from 150 to 200 km.
For comparison, we note that the average total number densities of nitrogen and
oxygen molecules range from 7
10
9
cm
3
, and the number density of
10
12
to 3
10
9
cm
3
asthealtitudevaries
from 100 up to 200 km. Thus, atomic oxygen is one of the basic components of the
upper atmosphere at high altitudes.
To analyze the absorption of short-wave solar radiation as a result of photodisso-
ciation of molecular oxygen, we write the balance equation for the intensity
I
ω
of
solar radiation of a given frequency in the atmosphere in the form
atomic oxygen is in the range from 6
10
11
to 4
dI
ω
dh
D
I
ω
σ
ω
[O
2
] ,
(6.96)
where
h
is the altitude, [O
2
] is the number density of molecular oxygen, and
σ
ω
is the photodissociation cross section. We assume that incident solar radiation is
perpendicular to the Earth's surface, and the number density of molecular oxygen
varies according to the barometric formula (6.95), [O
2
]
D
N
0
exp(
h
/
L
), where
L
D
T
/
mg
10 km. Then the solution of (6.96) is
)exp
exp
,
h
h
0
I
ω
(
h
)
D
I
ω
(
1
(6.97)
L
where
I
ω
(
1
) is the intensity of solar radiation above the atmosphere, and the alti-
tude
h
0
is determined by the relation
σ
ω
L
[O
2
](
h
0
)
D
1. Formula (6.97) shows that
the principal portion of the solar radiation of this part of the spectrum is absorbed
near
h
0
. Because the photodissociation cross section is in the range of
σ
ω
10
19
-
10
17
cm
2
, this absorption takes place at altitudes where [O
2
]
10
11
-10
13
cm
3
.
It is instructive to compare the decay time for the photodissociation of molecular
oxygen and a typical time for transport of molecular oxygen to the altitudes at which
absorption occurs. A typical dissociation time is
1
4
Z
dI
ω
σ
ω
„
ω
1
10
6
s,
τ
2
dis
where the factor 1/4 results from averaging the radiation flux over the entire surface
of the Earth, and
10 eV is the photon energy. The drift velocity of an atom
or molecule as a result of its own weight is, according to the Einstein relation (4.38),
„
ω
D
6
g
N
g
r
m
T
1
10
13
cm
2
s
1
N
Dmg
T
3
w
D
σ
,
(6.98)
whe
re
we use the estimate (4.53) for the diffusion coefficient
D
of oxygen atoms
and
10
15
cm
2
is of the order of the gas-kinetic cross section for at-
mospheric molecules and atoms. In this expression,
N
is the total number density
of atoms and molecules at a given altitude of the atmosphere. Assuming molecular
nitrogen to be the primary component of the atmosphere at altitudes of maximum
σ
σ
3
g
