Geoscience Reference
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in polluted air usually peak between 0.05 ppmv and
0.25 ppmv. The reduction in radiation intensity (where
I denotes intensity) at a given wavelength with distance
through an absorbing gas can now be defined as
I 0 e σ a , g , q ( x x 0 )
I 0 e N q b a , g , q ( x x 0 )
I
=
=
(7.2)
Equation 7.2 states that incident radiation I 0 is
reduced by a factor exp[- N q b a,g,q ( x - x 0 )] between
points x 0 and x by gas absorption. From this equation, it
is evident that the absorption cross section of a gas can
be determined experimentally by measuring the atten-
uation of radiation through a homogenous gas column,
such as the one shown in Figure 7.2, of known path
length N q ( x-x 0 )(moleccm 2 ), and then extracting the
cross section from Equation 7.2.
Figure 7.4. Probability distribution of where incident
energy is scattered by a gas molecule (located at the
center of the diagram).
abundant gases in the air, these are the most impor-
tant Rayleigh scatterers. Rayleigh scattering is named
after Lord Baron Rayleigh , born John William Strutt
(1842-1919; Figure 7.5), who also discovered argon
gaswith Sir William Ramsay in 1894 (Chapter 1).
Rayleigh's theoretical
Example 7.1
Find the fraction of incident radiation intensity
(the transmission) passing through a uniform gas
column of length 1 km when the number concen-
tration of the gas is N q
work on
gas
scattering
was
10 12 molec cm −3 and
the absorption cross section of a gas molecule is
b a,g,q =
=
10 −19 cm 2 per molecule.
Solution
From Equation 7.1, the extinction coefficient
through the gas is
10 −7 cm −1 .
From Equation 7.2, the transmission is I / I 0
σ a,g,q =
N q b a,g,q =
=
exp(
0.99. Thus, 99 percent of
incident radiation traveling through this column
reaches the other side.
10 −7
×
10 5 )
=
7.1.2. Gas Scattering
Gas scattering is the redirection of radiation by a
gasmolecule without a net transfer of energy to the
molecule. When a gas molecule scatters, incident radi-
ation is redirected symmetrically in the forward and
backward direction and somewhat off to the side, as
shown in Figure 7.4. The figure gives the probabil-
ity distribution of incident energy scattered by a gas
molecule.
The scattering of radiation by gas molecules or
aerosol particles much smaller than the wavelength
of light is called Rayleigh scattering .Because gas
molecules are on the order of 0.0005
mindiameter
and a typical wavelength of visible light is 0.5
m,
all gas molecules are Rayleigh scatterers. Because
molecular nitrogen [N 2 (g)], molecular oxygen [O 2 (g)],
argon [Ar(g)], and water vapor [H 2 O(g)] are the most
Figure 7.5. Lord Baron Rayleigh (John William Strutt)
(1842-1919). Edgar Fahs Smith Collection, University
of Pennsylvania Library.
 
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