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less so than black carbon, whereas nitrobenzene is a
strong UV absorber but a weaker visible absorber.
I
0
I
Example 7.2
Find the fraction of incident radiation intensity
that transmits through a uniform particle of diam-
eter 0.1
d
x
x
0
x
mwhen
the particle is composed of (a) black carbon and
(b) water.
matawavelength of 0.5
Figure 7.11.
Attenuation of incident radiation
I
0
due
to absorption by a spherical aerosol particle.
Solution
From Table 7.2, the imaginary refractive indices
of black carbon and water at
example,
sodium chloride
[NaCl(s)],
ammonium sul-
fate
[(NH
4
)
2
SO
4
(s)], and
sulfuric acid
[H
2
SO
4
(aq)]
are
=
0.5
mare
0.74 and 10
−9
,respectively. From Equation
7.4, the transmission of light through (a) black
carbon is
I
=
all
very
weak
absorbers
of
visible
and
UV
radiation.
0.16
and that through (b) liquid water is 0.999999997.
Thus, a 0.1-
/
I
0
=
exp(-4
×
0.74
×
0.1
/
0.5)
=
mblack carbon particle absorbs 84
percent of incident radiation, whereas a 0.1-
7.1.3.2. The Imaginary Refractive Index
Figure 7.11 shows a possible path of radiation through
asingle spherical aerosol particle.
The attenuation, due to absorption, of incident radi-
ation
I
0
of wavelength
m
water particle absorbs only 0.0000003 percent of
incident visible radiation passing through it. As
such, black carbon is a strong absorber of visible
light, but liquid water is not.
as it travels through a single
particle is
I
0
e
−
4
(
x
−
x
0
)
/
I
=
(7.4)
where
is the imaginary index of refraction, and
x
-
x
0
is the distance through the particle. The
imaginary
index of refraction
is a measure of the extent to which a
particle absorbs radiation. The term 4
7.1.3.3. Effects of Aerosol Particle Absorption
on Ultraviolet Radiation
Figure 7.10 shows the wavelength-dependent imaginary
refractive indices of important absorbing components
in aerosol particles, namely, black carbon, nitrated aro-
matic compounds, and tar balls. It indicates that black
carbon absorbs evenly across the UV and visible spec-
tra. Tar balls also absorb across these spectra but with
greater preference for UV absorption. Although nitrated
aromatics absorb preferentially in the UV spectrum,
is an absorp-
tion extinction coefficient for a single aerosol particle.
Table 7.2 gives imaginary refractive indices for some
substances at wavelengths of 0.3, 0.5, and 10
/
m. Black
carbon has the largest imaginary indices of refraction
across the entire spectrum among the substances shown.
Tar balls also strongly absorb UV and visible light but
Table 7.2.
Real and imaginary indices of refraction for substances at
=
0.3, 0.5, and 10
m
=
0.3
m
=
0.5
m
=
10
m
Real (
n
)
I a inary (
) al (
n
)
I a inary (
) al (
n
)
I a inary (
)
H
2
O(aq)
a
1.0
×
10
−
8
1.0
×
10
−
9
1.35
1.34
1.22
0.051
Black carbon (s)
b
1.80
0.74
1.82
0.74
2.40
1.0
1.47
c
0.38
c
1.67
c
0.27
c
1.77
b
0.12
b
Tarballs (s)
Nitrobenzene (aq)
1.64
d
0.32
d
1.59
d
0.03
d
1.77
b
0.12
b
Low-absorbing OM
b
1.45
0.001
1.45
0.001
1.77
0.12
H
2
SO
4
(aq)
b
1.47
1.0
×
10
−
8
1.43
1.0
×
10
−
8
1.89
0.46
OM, organic matter.
a
Hale and Querry (1973);
b
Krekov (1993);
c
Alexander et al. (2008);
d
Foster (1992).
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