Atmo II 170
Physics of the Atmosphere II
(7) Absorption – UV
Atmo II 171
Caveat
wave number ≠ wave number (!)
From section (1) we recall that the (angular) wave number, k [rad/m], is
defined as:
2
k

and
ω  2 
and

c
k
thus
c  
But in spectroscopy we will often stumble over the (spectroscopic)
wave number – which is frequently given in [cm–1].
1
~
 

thus

~
 
c
A (spectroscopic) wave number of 1 cm–1 therefore corresponds to a
wavelength of 1 cm (microwave), and a frequency of 30 GHz.
Atmo II 172
Bohr and more
K. N. Liou
100 years ago (1913) Niels
Bohr postulated, that the
circular orbits of electrons
in a hydrogen atom are
quantized: their angular
momentum can have
only integral multiples of
a basic value.
Radiation occurs only
when the atom makes a
transition from an excited
state with energy Ek to a
state with lower energy Ej.
E  Ek  E j  h
The lowest energy is called ground state – and yes:
E   
Atmo II 173
Bohr and more
Niels Bohr further postulated that that the angular momentum L can only
take on discrete values (n = 1, 2, 3, …) (NIST):
h
L n
 n
2
h

 1.054 571 726  10  34 Js
2
From the equation of motion for an electron (with mass me and charge e)
Bohr derived the total energy state of the system (n = 1, 2, 3, …):
mee 4 1
R  hc
En   2 2 2  
8 0 h n
n2
with the Rydberg constant (after Johannes Rydberg) for the hydrogen atom
(NIST):
R   1.097 373 156 8539  10 7 m  1  1.1  10 5 cm  1
Atmo II 174
Bohr and more
The (spectroscopic) wave
number of emission or
absorption lines in the
hydrogen spectrum is thus:
 1 1 
~
  R   2  2 
k 
j
which can be converted to
energy, with:
R  hc  13.605 692 53 eV
being the ionization
energy of hydrogen.
1 eV  1.602 176 565  10  19 J
K. N. Liou
Atmo II 175
Bohr and more
The Lyman series (after
Theodore Lyman) is in the
UV part of the spectrum.
Lyman-α (k = 2, j = 1) has
a wavelength of 1216 Å
(Ångström).
The Balmer series (after
Johann Balmer) is in the
visible. The famous H-α
line corresponds to k = 3
and j = 2. The color is ..
wiki The Paschen series (after
Friedrich Paschen) is in the
infrared. (j = 3)
Atmo II 176
H–Alpha
The sun in H–α (left, NASA).
Details close to a sunspot
(SST, O. Engvold et al.)
Atmo II 177
Line Broadening
Based on the considerations so far, we would expect infinitesimally thin
absorption and emission lines in a spectrum. But monochromatic
emission is essentially never observed, since energy levels during
energy transitions are usually changed slightly due to external influences
on the atoms and molecules, and due to the loss of energy in emission –
resulting in line broadening.
(1) Natural broadening results from the finite lifetime of excited states,
which gives – via Heisenberg's uncertainty principle – an uncertainty
in energy. The effect is usually insignificant compared to the others:
(2) Pressure broadening or collision broadening is predominant below
~20 km altitude. The collision of other particles with the emitting one
interrupts the emission process, thereby shortening the characteristic
time for the process, which increases the uncertainty in the emitted
energy.
Atmo II 178
Line Broadening
Natural and pressure broadening
result in Lorentzian line shapes.
The Lorentz distribution (also
known as Cauchy distribution)
looks – superficially – like a
Gaussian, but it is a perfect
example for a pathological
distribution: Mean and variance
are undefined (!).
M. Burton
(3) Doppler broadening: Molecules are in motion (in the line of sight) when
they absorb. This causes a change in the frequency (Doppler effect) of
the incoming radiation as seen in the reference frame of the molecule.
The result is a Gaussian line shape.
Atmo II 179
Line Broadening
The general
solution will be
a Voigt profile:
a convolution
of a Lorentzian
line shape and
a Gaussian
line shape.
M. Salby
Atmo II 180
Line Broadening
Pressure and Doppler broadening
(for H2O and CO2 – see next
slides) is crucial in explaining the
intimidating magnitude of the
“greenhouse effect” on Venus.
(left: NASA, above: ESA) – and on
Earth (keyword: “CO2 saturation”)
Atmo II 181
Molecular Absorption
Atoms can only produce line spectra associated with electronic energy
(mainly in the UV and visible part of the spectrum). For molecules there are
also other options – rotation and vibration.
In radiative transitions, the molecule must couple with an electromagnetic
field so that energy exchanges can take place. This coupling is generally
provided by the molecules electric dipole moment. Radiatively active
gases in the infrared, like H2O and O3, have permanent electric dipole
moments due to their asymmetric charge distributions.
Linear homoatomic molecules such as N2 and O2, however, are inactive
in the infrared because of their symmetric charge distributions.
However, they have weak magnetic dipole moments that allow for radiative
activities in the ultraviolet and (to a lesser extent) in the visible region.
Rotational energy changes are relatively small, with a minimum of about
1 cm−1 (corresponding wavelength). For this reason, pure rotational lines
occur only in the microwave and far-infrared spectra.
Atmo II 182
Molecular Absorption
Changes in vibrational energy are generally greater than 600 cm−1, which
is much larger than the minimum changes in rotational energy. Thus,
vibrational transitions never occur alone but are coupled with
simultaneous rotational transitions. This coupling gives rise to a group of
lines known as the vibrational–rotational band in the intermediate infrared
spectrum.
K. N. Liou The two nuclei of diatomic
molecules (N2, O2, CO) can
only move toward and away
from each other - they have
just one vibrational mode,
the symmetric stretch.
N2 and O2 molecules also
lack a permanent dipole
moment – resulting in little
radiative activity in the
visible and infrared.
Atmo II 183
Molecular Absorption
Triatomic molecules with a linear symmetrical configuration (CO2, N2O),
show three vibrational modes: symmetric stretch, bending motion, and
antisymmetric stretch.
The triatomic molecules H2O and O3 form obtuse, isosceles triangles
(known as the asymmetric top (bent triatomic) configuration). This molecular
shape has three fundamental vibration modes.
The CH4 has even four fundamental vibration modes.
K. N. Liou
Diatomic and a linear
triatomic molecule have
two equal moments of
inertia and two degrees of
rotational freedom.
Asymmetric top molecules
have three unequal moments and three degrees
of rotational freedom.
Atmo II 184
Molecular Absorption
For the rotational states, the kinetic energy of a rigid rotating dipole is:
L
E kin 
2
L  I
I 2
E kin 
2
with L being the angular momentum, and I being the moment of inertia.
[Similar to the well known relations p = mv and Ekin = ½mv2]
From the solution of the time-independent Schrödinger equation, the
quantum restrictions on angular momentum are given by:
1
h
J J  1 2
L
2π
where J is the (integer)
rotational quantum number.
The quantized rotational energy can be written as (B is the rotational
constant):
E J  B hc J J  1
h
B 2
8 Ic
Atmo II 185
Molecular Absorption
The selection rule for radiation transition is governed by ΔJ = ±1 and the
spectral line location will therefore be:
~  2 B J 
where J’ can be any quantum number.
Because of the selection rule, the separation in wave number of adjacent
lines is simply 2B:
Reminder: pure
rotational spectra occur
only in the far infrared
and microwave
regions.
K. N. Liou
~
Atmo II 186
Molecular Absorption
For the vibrational states, the quantized energy levels for a harmonic
oscillator are given by:

Ev  h k v k  1
2
where vk is the (integer) vibrational
quantum number.
The subscript k refers to the normal modes. For triatomic molecules (e.g.
H2O and O3), there are three normal modes – also known as fundamentals.
For linear molecules such as CO2 and NO2, there are four (!) fundamentals,
but two orthogonal bending modes are degenerate and so only
three fundamentals exist.
The term “degenerate” should not be taken personally – it just means states
with the same energy but with different sets of quantum numbers.
Atmo II 187
Molecular Absorption
~
K. N. Liou
Molecular vibration produces
an oscillating electric dipole
moment that is sufficient
for both vibrational and
rotational transitions.
Thus, both transitions occur
simultaneously and the
resulting energy level is the
sum of the separate transition
energies.
Since many rotational levels
are active, the spectrum of the
combined transitions is an
array of rotational lines
grouped around the
vibrational wave number –
absorption band.
Atmo II 188
UV Absorption
Absorption in the ultraviolet
Molecular Nitrogen
Lyman–Birge–Hopfield bands from about 1450 to 1120 Å. Absorption of N2
in the solar spectrum is generally considered insignificant. Also the
photodissociation of N2 in the atmosphere plays only a minor role in
atmospheric chemistry below 100 km.
Molecular Oxygen
Herzberg continuum between 2600 and 2000 Å, due primarily to the
forbidden ground-state transition and dissociation continuum, which lead
to the formation of two oxygen atoms (ground state). Absorption by this
band system is weak and of little importance because of an overlap with the
much stronger O3 bands in this spectral region. But it is significant for the
formation of Ozone.
Atmo II 189
Oxygen Absorption
K. N. Liou
Atmo II 190
UV Absorption
Molecular Oxygen (cont.)
Schumann–Runge bands are produced by ground-state transitions in the
spectral region from 2000 to 1750 Å.
At 1750 Å, the bands converge to a stronger dissociation continuum (with
one of the oxygen atoms in an excited state) – known as
Schumann–Runge continuum, it extends to about 1300 Å and represents
the most important absorption spectrum of O2.
The Lyman α line located at 1216 Å is of particular interest, since it happens
to lie in an atmospheric window.
Hopfield bands between 850 and 1100 Å are associated with transitions
between excited states.
Below ~ 1026 Å, O2 absorption is in the form of an ionization continuum –
and leads to the formation of the ionosphere.
Atmo II 191
UV Absorption
Ozone
The absorption of ozone in the solar spectral region is due to electronic
transitions.
Hartley bands from 2000 to 3000 Å (UV-C + UV-B), centered at 2553 Å are
the strongest ozone bands. Absorption of solar flux in these bands is
important in the upper stratosphere and in the mesosphere.
Huggins bands between 3000 and 3600 Å are weaker and more
structured, they are important as UV-A and UV-B absorbers.
Chappuis bands are responsible for absorption in the visible and near-IR
regions from about 4400 to 11,800 Å.
Atmo II 192
UV Absorption
K. N. Liou
Penetration depth (corresponding to optical depth = 1) of EUV and UV in
the Earth’s atmosphere (K. N. Liou).
Atmo II 193
UV Absorption – Summary
The EUV (extreme ultraviolet) fluxes are absorbed at high altitudes,
resulting in dissociation and ionization of the major constituents in the
thermosphere and leading to the formation of the layers of the ionosphere.
At longer wavelengths, from 1750 to ~ 2400 Å, the solar flux penetrates
deeper into the atmosphere and is chiefly absorbed by O2 in the
Schumann–Runge band and Herzberg continuum, leading to the
production of atomic oxygen and ozone.
Maximum ozone absorption occurs at about 50 km in the Hartley band at
wavelengths from 2400 to 3100 Å .
Above 3100 Å, the atmosphere is relatively transparent except for
Rayleigh scattering and scattering by aerosols and clouds.