(7) Absorption – UV

Physics of the Atmosphere II

Atmo II 170

wave number ≠ wave number (!)

Atmo II 171

Caveat

and 2ω

But in spectroscopy we will often stumble over the (spectroscopic) wave number – which is frequently given in [cm–1].

From section (1) we recall that the (angular) wave number, k [rad/m], is defined as:

2

k andk

c

cthus

1

~ thusc

~

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

100 years ago (1913) Niels Bohr postulated, that the circular orbits of electrons in a hydrogen atom are quantized: their angular momentum can haveonly 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.

hEEE jk

The lowest energy is called ground state – and yes: E

K. N. Liou

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):

nh

nL 2

Js7265711.0542

34 10h

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, …):

22220

4e

n1

8 n

hcR

nh

emE

with the Rydberg constant (after Johannes Rydberg) for the hydrogen atom (NIST):

1517 cm101.1m1085391563731.097 R

Atmo II 174

Bohr and more

The (spectroscopic) wave number of emission or absorption lines in the hydrogen spectrum is thus:

22

11

kjR~

K. N. Liou

eV5369213.605hcR

which can be converted to energy, with:

J10565 176 1.602eV1 19

being the ionization energy of hydrogen.

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).

wiki

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 ..

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.

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.

K. N. Liou

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 havetwo equal moments of inertia and two degrees of rotational freedom. Asymmetric top molecules have three unequal mo-ments and three degrees of rotational freedom.

Atmo II 184

Molecular Absorption

For the rotational states, the kinetic energy of a rigid rotating dipole is:

with L being the angular momentum, and I being the moment of inertia. [Similar to the well known relations p = mv and Ekin = ½mv2]

2

LEkin IL

2

2IEkin

From the solution of the time-independent Schrödinger equation, the quantum restrictions on angular momentum are given by:

21

1JJ2

hL

πThe quantized rotational energy can be written as (B is the rotational constant):

1 JJBhcE J Ic

hB

28

where J is the (integer) rotational quantum number.

Atmo II 185

Molecular Absorption

The selection rule for radiation transition is governed by ΔJ = ±1 and the spectral line location will therefore be:

where J’ can be any quantum number.

Because of the selection rule, the separation in wave number of adjacent lines is simply 2B:

JB 2~

K. N. Liou~

Reminder: pure rotational spectra occur only in the far infrared and microwave regions.

For the vibrational states, the quantized energy levels for a harmonic oscillator are given by:

Atmo II 186

Molecular Absorption

where vk is the (integer) vibrational quantum number.

21 kkv vhE

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 onlythree fundamentals exist.

The term “degenerate” should not be taken personally – it just means stateswith the same energy but with different sets of quantum numbers.

Atmo II 187

Molecular Absorption

Molecular vibration produces an oscillating electric dipole moment that is sufficientfor both vibrational and rotational transitions. Thus, both transitions occursimultaneously 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.K. N. Liou

~

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 inatmospheric 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

K. N. Liou

Penetration depth (corresponding to optical depth = 1) of EUV and UV in the Earth’s atmosphere (K. N. Liou).

UV Absorption

Atmo II 193

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.

UV Absorption – Summary