Gas Absorption Line Broadening

April 6

Summary in Words of Gas Transitions

• 3 types of quantized transitions important to us:• Electronic (highest energy: UV-Vis)• Vibrational (medium energy: Vis-NIR-Thermal IR)• Rotational (Far IR & Microwave)

• Other types of absorption are not quantized:• Photo-Ionization : Ripping electronic off to make ion

(Occurs when photon energy > ionization energy of molecule)• Photo-Dissociation: Tearing an atom off a molecule

(E.g. O3 O2 + O* - critical for stratospheric chemistry)(Occurs when photon energy > dissociation energy of molecule)

• Pure rotational transitions can happen ONLY if molecule has a permanent electric dipole moment: (e.g. H2O, CO, O3).

• Symmetric linear molecules (N2, CO2, N2O) do not have a permanent dipole moment.

From last time…

Summary in Words of Gas Transitions (pg 2)

• Rotational transitions often accompany vibrational transitions

• Rotational quantum number J changes by (-1,0, or 1) when vibrational quantum number v changes by ± 1. • ΔJ = -1 “P-branch”• ΔJ = 0 “Q-branch” if it exists! Only allowed if the vibrational transition is

“degenerate” , e.g. the ν2 transition of CO2!• ΔJ = +1 “R-branch”

• The energy associated with ΔJ = ±1 is proportional to the starting J state For example: J = 34 takes 3 times more energy than J = 01 !

• The energy associated with Δv = ±1 does not depend on starting v state: they all take the same energy.

Doppler Broadening

Molecules travel in velocities according the Maxwell-Boltzmann Distribution.

For any velocity component vs , the distribution of vs is given by:

where v0 is the “Root-Mean-Squared” (RMS) velocity along that direction.The frequency shift that is induced by a relative velocity vs is given by:

Solving for vs , substituting into p(vs) and renormalizing leads to:

(frequency shift)

Summary of Broadening Mechanisms: Doppler

Doppler Broadening is due to the doppler effect of moving molecules and leads to a Gaussian shape (weak wings):

The Half-Width-at-Half Max (HWHM) of the distribution is:

• Prop. to transition frequency: bigger for higher-energy transitions. • O2 @ 0.76 μm is 6600x larger freq. than O2 @ 60 GHz, so Doppler

Broadening will be 6600x larger!

• Prop to sqrt(T). T=310 K (hot temp) is only 30% larger than T=180 K (cold temp)!

Pressure Broadening is due to collisions between molecules as they absorb photons. The Shape is a “Lorentzian”:

The HWHM of pressure broadening goes like:

Summary of Broadening Mechanisms: Pressure

• Prop. To Pressure! So can vary many orders of magnitude. Strongest at surface.

• T-dependence goes like 1/sqrt(T). So again relatively weak.

• Shape & Width not dependent on transition frequency ν0.

PRESSURE BROADENING

• Doppler prop to ν0, so becomes important closer to the earth’s surface for higher energy transitions.

• Pressure broadening decreases with pressure and hence altitude Z.

The Voigt Line Shape

• When both Doppler & Pressure broadening are comparable, you can’t neglect either one.

• Then you get the “Voigt” lineshape, which is the convolution of a Lorentz function with a Gaussian distribution.

Summary in Words of Gas Transitions

• 3 types of quantized transitions important to us:• Electronic (highest energy: UV-Vis)• Vibrational (medium energy: Vis-NIR-Thermal IR)• Rotational (Far IR & Microwave)

• Other types of absorption are not quantized:• Photo-Ionization : Ripping electronic off to make ion

(Occurs when photon energy > ionization energy of molecule)• Photo-Dissociation: Tearing an atom off a molecule

(E.g. O3 O2 + O* - critical for stratospheric chemistry)(Occurs when photon energy > dissociation energy of molecule)

• Pure rotational transitions can happen if molcule has permanent electric dipole moment: (e.g. H2O, CO, O3). Symmetric linear molecules (N2, CO2, N2O) do not have permanent dipole moment.

Summary in Words of Gas Transitions (pg 2)

• Rotational transitions accompany vibrational transitions

• Rotational quantum number J changes by (-1,0, or 1) when vibrational quantum number v changes by ± 1. • ΔJ = -1 “P-branch”• ΔJ = 0 “Q-branch” if it exists! Only allowed if the vibrational transition is

“degenerate” , e.g. the ν2 transition of CO2!• ΔJ = +1 “R-branch”

• The energy associated with ΔJ = ±1 is proportational to the starting J state, so e.g. J = 34 takes 3 times more energy than J = 01

• The energy associated with Δv = ±1 does not depend on starting v state: they all take the same energy.