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. O 3  O 2 + 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. H 2 O, CO, O 3 ). Symmetric linear molecules (N 2, CO 2, N 2 O) 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 ν 2 transition of CO 2 ! ΔJ = +1  “R-branch” The energy associated with ΔJ = ±1 is proportional to the starting J state For example: J = 3  4 takes 3 times more energy than J = 0  1 ! 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 v s, the distribution of v s is given by: where v 0 is the “Root-Mean-Squared” (RMS) velocity along that direction. The frequency shift that is induced by a relative velocity v s is given by: Solving for v s, substituting into p(v s ) 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 μm is 6600x larger freq. than 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 ν 0.

PRESSURE BROADENING

Doppler prop to ν 0, 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. O 3  O 2 + 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. H 2 O, CO, O 3 ). Symmetric linear molecules (N 2, CO 2, N 2 O) 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 ν 2 transition of CO 2 ! ΔJ = +1  “R-branch” The energy associated with ΔJ = ±1 is proportational to the starting J state, so e.g. J = 3  4 takes 3 times more energy than J = 0  1 The energy associated with Δv = ±1 does not depend on starting v state: they all take the same energy.