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A little spectroscopy
Homework…
Dipole Moments An electric dipole is a separation of positive & negative charges.
A dipole moment is a vector pointing from the negative to the positive charge with a magnitude equal to the strength of each charge times the separation between the charges. The overall dipole moment of a molecule may be approximated as a vector sum of bond dipole moments. Pm=picometre=1012 m
Which molecule has the highest & lowest dipole moment?
Potassium bromide carbon dioxide: carbon monoxide: ozone: water vapor: hydrogen cyanide:
Which molecule has the highest & lowest dipole moment?
Potassium bromide 10.41 D carbon dioxide: 0 carbon monoxide: 0.112 D ozone: 0.53 D water vapor: 1.85 D hydrogen cyanide: 2.98 D
1 Debye = 1×10−18 statcoulomb-centimetre 1 statC =dyn1/2 cm1 & 1newton = 105 dyne
Permanent dipoles: One atom attracts electrons more than another, becoming more negative, while the other atom becomes more positive. These molecules are called polar molecules, e.g. water. Instantaneous dipoles: These occur when electrons become concentrated in one place than another in a molecule, creating a temporary dipole. Induced dipoles: These can occur when one molecule with a permanent dipole repels another molecule's electrons, inducing a dipole moment in that molecule. A molecule is polarized when it carries an induced dipole. This process adds to Titan’s greenhouse effect.
Rotation Spectra: (Rigid Rotor)
Classical Mechanics:
Where I is the moment of inertia and ω the angular momentum
Quantum Mechanics:
Quantize L with a value of ħJ where ħ = h/2π and J is an integer specifying the state
The energy difference between 2 successive orders: = ħ/I ~ 10-3 to 10-4 eV Compare to translational energy at room temp 3/2 k T = ~ 10-2 eV
I for 2 masses a distance R : I = m1 m2/(m1+m2) R2
Rotational transitions: wavelength spacing
What is the wavenumber (or frequency) spacing between rotational lines?
Note:
Rotational transitions: wavelength spacing
Selection Rule: ΔJ = ± 1
Degeneracy of rotational states: 2 J + 1
Centrifugal Distortion
When a molecule rotates, the centrifugal force pulls the atoms apart, which causes the moment of inertia to increase, thus decreasing the rotation constant, B, used for the rigid rotor.
For a diatomic molecule for example one adds more terms to account for this effect.
The spacing of the lines is no longer constant with frequency, and decreases with increasing quantum number.
Rotational transitions: wavelength spacing
What is the wavelength spacing between rotational lines?
=
Taking the derivative:
Example
Titan
Vibrational states
For the lowest states – can approximate as a simple harmonic oscillator. Quantum Mechanics:
Where νk is the mode frequency and v (an integer) is the vibration quantum number
What is the separation between vibrational states?
Consider CO
Lowest Energy State: E = hν = hv1/2 Wavenumber (ν/c) = 2127 cm-1 or 4.7 um
The 1-> 0 and 2 -> 1 transition lines emit radiation at this wavelength
The 2->0 lines emit radiation at what frequency?
CO has only 1 mode
Consider CO
Lowest Energy State: E = hν = hv1/2 Wavenumber (ν/c) = 2127 cm-1 or 4.7 um
The 1-> 0 and 2 -> 1 transition lines emit radiation at this wavelength
CO has only 1 mode
The 2->0 lines emit at 2 x 2127 cm-1 = 4254 cm-1 or 2.35 um
CO spectrum
Rotation transitions: Selection rules ---
Also: ΔJ = 0 For spherical top molecules Not diatomic molecules
Rovibrational Transitions
R P
Overtones
For Δv=1 à4.7 um or 2127 cm-1 For Δv=2 à2.3 um or 4254 cm-1 For Δv=3 à1.6 um or 6381 cm-1
Calculations of cross sections for hot gasses, from UCL ~ 10 million transitions
How many vibrational modes of an N>2 molecule?
How many vibrational modes of an N>2 molecule?
A molecule with N atoms has a total of 3N degrees of freedom (each nucleus can be independently displaced in three perpendicular directions). Three of these degrees of freedom correspond to translational motion of the center of mass. For a nonlinear molecule, three more degrees of freedom determine the orientation of the molecule in space, and thus its rotational motion. This leaves 3N - 6 vibrational modes. For a linear molecule, there are just two rotational degrees of freedom, which leaves 3N - 5 vibrational modes.
3N
3N-3
3N-3-3
3N-3-2
Summary vibrational Transitions
ν1 mode of CO
0->1, 1à2, 2à3...
CO2
How many vibrational bands does CO2 have? Are we missing any?
Do they all interact with radiation?
CO2
Symmetric Stretch ν1 No electric dipole
No radiative interaction
Asymmetric Stretch ν2 4.26 μm 2349 cm-1
Bend ν2 & ν4 15.0 μm 667 cm-1
Greenhouse warming
Earth’s IR emission spectrum
CH4
ν1 3.2 μm
3025.5 cm-1
ν3 3.3 μm
3156.8 cm-1
ν2 6.3 μm
1582.7 cm-1
ν4 7.3 μm
1365.4 cm-1
Whooping feature
CH4
ν1 3.2 μm
3025.5 cm-1 (inactive)
ν3 3.3 μm
3156.8 cm-1
ν2 6.3 μm
1582.7 cm-1
ν4 7.3 μm
1365.4 cm-1
Methane ν3 spectrum
Optical reflection spectra
H2O
H2O
ν3 2.7 μm
3755.9 cm-1
ν2 6.3 μm
1594.8 cm-1
ν1 2.7 μm
3657.1 cm-1
For Δv=2 à3190 (3.1 um), For Δv=3 à4784 (2.1 um) For Δv=2 à7512 (1.3 um)
Burrows 2013
ν1 ν3
ν3,1
ν3,1
Fp/F
s
CO model of an exoplanet
Fp/F
s
Solar Abundance of Elements
Main Molecules in H2 atmopheres
Thermochemical Equilibrium!Chemistry driven by the thermal energy of the system.
In equilibrium, the Gibbs free energy, G, is a minimum.
Definitions:
H= enthalpy, S=Entropy, T=temperature
Then:
Substituting for dH:
Isothermal process in which the pressure is changed alters G by:
i.e.
Composition!
VENUS gas! Abundance! EARTH gas! Abundance!
CO2! 96.4 %! N2! 78.1 %!N2! 3.5 %! O2! 21.0 %!SO2! 0.015 %! H2O! 0.01-4 %!Ar! 0.007 %! Ar! 0.93 %!H2O! 0.002 %! CO2! 0.40 %!
Volcanic Gases from Kilauea!
Ninety-nine percent of the gas molecules emitted during a volcanic eruption at Kilauea volcano are water vapor (H2O), carbon dioxide (CO2), and sulfur dioxide (SO2). The remaining one percent is made up of hydrogen sulfide (H2S), carbon monoxide (CO), hydrogen chloride (HCl), hydrogen fluoride (HF). There is also N2 and Ar.!
VENUS gas!
Abundance!
CO2! 96.4 %!N2! 3.5 %!SO2! 0.015 %!Ar! 0.007 %!H2O! 0.002 %!
Carbon: Earth vs Venus!
Venus CO2: equivalent to 0.88 km of calcium carbonate (CaCO3) !This is 2 times the calcium carbonate in Earth’s crust.!Origin of CO2 is volcanism. !!Earth CO2: 25% is anthropogenic and 75% biological. Volcanism: minor source!Most of the carbon is in calcium carbonate, mainly skeletal fragments of marine organisms such as coral, forams and molluscs!
Which if any molecule is stable in Earth’s
atmosphere?
N2 cycle "(even triply bonded N2!)!
N2 fixation:! N2 + 8H+ + 8e- è 2NH3 + H2 !
Through enzymes (nitrogenase) !produced by prokaryotes !(both bacteria and archaea) !
Nitrification! Bacteria convert NH4
+ to NO2−!
then (with other bacteria) to NO3−!
Ammonification ! Bacteria & Fungi produce NH4
+!
from plant & animal remains!
Denatrification! Bacteria convert NO3
− to N2! !
Earth
Processes that establish composition
n Earth, Venus & Mars require surface interaction to explain the atmospheres !!n Cache elements (rust and oxygen on Mars) !n Supply elements such as sulfur (volcanism of S02)!n Participate in the molecular changes (N cycle) !
n Small & hot planets are susceptible to volatile loss. !n Mars’ lack of volatiles!n Small hot Jupiters!
n Large and cool Jovian Planets are simpler*.!n Thermochemical equilibrium !n Photochemistry!n Disequilibrium from transport in conditions out of equilibrium!
Summary: "Lower Atmosphere !
Earth’s biosphere is totally dependent on life.!
Rotational and Vibrational
Probe the molecular abundances of lower atmospheres Span near-IR to microwave wavelengths. With pure rotational bands at long wavelengths. And Rovibrational bands at IR wavelengths
Strength of spectroscopic lines
� Probability of a transition
� Population of states
Absorption Coefficients
The intensity of a spectral line depends on: 1) the probability that the molecule or atom makes the transition 2) the occupation of the initial state
The latter depends on the temperature
Line strengths are generally determined at room temperature, and listed in large data bases. The strengths at different temperatures are determined by considering the occupation of states.
DO 600 KL=1,NLAY ! Print *, 'gettin all silly with layer ', kl, ' ,yo!' Do 29 i=1,ngas do 30 ialfa=1,100 alfa=0.001*ialfa
Call Profiles(nw,np,w0,mw(i),t(kl),p(kl),alfa,ialfa,w1,f1) ! nw=25 do k=1,nw width(k,ialfa,i) = w1(k,ialfa) ! Voigt profile for Lorentz with of ialfa/1000 ff(k,ialfa,i) = f1(k,ialfa) ! Voigt profile at width for a=iafa/1000 end do
do 20 k=1,nw-1 k1=k+1 ffww3(k,ialfa,i)=(ff(k,ialfa,i)-ff(k1,ialfa,i))/ * (width(k1,ialfa,i)-width(k,ialfa,i)) 20 continue 30 continue Do j=1,ng(i) If (e(j,i).eq.-1.) then
e(j,i)=550. End if ! Print *, 'First intensity ', j, T(kl), S(j,i) ! Print *, 'Energy ', H2*E(j,i), E(j,i) ! Print *, 'Temp and term ', T(kl),(1./296.-1./T(kl)) Sl(j,i)=S(j,i)*((T0/T(kl))**xgeo(i))* ! xgeo=molecule geometry * (EXP(H2*E(j,i)*(1./T0-1./T(kl)))) ! linear =1/nonlin=1.5 ! Print *, 'After partition function ', Sl(j,i)
Sl(j,i)=Sl(j,i)*( 1-exp(-H2*f(j,i)/t(kl)) )/ . ( 1-exp(-H2*f(j,i)/T0) ) ! stimulated emission ! Print *, 'After stimulated emission ', Sl(j,i) Sl(j,i)=Sl(j,i)*2.68E+19*1.E+05 ! intensity (km*amag)-1 ! Print *, 'Units to km amagat-1 ', Sl(j,i) ! Read(5,*) istop Sl(j,i)=Sl(j,i) * mix(i,kl) ! times mixing ratio ! If (kl.eq.1) print *, j, Sl(j,i), a(j,i) End do 29 End do ! Print *, 'Finished reading intensities ' ! Read(5,*) istop
Summary
A few questions
� Why are absorption bands of solid material broad?
� For what kind of observations/studies do we need high spectral resolution data?
� What information can we gather about planetary formation, surface composition, surface processes, atmospheric composition, atmospheric dynamics, chemistry and evolution through spectroscopy?
Absorption Coefficients
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