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Size: 8188
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← Revision 56 as of 2019-09-17 22:20:59 ⇥
Size: 9930
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 8: | Line 8: |
| α(F-m²) = 4e-6 π ε₀ α(cm³) ( see https://en.wikipedia.org/wiki/Polarizability#Definition ) | α(F-m²) = 4e-6 π ε₀ α(cm³) ... https://en.wikipedia.org/wiki/Polarizability#Definition |
| Line 23: | Line 23: |
| . ?????????????? | |
| Line 24: | Line 25: |
| σ(nm²) = β / λ(nm)⁴ | σ(nm²) = β / λ(nm)⁴ |
| Line 26: | Line 27: |
| .... ok, something's wrong, the numbers are WAY too small | ... ok, something's wrong, the numbers are WAY too small ... Maybe not, actually; the cross section for blue versus red in the atmosphere involves megatonnes of air TBD |
| Line 30: | Line 32: |
| || || α(cgs!) || Page || Wt || Ref ||<|99>|| 1st eV || Page || β || || || 1e-24 cm³ || || || || || || || nm⁶ || || Hydrogen (atomic) || 0.666793 || 10-96 || 1 || a 1 || 13.598433 || 10-111 || 4.353e-3 || || Carbon (atomic) || 1.67 || 10-96 || 12 || a 5 || 11.26030 || 10-111 || 10.9e-3 || || Nitrogen (atomic) || 1.1 || 10-96 || 14 || a 40 || 14.5341 || 10-111 || 7.1e-3 || || Oxygen (atomic) || 0.77 || 10-96 || 16 || a 2 || 13.61805 || 10-111 || 5.02e-3 || || Fluorine (atomic) || 0.557 || 10-96 || 19 || a 1 || 17.4228 || 10-111 || 3.64e-3 || || Chlorine (atomic) || 2.16 || 10-97 || 36 || a 6 || 12.96763 || 10-111 || || Aluminum || 8.22 || 10-97 || 27 || a 31 || _5.985768 || 10-111 || || Helium || 0.2050522 || 10-96 || 4 || a 3 || 24.587387 || 10-111 || || Neon || 0.39432 || 10-96 || 20 || a 6 || 21.56454 || 10-111 || || Argon || 1.6411 || 10-97 || 40 || a 13 || 16.759610 || 10-111 || || Krypton || 2.4844 || 10-97 || 84 || a 13 || 13.99961 || 10-111 || || Xenon || 4.044 || 10-98 || 131 || a 1 || 12.12984 || 10-112 || || Hydrogen H₂ || 0.842 || 10-105 || 2 || m 6 || 15.42593 || 10-123 || || Nitrogen N₂ || 1.7403 || 10-106 || 28 || m 6 || 15.5808 || 10-126 || || Oxygen O₂ || 1.5689 || 10-107 || 32 || m 34 || 12.0697 || 10-127 || || Fluorine F₂ || 1.38 || 10-104 || 38 || m 7 || 15.697 || 10-122 || || Chlorine Cl₂ || 4.61 || 10-101 || 71 || m 3 || 11.480 || 10-118 || || Hydroxyl HO || 1.50 || other || 17 || m 99 || 13.0170 || 10-123 || || Nitric Oxide NO || 1.70 || 10-106 || 30 || m 2 || _9.26438 || 10-126 || || Nitrous Oxide N₂O || 3.03 || 10-106 || 44 || m 8 || 12.886 || 10-127 || || Water H₂O || 1.45 || 10-109 || 18 || m 2 || 12.606 || 10-131 || || Carbon Monoxide CO || 1.95 || 10-101 || 28 || m 3 || 14.010 || 10-117 || || Carbon Dioxide CO₂ || 2.911 || 10-101 || 44 || m 8 || 13.773 || 10-117 || || Ammonia NH₃ || 2.22 || 10-99 || 17 || m 33 || 10.070 || 10-115 || || Methane CH₄ || 2.593 || 10-105 || 16 || m 6 || 12.61 || 10-125 || || Ethane !C₂H₆ || 4.47 || 10-103 || 30 || m 3 || 11.56 || 10-121 || || Propane !C₃H₈ || 6.37 || 10-107 || 44 || m 2 || 10.95 || 10-128 || || Butane !C₄H₁₀ || 8.20 || 10-100 || 58 || m 2 || 10.53 || 10-117 || || Pentane !C₅H₁₂ || 9.99 || 10-107 || 72 || m 2 || 10.28 || 10-127 || || Hexane !C₆H₁₄ || 11.9 || 10-104 || 86 || m 2 || 10.13 || 10-123 || || Heptane !C₇H₁₆ || 13.61 || 10-104 || 100 || m 2 || _9.93 || 10-123 || || Octane !C₈H₁₈ || 15.9 || 10-106 || 114 || m 2 || _9.80 || 10-127 || || Nonane !C₉H₂₀ || 17.36 || 10-106 || 128 || m 27 || _9.71 || 10-127 || || Decane !C₁₀H₂₂ || 19.10 || 10-102 || 142 || m 27 || _9.65 || 10-119 || || Benzene !C₆H₆ || 10.32 || 10-99 || 78 || m 33 || _9.24378 || 10-116 || || Methanol !CH₄O || 3.29 || 10-105 || 32 || m 2 || 10.85 || 10-125 || || Ethanol !C₂H₆O || 5.41 || 10-103 || 46 || m 2 || 10.43 || 10-121 || |
|| || α(cgs!) || Page || Wt || Ref || β ??? ||<|99>|| 1st eV || Page ||<-2> HITRAN || || || 1e-24 cm³ || || || || nm⁶ || || ||<|99>|| nm/UV || || Hydrogen (atomic) || 0.666793 || 10-96 || 1 || a 1 || 4.353e-3 || 13.598433 || 10-111 || || || Carbon (atomic) || 1.67 || 10-96 || 12 || a 5 || 10.9e-3 || 11.26030 || 10-111 || || || Nitrogen (atomic) || 1.1 || 10-96 || 14 || a 40 || 7.1e-3 || 14.5341 || 10-111 || || || Oxygen (atomic) || 0.77 || 10-96 || 16 || a 2 || 5.02e-3 || 13.61805 || 10-111 || 63170 || || Fluorine (atomic) || 0.557 || 10-96 || 19 || a 1 || 3.64e-3 || 17.4228 || 10-111 || || || Chlorine (atomic) || 2.16 || 10-97 || 36 || a 6 || || 12.96763 || 10-111 || || || Aluminum || 8.22 || 10-97 || 27 || a 31 || || _5.985768 || 10-111 || || || Helium || 0.2050522 || 10-96 || 4 || a 3 || || 24.587387 || 10-111 || || || Neon || 0.39432 || 10-96 || 20 || a 6 || || 21.56454 || 10-111 || || || Argon || 1.6411 || 10-97 || 40 || a 13 || || 16.759610 || 10-111 || || || Krypton || 2.4844 || 10-97 || 84 || a 13 || || 13.99961 || 10-111 || || || Xenon || 4.044 || 10-98 || 131 || a 1 || || 12.12984 || 10-112 || || || Hydrogen H₂ || 0.842 || 10-105 || 2 || m 6 || || 15.42593 || 10-123 || 368 || || Nitrogen N₂ || 1.7403 || 10-106 || 28 || m 6 || || 15.5808 || 10-126 || 1069 || || Oxygen O₂ || 1.5689 || 10-107 || 32 || m 34 || || 12.0697 || 10-127 || 579 || || Fluorine F₂ || 1.38 || 10-104 || 38 || m 7 || || 15.697 || 10-122 || || || Chlorine Cl₂ || 4.61 || 10-101 || 71 || m 3 || || 11.480 || 10-118 || || || Hydroxyl HO || 1.50 || other || 17 || m 99 || || 13.0170 || 10-123 || 279 || || Nitric Oxide NO || 1.70 || 10-106 || 30 || m 2 || || _9.26438 || 10-126 || 422 || || Nitrous Oxide N₂O || 3.03 || 10-106 || 44 || m 8 || || 12.886 || 10-127 || 283/170 || || Water H₂O || 1.45 || 10-109 || 18 || m 2 || || 12.606 || 10-131 || 389/U? || || Carbon Monoxide CO || 1.95 || 10-101 || 28 || m 3 || || 14.010 || 10-117 || 691 || || Carbon Dioxide CO₂ || 2.911 || 10-101 || 44 || m 8 || || 13.773 || 10-117 || 711 || || Ammonia NH₃ || 2.22 || 10-99 || 17 || m 33 || || 10.070 || 10-115 || 967 || || Methane CH₄ || 2.593 || 10-105 || 16 || m 6 || || 12.61 || 10-125 || 870 || || Ethane !C₂H₆ || 4.47 || 10-103 || 30 || m 3 || || 11.56 || 10-121 || 3333 || || Propane !C₃H₈ || 6.37 || 10-107 || 44 || m 2 || || 10.95 || 10-128 || || || Butane !C₄H₁₀ || 8.20 || 10-100 || 58 || m 2 || || 10.53 || 10-117 || || || Pentane !C₅H₁₂ || 9.99 || 10-107 || 72 || m 2 || || 10.28 || 10-127 || || || Hexane !C₆H₁₄ || 11.9 || 10-104 || 86 || m 2 || || 10.13 || 10-123 || || || Heptane !C₇H₁₆ || 13.61 || 10-104 || 100 || m 2 || || _9.93 || 10-123 || || || Octane !C₈H₁₈ || 15.9 || 10-106 || 114 || m 2 || || _9.80 || 10-127 || || || Nonane !C₉H₂₀ || 17.36 || 10-106 || 128 || m 27 || || _9.71 || 10-127 || || || Decane !C₁₀H₂₂ || 19.10 || 10-102 || 142 || m 27 || || _9.65 || 10-119 || || || Benzene !C₆H₆ || 10.32 || 10-99 || 78 || m 33 || || _9.24378 || 10-116 || 239/A || || Methanol !CH₄O || 3.29 || 10-105 || 32 || m 2 || || 10.85 || 10-125 || 7107 || || Ethanol !C₂H₆O || 5.41 || 10-103 || 46 || m 2 || || 10.43 || 10-121 || || |
| Line 91: | Line 93: |
| == HITRAN == | |
| Line 92: | Line 95: |
| https://hitran.org/ : mostly infrared data, little optical and almost no UV, the large wavenumber, short wavelength spectrum where Rayleigh scattering, ionization, and photodissociation are significant. At very low densities, collisions will be far less common than photon interactions, so Beers-Lambert broadening probably won't be important. ------- === Photoionization === ||<-3> Oxygen [[ https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880014868.pdf | NASA ]] [[ attachment=19880014868.pdf | local ]] || || λ nm || eV || Cross Section || || 91 nm || 13.6 ||<)> 0.15e-22 m² || || 90 nm || 13.8 ||<)> 2.8e-22 m² || || 80 nm || 15.5 ||<)> 3.5e-22 m² || || 70 nm || 17.7 ||<)> 9.3e-22 m² || || 60 nm || 20.7 ||<)> 13.3e-22 m² || || 50 nm || 24.8 ||<)> 11.9e-22 m² || ------ |
Polarizability
... and first ionization energy
Speed of light c: 299792458 m/s |
Planck Constant h: 6.62607015e-34 J-s |
electronic charge q: 1.602176634e−19 colombs |
hc/q = 1239.8419 eV-nm |
Lyman alpha: n 2→1 . . 121.567 nm . . 82259.2 cm-1 . . 2.46607e15 Hz . . 10.1988 eV |
|
Converting polarizability from cgs to MKS
α(F-m²) = 4e-6 π ε₀ α(cm³) ... https://en.wikipedia.org/wiki/Polarizability#Definition
Computing MKS Cross Section
ω = 2 π c / λ
σ(m²) = ω⁴ α(F-m²)² /( 12 π ε₀² c⁴ )
- = ω⁴ 16e-12 π² ε₀² α(cm³)² / ( 12 π ε₀² c⁴ )
- = ω⁴ 4e-12 π α(cm³)² / ( 3 c⁴ )
- = 64e-12 π⁵ α(cm³)² / ( 3 λ⁴ )
- = 64e24 π⁵ α(cm³)² / ( 3 λ(nm)⁴ )
Define β = 64e24 π⁵ α(cm³)² / 3 = 6.52842e27 α(cm³)²
- β = 6.52842e-3 (nm⁶) (table value)²
- ??????????????
σ(nm²) = β / λ(nm)⁴
... ok, something's wrong, the numbers are WAY too small ... Maybe not, actually; the cross section for blue versus red in the atmosphere involves megatonnes of air TBD
From 100th CRC handbook
|
α(cgs!) |
Page |
Wt |
Ref |
β ??? |
1st eV |
Page |
HITRAN |
||
|
1e-24 cm³ |
|
|
|
nm⁶ |
|
|
nm/UV |
||
Hydrogen (atomic) |
0.666793 |
10-96 |
1 |
a 1 |
4.353e-3 |
13.598433 |
10-111 |
|
||
Carbon (atomic) |
1.67 |
10-96 |
12 |
a 5 |
10.9e-3 |
11.26030 |
10-111 |
|
||
Nitrogen (atomic) |
1.1 |
10-96 |
14 |
a 40 |
7.1e-3 |
14.5341 |
10-111 |
|
||
Oxygen (atomic) |
0.77 |
10-96 |
16 |
a 2 |
5.02e-3 |
13.61805 |
10-111 |
63170 |
||
Fluorine (atomic) |
0.557 |
10-96 |
19 |
a 1 |
3.64e-3 |
17.4228 |
10-111 |
|
||
Chlorine (atomic) |
2.16 |
10-97 |
36 |
a 6 |
|
12.96763 |
10-111 |
|
||
Aluminum |
8.22 |
10-97 |
27 |
a 31 |
|
_5.985768 |
10-111 |
|
||
Helium |
0.2050522 |
10-96 |
4 |
a 3 |
|
24.587387 |
10-111 |
|
||
Neon |
0.39432 |
10-96 |
20 |
a 6 |
|
21.56454 |
10-111 |
|
||
Argon |
1.6411 |
10-97 |
40 |
a 13 |
|
16.759610 |
10-111 |
|
||
Krypton |
2.4844 |
10-97 |
84 |
a 13 |
|
13.99961 |
10-111 |
|
||
Xenon |
4.044 |
10-98 |
131 |
a 1 |
|
12.12984 |
10-112 |
|
||
Hydrogen H₂ |
0.842 |
10-105 |
2 |
m 6 |
|
15.42593 |
10-123 |
368 |
||
Nitrogen N₂ |
1.7403 |
10-106 |
28 |
m 6 |
|
15.5808 |
10-126 |
1069 |
||
Oxygen O₂ |
1.5689 |
10-107 |
32 |
m 34 |
|
12.0697 |
10-127 |
579 |
||
Fluorine F₂ |
1.38 |
10-104 |
38 |
m 7 |
|
15.697 |
10-122 |
|
||
Chlorine Cl₂ |
4.61 |
10-101 |
71 |
m 3 |
|
11.480 |
10-118 |
|
||
Hydroxyl HO |
1.50 |
other |
17 |
m 99 |
|
13.0170 |
10-123 |
279 |
||
Nitric Oxide NO |
1.70 |
10-106 |
30 |
m 2 |
|
_9.26438 |
10-126 |
422 |
||
Nitrous Oxide N₂O |
3.03 |
10-106 |
44 |
m 8 |
|
12.886 |
10-127 |
283/170 |
||
Water H₂O |
1.45 |
10-109 |
18 |
m 2 |
|
12.606 |
10-131 |
389/U? |
||
Carbon Monoxide CO |
1.95 |
10-101 |
28 |
m 3 |
|
14.010 |
10-117 |
691 |
||
Carbon Dioxide CO₂ |
2.911 |
10-101 |
44 |
m 8 |
|
13.773 |
10-117 |
711 |
||
Ammonia NH₃ |
2.22 |
10-99 |
17 |
m 33 |
|
10.070 |
10-115 |
967 |
||
Methane CH₄ |
2.593 |
10-105 |
16 |
m 6 |
|
12.61 |
10-125 |
870 |
||
Ethane C₂H₆ |
4.47 |
10-103 |
30 |
m 3 |
|
11.56 |
10-121 |
3333 |
||
Propane C₃H₈ |
6.37 |
10-107 |
44 |
m 2 |
|
10.95 |
10-128 |
|
||
Butane C₄H₁₀ |
8.20 |
10-100 |
58 |
m 2 |
|
10.53 |
10-117 |
|
||
Pentane C₅H₁₂ |
9.99 |
10-107 |
72 |
m 2 |
|
10.28 |
10-127 |
|
||
Hexane C₆H₁₄ |
11.9 |
10-104 |
86 |
m 2 |
|
10.13 |
10-123 |
|
||
Heptane C₇H₁₆ |
13.61 |
10-104 |
100 |
m 2 |
|
_9.93 |
10-123 |
|
||
Octane C₈H₁₈ |
15.9 |
10-106 |
114 |
m 2 |
|
_9.80 |
10-127 |
|
||
Nonane C₉H₂₀ |
17.36 |
10-106 |
128 |
m 27 |
|
_9.71 |
10-127 |
|
||
Decane C₁₀H₂₂ |
19.10 |
10-102 |
142 |
m 27 |
|
_9.65 |
10-119 |
|
||
Benzene C₆H₆ |
10.32 |
10-99 |
78 |
m 33 |
|
_9.24378 |
10-116 |
239/A |
||
Methanol !CH₄O |
3.29 |
10-105 |
32 |
m 2 |
|
10.85 |
10-125 |
7107 |
||
Ethanol !C₂H₆O |
5.41 |
10-103 |
46 |
m 2 |
|
10.43 |
10-121 |
|
||
Ref |
|
a 1 |
|
a 2 |
|
a 3 |
JW Schmidt, RM Glavioso, EF May, MR Moldover - Phys. Rev. Lett. 98, 254504, 2007 |
a 5 |
|
a 6 |
|
a 13 |
|
a 31 |
|
a 40 |
BO Roos, R Lindh, PÅ Malmqvist, V Veryazov, PO Widmark - J. Phys. Chem. A 108, 2851, 2004 |
m 2 |
AA Marryott, F Buckley - U.S. National Bureau of Standard Circular No. 537, 1953 |
|
multiply molar polarization by 3/(4 pi Na) = 0.3964308e-30 m³ |
m 3 |
JO Hirshfelder, CF Curtis, RB Bird - Molecular Theory of Gases and Liquids, Wiley, 1954 p. 954 / PSU QC173.H54 |
m 6 |
|
m 7 |
TC Jao, NHF Beebe, WB Person, JR Sabin - Chem. Phys. Lett. 26, 474, 1974 |
m 8 |
|
m 27 |
KT No, KH Cho, MS Jhon, HA Scheraga - J. Am. Chem. Soc. 115, 2005, 1993 |
m 33 |
|
m 34 |
EF May, MR Moldover, JW Schmidt - Phys. Rev. A 78, 032522 (2008) |
m 99 |
HITRAN
https://hitran.org/ : mostly infrared data, little optical and almost no UV, the large wavenumber, short wavelength spectrum where Rayleigh scattering, ionization, and photodissociation are significant. At very low densities, collisions will be far less common than photon interactions, so Beers-Lambert broadening probably won't be important.
Photoionization
λ nm |
eV |
Cross Section |
91 nm |
13.6 |
0.15e-22 m² |
90 nm |
13.8 |
2.8e-22 m² |
80 nm |
15.5 |
3.5e-22 m² |
70 nm |
17.7 |
9.3e-22 m² |
60 nm |
20.7 |
13.3e-22 m² |
50 nm |
24.8 |
11.9e-22 m² |
Spectrum
color |
nm |
cm-1 |
THz |
eV |
Wein Temp |
|||||
lyman α |
121.567 |
82259.2 |
2466.07 |
10.1988 |
7626 K |
|||||
violet |
380 |
450 |
26300 |
22200 |
789 |
666 |
3.26 |
2.76 |
7630 |
6440 |
blue |
450 |
495 |
22200 |
20200 |
666 |
606 |
2.76 |
2.67 |
6440 |
5850 |
Sun peak |
502 |
19900 |
598 |
2.47 |
5776 K |
|||||
green |
495 |
570 |
20200 |
17500 |
606 |
526 |
2.67 |
2.18 |
5850 |
5080 |
yellow |
570 |
590 |
17500 |
16900 |
526 |
508 |
2.18 |
2.10 |
5080 |
4910 |
orange |
590 |
620 |
16900 |
16100 |
508 |
484 |
2.10 |
2.00 |
4910 |
4670 |
red |
620 |
750 |
16100 |
13300 |
484 |
400 |
2.00 |
1.65 |
4670 |
3860 |