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Size: 3439
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Size: 8700
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 2: | Line 2: |
| === ... 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 ||<-2> Lyman alpha: n 2→1 . . 121.567 nm . . 82259.2 cm^^-1^^ . . 2.46607e15 Hz . . 10.1988 eV || ------ === Converting polarizability from cgs to MKS === |
|
| Line 3: | Line 8: |
| From 100th CRC handbook | α(F-m²) = 4e-6 π ε₀ α(cm³) ... https://en.wikipedia.org/wiki/Polarizability#Definition |
| Line 5: | Line 10: |
| || || α 1e-30 m³ || Page || Wt || Ref || || Hydrogen (atomic) || 0.666793 || 10-96 || 1 || 1 || || Carbon (atomic) || 1.67 || 10-96 || 12 || 5 || || Nitrogen (atomic) || 1.1 || 10-96 || 14 || 40 || || Oxygen (atomic) || 0.77 || 10-96 || 16 || 2 || || Fluorine (atomic) || 0.557 || 10-96 || xx || 1 || || Chlorine (atomic) || 2.16 || 10-97 || xx || 6 || || Aluminum || 8.22 || 10-97 || xx || 33 || || Helium || 0.2050522 || 10-96 || 4 || 3 || || Neon || 0.39432 || 10-96 || xx || 6 || || Argon || 1.6411 || 10-97 || xx || 13 || || Krypton || 2.4844 || 10-97 || xx || 13 || || Xenon || 4.044 || 10-98 || xxx || 1 || || Hydrogen H₂ || 0.842 || 10-105 || 2 || 6 || || Nitrogen N₂ || 1.7403 || 10-106 || 28 || 6 || || Oxygen O₂ || 1.5689 || 10-107 || 32 || 34 || || Fluorine F₂ || 1.38 || 10-104 || xxx || 7 || || Chlorine Cl₂ || 4.61 || 10-101 || xxx || 3 || || Hydroxyl HO || || Nitric Oxide NO || 1.70 || 10-106 || 30 || 2 || || Nitrous Oxide N₂O || 3.03 || 10-106 || 44 || 8 || || Water H₂O || 1.45 || 10-109 || 18 || 2 || || Carbon Monoxide CO || 1.95 || 10-101 || 28 || 3 || || Carbon Dioxide CO₂ || 2.911 || 10-101 || 44 || 8 || || Ammonia NH₃ || 2.22 || 10-99 || 17 || 33 || || Methane CH₄ || 2.593 || 10-105 || 16 || 6 || || Ethane C₂H₆ || 4.47 || 10-103 || 30 || 3 || || Propane C₃H₈ || 6.37 || 10-107 || 44 || 2 || || Butane C₄H₁₀ || 8.20 || 10-100 || 58 || 2 || || Pentane C₅H₁₂ || 9.99 || 10-107 || 72 || 2 || || Hexane C₆H₁₄ || 11.9 || 10-104 || 86 || 2 || || Heptane C₇H₁₆ || 13.61 || 10-104 || 100 || 2 || || Octane C₈H₁₈ || 15.9 || 10-106 || 114 || 2 || || Nonane C₉H₂₀ || 17.36 || 10-106 || 128 || 27 || || Decane C₁₀H₂₂ || 19.10 || 10-102 || 142 || 23 || || Benzene C₆H₆ || 10.32 || 10-99 || 78 || 33 || || Methanol CH₄O || 3.29 || 10-105 || 32 || 2 || || Ethanol C₂H₆O || 5.41 || 10-103 || 46 || 2 || |
-------- === Computing MKS Cross Section === |
| Line 44: | Line 13: |
| || Ref || || 1 || [[ | T.M.Miller & B.Bederson, Adv. At Mol. Phys. 13, 1, 1977 ]] || || 2 || [[ | R.A.Alpher & D.R.White, Phys. Fluids 2, 153, 1959 ]] || || 3 || [[ | J.W.Schmidt, R.M.Glavioso, E.F.May & M.R.Moldover, Phys. Rev. Let. 98, 254504, 2007 ]] || || 5 || [[ | C.Thierfelder, B.Assadollahzadeh, P.Schwerdtfeger, S.Schäfer, R.Schäfer, Phys. Rev. A. 78, 052506, 2008 ]] || || 6 || [[ | C.Gaiser, B.Fellmuth, Eur. Phys. Lett. 90, 63002, 2010 ]] || || 7 || [[ | || 8 || [[ | || 13 || [[ | || 23 || [[ | || 27 || [[ | || 33 || [[ | || 34 || [[ | || 40 || [[ | |
ω = 2 π c / λ |
| Line 59: | Line 15: |
| 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 ) |
|
| Line 60: | Line 21: |
| Define β = 64e24 π⁵ α(cm³)² / 3 = 6.52842e27 α(cm³)² . β = 6.52842e-3 (nm⁶) (table value)² . ?????????????? |
|
| Line 61: | Line 25: |
| 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 ??? ||<|99>|| 1st eV || Page || || || 1e-24 cm³ || || || || nm⁶ || || || || 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 || || 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 || || 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 || || Ref || || a 1 || [[ https://doi.org/10.1016/S0065-2199(08)60054-8| TM Miller, B Bederson - Adv. At. Mol. Phys. 13, 1, 1978 ]] || || a 2 || [[ https://doi.org/10.1063/1.1705906 | RA Alpher, DR White - Phys. Fluids 2, 153, 1959 ]] || || a 3 || [[ https://doi.org/10.1103/PhysRevLett.98.254504 | JW Schmidt, RM Glavioso, EF May, MR Moldover - Phys. Rev. Lett. 98, 254504, 2007 ]] || || a 5 || [[ attachment:Relativistic_and_Electron_Correlation_Ef.pdf | C Thierfelder, B Assadollahzadeh, P Schwerdtfeger, S Schäfer, R Schäfer - Phys. Rev. A. 78, 052506, 2008 ]] || || a 6 || [[ https://doi.org/10.1209/0295-5075/90/63002 | C Gaiser, B Fellmuth - Europhysics Letters 90, 63002, 2010 ]] || || a 13 || [[ https://doi.org/10.1063/1.1840728 | RH Orcutt, RH Cole - J. Chem. Phys. 46, 697, 1967 ]] || || a 31 || [[ https://doi.org/10.1103/PhysRevA.72.052506 | T Flieg - Phys. Rev. A 72, 052506, 2005 ]] || || a 40 || [[ https://doi.org/10.1021/jp031064+ | BO Roos, R Lindh, PÅ Malmqvist, V Veryazov, PO Widmark - J. Phys. Chem. A 108, 2851, 2004 ]] || || m 2 || [[ https://archive.org/details/circularofbureau537mary | AA Marryott, F Buckley - U.S. National Bureau of Standard Circular No. 537, 1953 ]] || || || multiply molar polarization by 3/(4 pi N,,a,,) = 0.3964308e-30 m³ || || m 3 || [[ https://archive.org/details/moleculartheoryo0000hirs | JO Hirshfelder, CF Curtis, RB Bird - Molecular Theory of Gases and Liquids, Wiley, 1954 p. 954 ]] / PSU QC173.H54 || || m 6 || [[ https://doi.org/10.1063/1.1713942 | AC Newell, RC Baird - J. Appl. Phys. 36, 3751, 1965 ]] || || m 7 || [[ https://doi.org/10.1016/0009-2614(74)80394-5 | TC Jao, NHF Beebe, WB Person, JR Sabin - Chem. Phys. Lett. 26, 474, 1974 ]] || || m 8 || [[ https://doi.org/10.1063/1.1672658 | TK Bose, RH Cole - J. Chem. Phys. 52, 140, 1970 ]] || || m 27 || [[ https://doi.org/10.1021/ja00058a056 | KT No, KH Cho, MS Jhon, HA Scheraga - J. Am. Chem. Soc. 115, 2005, 1993 ]] || || m 33 || [[ https://doi.org/10.1021/jp0223152 | GLD Ritchie, EW Blanch - J. Phys. Chem. A 107, 2093, 2003 ]] || || m 34 || [[ https://doi.org/10.1103/PhysRevA.78.032522 | EF May, MR Moldover, JW Schmidt - Phys. Rev. A 78, 032522 (2008) ]] || || m 99 || [[ https://doi.org/10.1063/1.1706187 | D.R.White - The Physics of Fluids 4, 40 (1961) ]] || ------- === Spectrum === || color ||<-2:> nm ||<-2:> cm^-1^ ||<-2:> THz ||<-2:> eV ||<-2:>Wein Temp|| || lyman α ||<-2:>121.567 ||<-2:> 82259.2 ||<-2:>2466.07||<-2:> 10.1988 ||<-2:> 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||<-2:> 502 ||<-2:> 19900 ||<-2:> 598 ||<-2:> 2.47 ||<-2:> 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 || |
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 |
|
|
1e-24 cm³ |
|
|
|
nm⁶ |
|
|
|
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 |
|
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 |
|
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 |
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 |
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 |