Differences between revisions 25 and 52 (spanning 27 versions)

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	TM Miller, B Bederson - Adv. At. Mol. Phys. 13, 1, 1978
a 2	RA Alpher, DR White - Phys. Fluids 2, 153, 1959
a 3	JW Schmidt, RM Glavioso, EF May, MR Moldover - Phys. Rev. Lett. 98, 254504, 2007
a 5	C Thierfelder, B Assadollahzadeh, P Schwerdtfeger, S Schäfer, R Schäfer - Phys. Rev. A. 78, 052506, 2008
a 6	C Gaiser, B Fellmuth - Europhysics Letters 90, 63002, 2010
a 13	RH Orcutt, RH Cole - J. Chem. Phys. 46, 697, 1967
a 31	T Flieg - Phys. Rev. A 72, 052506, 2005
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 N_a) = 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	AC Newell, RC Baird - J. Appl. Phys. 36, 3751, 1965
m 7	TC Jao, NHF Beebe, WB Person, JR Sabin - Chem. Phys. Lett. 26, 474, 1974
m 8	TK Bose, RH Cole - J. Chem. Phys. 52, 140, 1970
m 27	KT No, KH Cho, MS Jhon, HA Scheraga - J. Am. Chem. Soc. 115, 2005, 1993
m 33	GLD Ritchie, EW Blanch - J. Phys. Chem. A 107, 2093, 2003
m 34	EF May, MR Moldover, JW Schmidt - Phys. Rev. A 78, 032522 (2008)
m 99	D.R.White - The Physics of Fluids 4, 40 (1961)

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.

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

-  ⇤ ← Revision 25 as of 2019-09-07 20:18:47 → 
  Size: 6234
  Editor: KeithLofstrom
  Comment:
+   ← Revision 52 as of 2019-09-17 18:09:01 → ⇥
  Size: 9475
  Editor: KeithLofstrom
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 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:
-Lyman alpha: n 2→1 , 121.6 nm, 82237 cm^^-1^^, 2.465e15 Hz, 10.196 eV
+α(F-m²) = 4e-6 π ε₀ α(cm³) ... https://en.wikipedia.org/wiki/Polarizability#Definition
-Line 5:
+Line 10:
+--------
=== Computing MKS Cross Section ===
-Line 6:
+Line 13:
------
+ω = 2 π c / λ
-Line 8:
+Line 15:
-From 100th CRC handbook
+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 10:
+Line 21:
-||                    || α 1e-30 m³ || Page   ||  Wt || Ref  ||<|99>|| 1st eV || Page   ||
|| Hydrogen (atomic)  || 0.666793   || 10-96  ||   1 || a 1  ||     13.598433 || 10-111 ||
|| Carbon (atomic)    || 1.67       || 10-96  ||  12 || a 5  ||     11.26030  || 10-111 ||
|| Nitrogen (atomic)  || 1.1        || 10-96  ||  14 || a 40 ||     14.5341   || 10-111 ||
|| Oxygen (atomic)    || 0.77       || 10-96  ||  16 || a 2  ||     13.61805  || 10-111 ||
|| Fluorine (atomic)  || 0.557      || 10-96  ||  19 || a 1  ||     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 ||
+Define β = 64e24 π⁵ α(cm³)² / 3 = 6.52842e27 α(cm³)²
 .     β = 6.52842e-3 (nm⁶) (table value)²
 . ??????????????
-Line 49:
+Line 25:
-|| Ref ||
+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   ||<-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 ||        ||

|| Ref  ||
-Line 68:
+Line 91:
+-------
== 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.

-------

=== 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 ||

Diff for "Polarizability"