# 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 a 5 a 6 a 13 a 31 a 40 m 2 multiply molar polarization by 3/(4 pi Na) = 0.3964308e-30 m³ m 3 m 6 m 7 m 8 m 27 m 33 m 34 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

 Oxygen NASA 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

### 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

Polarizability (last edited 2019-09-17 22:20:59 by KeithLofstrom)