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 )

Define β = 64e24 π⁵ α(cm³)² / 3 = 6.52842e27 α(cm³)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

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

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 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

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)


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 2019-09-10 04:16:48 by KeithLofstrom)