## FUNDAMENTAL PHYSICAL CONSTANTS & USEFUL INFORMATION

UNITS

SI UNITS

 Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K

DERIVED SI UNITS

 Electric charge coulomb C = A s Electrical resistance ohm W= V/A = kg m2 A-2 s-3 Electrical conductance siemen S =1/W Electrical capacitance farad F = A s V-1 = A2 s4 kg-1 m-2 Electrical inductance henry H = V s A-1 = kg m2 s-1 A-2 Energy joule J = kg m2 s-2 = N m Force newton N = kg m s-2 Magnetic flux weber Wb = V s = kg m2 A-1 s-2 Magnetic flux density tesla T = Wb m-2 = V s m-2 = kg A-1 s-2 Pressure pascal Pa=N m-2 Power watt W=J s-1=kg m2 s-3 Electric potential difference volt V = N m C-1 = kg m2 s-3 A-1 Frequency hertz Hz = s-1

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#### GENERAL CONSTANTS

 Quantity Symbol SI System CGS System FPS System speed of light in vacuum c 2.99792458 x 108 m s-1 2.99792458 x 1010 cm s-1 9.83571056 x 108 ft s-1 angular velocity of earth on its axis 7.2921x10-5 rad s-1 mean angular velocity of earth in its orbit 1.9910x10-7 rad s-1 astronomical unit AU 1.49597870 x 1011 m 1.49597870 x 1013 cm 4.90806660 x 1011 ft light year ly 9.46053621 x 1015 m 9.46053621 x 1017 cm 3.10385045 x 1016 ft parsec pc 3.08567808 x 1016 m 3.08567808 x 1018 cm 1.01236157 x 1017 ft permeability of vacuum mo 4p x 10-7 N m-2 1 (dimensionless) 1.16745403 x 10-7 N ft-2 permittivity of vacuum eo 8.854187817 x 10-12 F m-1 1 (dimensionless) 2.698756447 x 10-12 F ft-1 gravitational constants G 6.67259 x 10-11 m3 kg-1 s-2 6.67259 x 10-12 cm3 g-1 s-2 1.068846 x 10-9 ft3 lb-1 s-2 standard gravity go 9.80665 m s-2 980.665 cm s-2 32.17404856 ft s-2 gravitational conversion factor gc 9.80665 m kg kgf-1 s-2 980.665 cm g gf-1 s-2 32.17404856 ft lb lbf-1 s-2 Planck constant h 6.6260755 x 10-34 J s 6.6260755 x 10-27 erg s 1.5723916 x 10-32 ft pdl s Planck mass mh 2.17671 x 10-8 kg 2.17671 x 10-5 g 4.79882 x 10-8 lb Planck constant (molar) Nah 3.99031323 x 10-10 J s mol-1 3.99031323 x 10-3 erg s mol-1 4.29513741 x 106 ft pdl s lb-mol-1 standard atmosphere atm 101325 Pa 1.01325 x 108 dyn cm-2 6.808726 x 104 pdl ft-2 permeability (dry air) mAIR 4p x 10-7 N m-2 1 (dimensionless) 1.16745403 x 10-7 N ft-2 permitivity (dry air or STP) eAIR 1.000590 F m-1 1.000590 x 10-2 F cm-1 0.304980 F ft-1 specific heat (dry air at constant P) CpAIR 1.00468 x 103 J (kg K)-1 1.00468 x 107 erg (g K)-1 6.00794 x 103 ft pdl (lb oR)-1 specific heat (dry air at constant V) CvAIR 7.17625 x 102 J (kg K)-1 7.17625 x 106 erg (g K)-1 4.29136 x 103 ft pdl (lb oR)-1 apparent molecular weigth (dry air) MwAIR 2.89644 x 10-2 kg mol-1 28.9644 g mol-1 28.9644 lb lb-mol-1 molecular gas constant (1 kg dry air) RAIR 287.05 J (kg K)-1 2.8705 x 106 erg (g K)-1 1.71654 x 103 ft pdl (lb oR) Avogadro constant NA 6.0221367 x 1023 mol-1 6.0221367 x 1023 mol-1 2.7315953 x 1026 lb-mol-1 atomic mass unit u 1.6605402 x 10-27 kg 1.6605402 x 10-24 g 3.6608649 x 10-27 lb electron volt eV 1.60217733 x 10-19 J 1.60217733 x 10-12 erg 3.80202455 x 10-18 ft pdl Faraday constant F 9.6485309 x 104 C mol-1 2.8925568 x 1014 cm3/2 g1/2 (s mol)-1 3.6609376 x 1013 ft3/2 lb1/2 (lb-mol s)-1 Boltzmann constant k 1.380658 x 10-23 J K-1 1.380658 x 10-16 erg K-1 1.820195 x 10-22 ft pdl oR-1 Ioschmidt constant no 2.686763 x 1025 m-3 2.686763 x 1019 cm-3 7.608066 x 1023 ft-3 Sackur-Tetrode constant So/R -1.164856 (at 101325 Pa) -1.151693 (at 106 dyn cm-2) -1.164856 (at 68087.26 pdl ft-2) Stefan-Boltzmann constant s 5.67051 x 10-8 W m-2 K-4 5.67051 x 10-3 erg cm-2 s-1 K-4 1.19088 x 10-8 pdl ft-1 s-1 oR-4 first radiation constant c1 3.7417749 x 10-16 W m2 3.7417749 x 10-3 erg cm2 s-1 9.5576708 x 10-14 ft3 pdl s-1 second radiation constant c2 0.01438769 m K 1.438769 cm K 8.4966673 x 10-2 ft oR Wien displacement law constant b 2.897756 x 10-3 m K 0.2897756 cm K 1.71127323 x 10-2 ft oR ideal gas molar volume at STP Vm 22.41410 L mol-1 22414.10 cm3 mol-1 359.0394 ft3 lb-mol-1 potential of electron at 1st Bohr orbit 27.211 V 27.211 V ionization potential from 1st Bohr orbit 13.606 V 13.606 V nuclear electric field at 1st Bohr orbit 5.1422 x 1011 V m-1 5.1422 x 1013 V cm-1 current in 1st Bohr orbit 3.5051 x 10-13 A dipole moment of nucleus and electron in 1st Bohr orbit 8.4784 x 10-30 C m 8.4784 x 10-28 C cm magnetic moment, atomic unit 2.542 x 10-21 J T-1 2.542 x 10-14 erg T-1 mass energy of unit atomic weight 1.4924 x 10-10 J 1.4924 x 10-3 erg proton-electron attraction at distance ao 8.2387 x 10-8 N frequency of 1st Bohr orbit 6.5797 x 1015 Hz frequency of free electron in magnetic field B (2.7992 x 1010 Hz T-1)B plasma frequency associated with electron density Ne (80.617 m3 Ne)1/2 Hz electron velocity in Bohr orbit 2.1877 x 106 m s-1 2.1877 x 108 cm s-1

c = 2.9979 x 108 m s-1 molar gas constant
e = 1.6021 x 10-19 C
me = 9.1091 x 10-31 kg
h = 6.62608 x 10-34 J s
h = h / 2p = 1.05459 x 10-31 J s
NA = 6.0221 x 1023 mol-1
k = 1.3807 x 10-23 J K-1
eo= 8.8542 x 10-12 F m-1
mo = 4p x 10-7 H m-1
Gas constant, R = NAk = 8.3144 J K-1 mol-1 = 1.987 cal K-1 mol-1
= 8.62 x 10-5 eV K-1 atom-1 = 0.083144 L bar K-1 mol-1
Rydberg constant, R*=1.0974 x 107 m-1 ; R =3.2880 x 1015 s-1
Bohr radius ao = 52.918 pm
Mass of proton = 1.67495 x 10-27 kg
Mass of hydrogen atom = 1.66 x 10-27 kg
Franck-Wiedemann-Lorenz coefficient = 2.32 x 10-8 W W K-2
Bohr Magneton = 9.2741 x 10-24 J T-1
Acceleration due to gravity (at 45° latitude), g =9.81 m s-2

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#### ATOMIC CONSTANTS

 Quantity Symbol SI System CGS System FPS System fine-structure constant a 7.29735308 x 10-3 (dimensionless) 7.29735308 x 10-3 (dimensionless) 4 x 10-30 7.29735308 x 10-3 (dimensionless) Rydberg constant R 1.0973731534 x 107 m-1 1.0973731534 x 105 cm-1 3.3447933716 x 106 ft-1 Bohr radius ao 5.29177249 x 10-11 m 5.29177249 x 10-9 cm 1.73614583 x 10-10 ft quantum of circulation h/2me 3.63694807 x 10-4 m2 s-1 3.63694807 cm2 s-1 3.91477832 x 10-3 ft2 s-1

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#### ELECTROMAGNETIC CONSTANTS

 Quantity Symbol SI System CGS System FPS System elementary charge e 1.60217733 x 10-19 C 4.80320680 x 10-10 cm3/2 g1/2 s-1 1.34021962 x 10-13 ft3/2 lb1/2 s-1 magnetic flux quantum fo 2.06783461 x 10-15 Wb 2.06783461 x 10-7 Mx 2.06783461 x 10-10 kilolines Josephson frequency-voltage quotient 2e/h 4.8359767 x 1014 Hz V-1 4.8359767 x 1022 s cm-3/2 g-1/2 1.7331634 x 1026 s ft-3/2 lb-1/2 quantized Hall conductance e2/h 3.87404614 x 10-5 S 3.87404614 x 10-14 s cm-1 1.18080926 x 10-12 s ft-1 quantized Hall resistance Rh 25812.8056  2.58128056 x 1013 cm s-1 8.46876824 x 1011 ft s-1 Bohr magneton µB 9.2740154 x 10-24 J T-1 9.2740154 x 10-21 erg Gs-1 2.3688754 x 10-29 ft3 pdl line-1 nuclear magneton µN 5.0507866 x 10-27 J T-1 5.0507866 x 10-24 erg Gs-1 1.2901299 x 10-32 ft3 pdl line-1

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#### ELECTRON, PROTON AND NEUTRON CONSTANT

 Quantity Symbol SI System CGS System FPS System electron mass me 9.1093897 x 10-31 kg 9.1093897 x 10-28 g 2.0082767 x 10-30 lb electron alpha-particle mass ratio me/ma 1.37093354 x 10-4 (dimensionless) 1.37093354 x 10-4 (dimensionless) 1.37093354 x 10-4 (dimensionless) electron specific charge -e/me -1.75881962 x 1011 C kg-1 -0.527280857 cm3/2 s-1 g-1/2 -6.67348104 x 10-2 ft3/2 s-1 lb-1/2 electron molar mass Me 5.48579903 x 10-7 kg mol-1 5.48579903 x 10-4 g mol-1 5.48579903 x 10-4 lb lb-mol-1 Compton wavelength lc 2.42631058 x 10-12 m 2.42631058 x 10-10 cm 7.96033655 x 10-12 ft classical electron radius re 2.81794092 x 10-15 m 2.81794092 x 10-13 cm 9.24521299 x 10-15 ft Thomson cross section se 6.6524616 x 10-29 m2 6.6524616 x 10-25 cm2 7.1606501 x 10-28 ft2 electron magnetic moment µe 9.2847701 x 10-24 J T-1 9.2847701 x 10-21 erg Gs-1 2.3716225 x 10-29 ft3 pdl line-1 proton mass mp 1.6726231 x 10-27 kg 1.6726231 x 10-24 g 3.6875027 x 10-27 lb proton specific charge e/mp 9.5788309 x 107 C kg-1 2.8716613 x 1014 cm3/2 s-1 g-1/2 3.6344913 x 1013 ft3/2 s-1 lb-1/2 proton molar mass MP 1.007276470 x 10-3 kg mol-1 1.007276470 g mol-1 1.007276470 lb lb-mol-1 proton Compton wavelength lc, p 1.32141002 x 10-15 m 1.32141002 x 10-13 cm 4.33533471 x 10-15 ft proton magnetic moment µP 1.41060761 x 10-26 J T-1 1.41060761 x 10-23 erg Gs-1 3.60313580 x 10-32 ft3 pdl line-1 neutron mass mn 1.6749286 x 10-27 kg 1.6749286 x 10-24 g 3.6925855 x 10-27 lb neutron molar mass Mn 1.008664904 x 10-3 kg mol-1 1.008664904 g mol-1 1.008664904 lb lb-mol-1 neutron compton wavelength lc, n 1.31959110 x 10-15 m 1.31959110 x 10-13 cm 4.32936713 x 10-15 ft neutron magnetic moment µn 9.6623707 x 10-27 J T-1 9.6623707 x 10-24 erg Gs-1 2.4680736 x 10-32 ft3 pdl line-1

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#### DEUTRON AND MUON CONSTANTS

 Quantity Symbol SI System CGS System FPS System deuteron mass md 3.3435860 x 10-27 kg 3.3435860 x 10-24 g 7.3713453 x 10-27 lb deuteron molar mass Md 2.013553214 x 10-3 kg mol-1 2.013553214 g mol-1 2.013553214 lb lb-mol-1 deuteron magnetic mass µn 4.3307375 x 10-27 J T-1 4.3307375 x 10-24 erg Gs-1 1.1062067 x 10-32 ft3 pdl line-1 muon mass mµ 1.8835327 x 10-28 kg 1.8835327 x 10-25 g 4.1524788 x 10-28 lb muon molar mass Mµ 1.13428913 x 10-4 kg mol-1 0.113428913 g mol-1 0.113428913 lb lb-mol-1 muon magnetic moment µµ 4.4904514 x 10-26 J T-1 4.4904514 x 10-23 erg Gs-1 1.1470026 x 10-31 ft3 pdl line-1 muon magnetic moment anomaly aµ 1.1659230 x 10-3 (dimensionless) 1.1659230 x 10-3 (dimensionless) 1.1659230 x 10-3 (dimensionless)

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#### THE erf(z) AND erfc(z) FUNCTIONS

Note: erfc(z) = 1 - erf(z)
Values calculated from Matlab (v. 4.1) for Macintosh

 z Erf(z) Erfc(z) z Erf(z) Erfc(z) 0 0.00000 1.000000 2.00 0.995 322 4.6777 x 10-3 0.01 0.00113 0.988 716 2.25 0.998 537 1.4627 x 10-3 0.05 0.0564 0.943 628 2.50 0.999 593 4.0695 x 10-4 0.10 0.1125 0.887 537 2.75 0.999 899 378 1.0062 x 10-4 0.25 0.2763 0.723 673 3.00 0.999 977 909 2.2090 x 10-5 0.50 0.5205 0.479 500 3.25 0.999 995 697 4.3027 x 10-6 0.75 0.7112 0.288 844 3.50 0.999 999 256 901 7.4309 x 10-7 1.00 0.84270 0.157 299 3.75 0.999 999 886 272 1.1372 x 10-7 1.25 0.92290 0.077 099 4.00 0.999 999 984 582 1.5417 x 10-8 1.50 0.96610 0.033 894 4.25 0.999 999 998 149 1.8505 x 10-9 1.75 0.98667 0.013 328 4.50 0.999 999 999 803 1.9661 x 10-10