Physical constants and conventions

1. Table of Fundamental Physical Constants

   This data is derived from the 1986 CODATA recommended values of the fundamental physical constants. It is not intended to be an authoritative source: typographical errors are possible and the data has been reformatted. You can find the more complete information from the NIST at hppt://physics.nist.gov/PhysRefData/codata86/codata86.html.


Constant

Symbol

Value

Units

1

Speed of light in vacuum

(c)

299792458

m s-1

2

Permeability of vacuum

(mu_0)

1.25663706143592e-06

NA-2

3

Permittivity of vacuum

(epsilon_0)

8.854187817e-12

F m-1

4

Newtonian constant of gravitation

(G)

6.67259e-11±8.5e-15

m3 kg-1s-2

5

Planck constat

(h)

6.6260755e-34± 4.0e-40

J s

6

Planck constant in eV

 

4.1356692e-15 ± 1.2e-21

eV s

7

h-bar

(h-bar)

1.05457266e-34 ± 6.3e-41

J s

8

h-bar in eV

 

6.582122e-16± 2.0e-22

eVs

9

Planck mass

(m_p)

2.17671e-08±1.4e-12

kg

10

Planck length

(l_p)

1.61605e-35±1.0e-39

m

11

Planck time

(t_p)

5.39056e-44 ±3.4e-48

s

12

Elementary charge

(e)

1.60217733e-19±4.9e-26

C

13

Magnetic flux quantum

(Phi_0)

2.067836461e-15±6.1e-22

Wb

14

Josephson frequency-voltage

quotient

 

483597670000000

±1.4e+0.8

V-1 s-1

15

Quantized Hall conductance

 

3.87404614e-0.5± 1.7e-12

Omega-1

16

Quantized Hall resistance

(R_H)

25812.8056±0.0012

Omega

17

Bohr magnetion

(mu_B)

9.2740154e-24±3.1e-30

J T-1

18

Bohr magneton in eV

 

5.78838263e-0.5±5.2e-12

e V T-1

19

Bohr magnetion in Hz

 

13996241800±4200

T-1 s-1

20

Bohr magnetion in wavenumbers

 

46.686437±1.4e-0.5

m-1T-1

21

Bohr magnetion in kelvins

 

0.6717099±5.7e-0.6

K T-1

22

Nuclear magneton

(mu_N)

5.0507866e-27±1.7e-33

J T-1

23

Nuclear magneton in eV

 

3.15245166e-0.8±2.8e-15

eV T -1

24

Nuclear magneton in Hz

 

76225591.4±2.3

T-1S-1

25

Nuclear magneton in wavenumbers

 

0.0254262281±7.7e-0.9

m-1 T-1

26

Nuclear magneton in kelvins

 

0.0003658246±3.1e-0.9

K T-1

27

Fine structure constant

(alpha)

0.00729735308 ± 3.3e-10

 

28

Inverse fine structure constant

 

137.0359895±6.1e-0.6

 

29

Rydberg constant

(Ry)

10973731.534 ± 0.013

m-1

30

Rydberg constant in Hz

 

3.2898419499e+15

±3.9e+0.6

s-1

31

Rydberg constant in joules

 

2.1798741e-18±1.3e-24

J

32

Rydberg constant in eV

 

13.6056981±4.0e-0.6

eV

33

Bohr radius

(a_0)

5.29177249e-11±2.4e-18

m

34

Hartree energy

(E_h)

4.3597482e-18±2.6e-24

J

35

Hartree energy in eV

 

27.2113961± 8.1e-0.6

eV

36

Quantum of circulation

 

0.000363694807±3.3e-11

m2  s-1

37

Electron mass

(m_e)

9.1093897e-31±5.4e -37

kg

38

Electron mass in u

 

0.000548579903±1.3e-11

u

39

Electron mass in eV

 

510999.06±0.15

eV

40

Electron-muon mass ration

 

0.00483633218±7.1e-10

 

41

Electron-proton mass ratio

 

0.000544617013 ±1.1e-11

 

42

Electron-deuteron mass ratio

 

0.00272443707±6e -12

 

43

Electron-alpha-particle mass ratio

 

0.000137093354±3e-12

 

44

Electron specific charge

 

-175881962000±-53000

C kg-1

45

Electron molar mass

 

5.48579903e-07±1.3e-14

kg mol-1

46

Electron Compton wavelength

(lambda

_C)

2.42631058e-12±2.2e-19

m

47

Electron Compton wavelength

over 2 pi

(lambda

-bar_C)

3.86159323e-13±3.5e-20

m

48

Electron classical radius

(r_e)

2.81794092e-15±3.8e-22

m

49

Electron Thomson cross section

(sigma

_e)

6.6524616 -29±1.8e -35

m2

50

Electron magnetic moment

 

9.2847701e-24±3.1e-30

J T-1

51

Electron magnetic moment

in Bohr magnetons

 

1.001159652193±1.0e-11

 

52

Electron magnetic moment

in umclear magnetons

 

1838.282 ±3.7-05

 

53

Electron magnetic moment anomaly

(a_e)

0.001159652193±1.0e-11

 

54

Electron g-factor

(g-e)

2.002319304386±2.0e-11

 

55

Electron-muon magnetic moment

ratio

 

206.766967 ±3.0e-05

 

56

Electron-proton magnetic moment

ratio

 

658.2106881±6.6e -06

 

57

Muon mass

 

1.8835327e-28±1.1e-34

kg

58

Muon mass in u

 

0.113428913±1.7e-08

u

59

Muon mass in eV

 

105658389±34

eV

60

Muon-electron mass ratio

 

206.768262±3.0e-05

 

61

Muon-molar mass

 

0.000113428913±1.7e-11

kg mol-1

62

Muon magnetic moment

 

4.4904514e-26±1.5e-32

J T-1

63

Muon magnetic moment

in Bohr magnetons

 

0.00484197097±7.1e-10

 

64

Muon magnetic moment

in nuclear magnetons

 

8.8905981±1.3e-06

 

65

Muon magnetic moment anomaly

(a_mu)

0.001165923±8.4e-09

 

66

Muon g-factor

(g_mu)

2.002331846±1.7e-08

 

67

Muon-proton magnetic moment

ratio

 

3.18334547±4.7e  -0.7

 

68

Proton mass

(m_p)

1.6726231e-27±1.0e-33

kg

69

Proton mass in u

 

1.00727647±1.2e- 08

u

70

Proton mass in eV

 

938272310±280

eV

71

Proton-electron mass ratio

 

1836.152701±3.7e-05

 

72

Proton-muon mass ratio

 

8.8802444±1.3e  -06

 

73

Proton specific charge

 

95788309±29

C kg-1

74

Proton molar mass

 

0.00100727647±1.2e-11

kg mol-1

75

Proton Compton wavelength

(lambda_C,p)

1.32141002e-15±1.2e-22

m

76

Proton magnetic moment

 

1.41060761e-26±4.7e-33

J T-1

77

Proton magnetic moment

in Bohr magnetons

 

0.001521032202±1.5e-11

 

78

Proton magnetic moment

in nuclear magnetions

 

2.792847386±6.3e-08

 

79

Diamagnetic shielding correction

for protons (H_2 O, spherical

sample, 298.15K)

(sigma_H2O)

2.56890e-05±1.5e  -08

 

80

Shielded proton moment

(H_2 O,spherical sample,298.15K)

(mu_p')

1.41057138e-26±4.7e-33

J T-1

81

Shielded proton moment

in Bohr magnetons

 

0.001520993129±1.7e-11

 

82

Shielded proton moment

in nuclear magnetions

 

2.792775642±6.4e-08

 

83

Proton gyromagnetic ratio

(gamma_p)

267522128±81

T-1s-1

84

 

(gamma_p)

42577469±13

T-1 s-1

85

Proton gyromagnetic ratio,

uncorrected(H_2 O, spherical

sample, 298.15K)

(gamma_p')

267515255±81

T-1 s-1

86

 

(gamma_p'/2pi)

42576375±13

T-1 s-1

87

Neutron mass

(m_n)

1.6749286e-27±1.0e-33

kg

88

Neutron mass in u

 

1.008664904±1.4e-08

u

89

Neutron mass in eV

 

939565630±280

eV

90

Neutron-electron mass ratio

 

1838.683662±4.0e -05

 

91

Neutron-proton mass ratio

 

1.001378404±9e -09

 

92

Neutron molar mass

 

0.001008664904±1.4e-11

kg mol-1

93

Neutron Compton wavelength

(lambda_C,n)

1.3195911e-15±1.2e-22

m

94

Neutron magnetic moment

 

9.6623707e-27±4.0e-33

J T-1

95

Neutron magnetic moment

in Bohr magnetios

 

0.00104187563±2.5e-10

 

96

Neutron magnetic moment

in nuclear magnetions

 

1.91304275±4.5e-07

 

97

Neutron-electron magnetic

moment ratio

 

0.00104066882±2.5e-10

 

98

Neutron-proton magnetic moment

ratio

 

0.68497934 ±1.6e-07

 

99

Deuteron mass

(m_d)

3.343586e-27±2.0e-33

kg

100

Deuteron mass in u

 

2.013553214±2.4e-08

u

101

Deuteron mass in eV

 

1875613390±570

eV

102

Deuteron-electron mass ratio

 

3670.483014±7.5e -05

 

103

Deuteron-proton mass ratio

 

1.999007496±6e-09

 

104

Deuteron molar mass

 

0.002013553214±2.4e-11

kg mol-1

105

Deuteron magnetic moment

(mu_d)

4.3307375e-27±1.5e-33

J T-1

106

Deuteron magnetic moment

in Bohr magnetons

 

0.0004669754479±9.1e-12

 

107

Deuteron magnetic moment

in nuclear magnetons

 

0.85743823±2.4e-08

 

108

Deuteron-electron magnetic

moment ratio

 

0.000466434546±9.1e-12

 

109

Deuteron-proton magnetic moment

ratio

 

0.3070122035±5.1e-09

 

110

Avagadro constant

(N_A)

6.0221367e+23±3.6e+17

mol-1

111

Atomic mass constant

(m_u)

1.6605402e-27±1.0e-33

kg

112

Atomic mass constant in eV

 

931494320±280

eV

113

Faraday constant

(F)

96485.309±0.029

C mol-1

114

Molar Planck constant

 

3.99031323e-10±3.6e -17

J s mol-1

115

 

(N_A hc)

0.11962658±1.1e-0.7

J m mol-1

116

Molar gas constant

(R)

8.31451±7.0e-05

J mol-1 K-1

117

Boltzmamm constant

(k)

1.380658-23±1.2e-28

J K-1

118

Boltzmamm constant in eV

 

8.617385e-05±7.3e-10

eV K-1

119

Boltzmann constant in Hz

 

20836740000 ±180000

K-1 s-1

120

Boltzmann constant in

wavenumbers

 

69.50387± 0.00059

m-1 K-1

121

Molar volume (ideal gas) , STP

(V_m)

0.0224141±1.9e-07

m3  mol-1

122

Loschmidt constant

(n_0)

2.686763e+25±2.3e+20

m-3

123

Stefan-Boltzmann constant

(sigma)

5.67051e-08±1.9e-12

W m-2 K-4

124

First radiation constant

(c_1)

3.7417749e-16±2.2e-22

W m2

125

Second radiation constant

(c_2)

0.01438769±1.2e-07

m K

126

Wien displacement law constant

(b)

0.002897756±2.4e-08

m K

127

Electron volt

(eV)

1.60217733e-19±4.9e-26

J

128

Atomic mass unit

(u)

1.6605402e-27±1.0e-33

kg

129

Standard atmosphere

(atm)

101325

pa

130

Standard acceleration of gravity

(g_n)

9.80665

m s-2

131

BIPM-maintained ohm,

Omega_69-B1 as of 1 Jan 85

(Omega-B185)

1-1.563e -6±5.0e-08

Omega

132

Drift rate of Omega_69-B1

(dOmega

_69-B1/dt)

-0.0566±-0.0015

MuOmega

/yr

133

BIPM-maintained volt 483 694

GHz(h/2e)

(V_76-B1)

1-7.59e-6±3.0e-07

V

134

BIPM maintained apere A_BIPM

(A_B185)

1-6.03e±3.0e-07

A

135

Cu x-unit:

(xu(CuKalpha1))

100207789e-13±7.0e -20

m

136

Mo x-unit:

(xu(MoKalpha1))

1.00209938e-13±4.5e-20

m

137

AA *:

(Aaangstrom

-star)

1.00001481e-10±9.2e-17

m

138

Lattice spacing of Si

(in vacuum, 295.65K)

(a)

5.4310196e-10±1.1e-16

m

139

Lattice spacing Si(220) plane

(d_220)

1.9201554e-10±4.0e-17

m

140

Molar volume of Si

(V_m(Si))

1.20588179e-05±8.9e-12

m3  mol-1

Table Version 1.0

 

 

2.Conversion of units

1   bohr                   =  0.529177249                                 angstrom

1   hartree                 =  27.2113961                             ev

                          =  219474.63068                            cm-1

=  627.50956                                 kcal

          1   electron mass    =5.4857990*10-4                                                        a.m.u.

                             =9.1093897*10-31                                                                       kg

          1  cal                            =4.184                                                   J (by definition)

          N_avogadro        =6.0221367*1023                                                      (per mol)

          1 Debye             =0.393456                                                     a.u.              

 

   

3.Atomic masses (including electrons ) of most abundant isotope in a.m.u.

        H                            1.007825

        D                            2.0140

        He                          4.0026

        C                             12

        N                         14.00307

        O                         15.99491

        F                          18.9984

        S                             31.97207

        Cl                            34.96885

 

 

4.Conversion of related units

                electric field

                                  1 au = 5.124*109  Vcm-1

           magnetic field

                                  1 au = 2.35*105   T

           time

                              1 au = 2.149*10-17 s

 

5.Values of some Fundamental Constants

Speed of light in vacuum

c

299792458 m s-1 (defined)

Permeability of vacuum

μ0

4π x10-7 = 1.2566371 x 10-6 N A-2 (defined)

Permittivity of vacuum

ε0

(μ0c2)-1 = 8.8541878 x 10-12 F m-1 (defined)b

Elementary charge

e

1.6021773 x 10-19 C

Planck constant

h

6.626076 x 10-34 J s

Avogadro constant

 N0

6.022137 x 1023 mol-1

Rest mass of electron

me

9.109390 x 10-31 kg

Rest mass of proton

mp

1.672623 x 10-27 kg

Atomic mass unit (amu)

mu

1.660540 x 10-27 kg

Faraday constant

F

96485.31 C mol-1

Bohr radius

a0

5.2917725 x 10-11 cm

Bohr magneton

ue ,μB

9.274015 x 10-24 J T-1

Nuclear magnetion

μN

5.050787 x 10-27 J T-1

Rydberg constant

10973731.53 m-1

Gas constant

R

8.31447 J K-1 mol-1

Boltzmann constatnt

k

1.38066 x 10-23 J K-1

Gravitational constant

G

6.6726 x 10-11 m3 kg-1 s-2

Standard gravity

g

9.80665 m s-2 (defined)

Triple point of water

Ttp

273.16K = 0.01ºCelsius (defined)

Normal atmosphere

po

101325 Pa (defined)

Standard volume

Vo

Vo (101325 Pa ≡ 1atm, 273.15K)  22.4141 L mol-1

(105Pa = 1bar, 273.15k)     

22.7111 L mol-1

     

 

6.Conversion of Units

 

Angstrom (Å)

1Å = 10-10 m = S0.1nm

Micron (μ)

1 μ = 1μm =10-6m

Inch (in.) ≡1/12 foot(ft)

1 inch = 2.54 x 10-2 m

Liter (L)

1 L ≡ 1 dm3 = 10-3 m3 (defined)

Pound (lb) ≡ 16 ounces (oz)

1 lb = 0.45359237kg

Dyne (dyn = g cm s-2)

1 dyn = 10-5 N

Erg (erg = g cm2 s-2)

1 erg = 10-7J

Thermochemical calorie (cal)

1 cal ≡ 4.184 J (defined)

Liter-atmosphere (L atm)

1 L atm ≡ 101.325J(defined)

Electron volt (eV)

1 eV= 1.60218 x 10-19J

     = 96.4853 kJ mol-1

Wavenumber (cm-1) energy

1 cm-1X hc = 1.986448 x 10-23 J

           = 11.9627 J mol-1

Bar (bar)

1 bar ≡ 105 Pa = 0.986924 atm (defined)

Torr (Torr)

1 Torr ≡ 1/760 atm ≈ 1/750.06 bar

Pounds per square inch (psi)

1 psi = 6.894757 X 103 Pa = 0.06895 bar

Poise(P)

1 P = 10-1 Pa s

Stokes(St)

1 St = 10-4 m2 s-1

Celsius temperature t(ºC)

t(ºC) ≡ T(K) - 273.15 (defined)

Rem ≈ roentgen (r)

1 rem ≈ 0.01 J kg-1

Emu of charge (emu)

1 emu = 10 C

Esu of charge (esu)c

1 esu = 10 C/|c| = 3.33564 X 10-10  C

Debye (D)

1D ≡ 10-18  esu cm = 3.33564 X 10-30  C m

Esu polarizability α ("cm3")

1 cm3  x 4πε0  =  1.11265 x 10-16  F  m2

Esu polarization P (esu  com -1)

4π  esu  cm-1  = 4.19169 x 10-7  C  m-1

Gauss (G)

1 G = 10-4   T

Oersted (Oe)

1 Oe  = 103  A m-1

Plane angle (deg = 60 min = 3600 sec)

1 deg = ( π / 180 ) rad

 

 

7. 

FRACTION

PREFIX

SYMBOL

MULTIPLE

PREFIX

SYMBOL

10-1

deci

d

10

deca

daa

10-1

centi

c

102

hecto

ha

10-1

milli

m

103

kilo

k

10-6

micro

μ

106

mega

M

10-9

nano

n

109

giga

G

10-12

pico

p

1012

tera

T

10-15

femto

f

1015

peta

pa

10-18

atto

a

1018

exa

Ea

aThese prefixed are rarely used.

   

8.The concentration units and symbols defined below are widely used in physical chemistry.

NAME

SYMBOL

DEFINTION

Weight percent

%

(Grams of solute per grams of solution) x 100

Moel fractiona

XA

Moles of A per total number of moles

Molarity

M

Moles of solute per liter of solutionb

Normality

N

Equivalents of solute per liter of solutionb

Formalityc

F

Formula weights of solute per liter of solutionb

Molatity

M

Moles of solute per kg of solvent

Weight formalityc

f

Formula weight of solute per kg of solvent

a The symbol YA is often used for the mole fraction of A in gas phased that is in equilibrium with a liquid solution.

b Note that 1 L=1 dm3,The SI concentration unit of mol m-3 is not very attractive for most work in chemistry, and non-SI concentrations based on the liter are widely used.

c These units are infrequently used but are of great convenience in expressing the overall composition of a solution when the solute is partially associated or dissociated

 

 

 

 

 

 

9.

PHYSICAL QUANTITY

NAME

SYMBOL

DEFINITION

Frequency f ( not ω = 2πf )

hertz

Hz

s-1

Force

newton

N

m kg s-2

Pressure, stress

pascal

Pa

N m-2 = m-1 kg s-2

Energy, work, heat

joule

J

N m = m2 kg s-2

Power, radiant flux

watt

W

J s-1 = m2 kg s-3

Electric change

coulomb

C

A s

Electric potential, electromtive force

volt

V

J C-1 = m2 kg s-3A-1

Electric resistance

ohm

Ω

V A-1 = m2 kg s-3 A-2

Electric capacitance

farad

F

C V-1 = m-2 kg-1 s4 A-2

Magnetic flux density

tesla

T

V s m-2 = kg s-2 A-1

Magnetic flux

weber

Wb

V s = m2 kg s-2 A-1

Inductance

henry

H

V A-1 s= m2 kg s-2 A-2

Luminous flux

lumen

lm

cd sr-1

Plane angle

radian

rad

 —

Solid angle

steradian

Sr

 —

 

 

 

10.

PHYSICAL QUANTITY

DEFINITION

Heart capacity, entropy

J K-1

Surface tension

N m-1

Heat flux density, irradiance

W m-2 = kg s-3

Thermal conductivity

W m-1 K-1= m kg s-3 K-1

Kinematic viscosity, diffusion coefficient

m2 s-1

Dynamic viscosity

N s m-2 = Pa s = m-1 kg s-1

Electric displacement, polarization

C m -2 = m-2 s A

Permittivity

F m-1 = m -3 kg-1 s 4 A 2

Permeability

H m-1  = m kg s-2 A-2

Electric field strength

V m-1  = m kg s -3 A-1

Magnetic field strength

A m-1

Luminance

cd m-2

Exposure( X - and  γ-rays)

C kg-1  = kg -1 s A

 

 

 

 

11.

PHYSICAL QUANTITY

NAME

SYMBOL

Length

meter

m

Mass

kilogram

kg

Time

second

s

Electric current

ampere

A

Thermodynamic temperature

kelvin

K

Amount of substance

mole

mol

Luminous intensity

candela

cd

 

 

 

12. Energy Conversion Table

 

K

cm-1

kJ mol-1

kcal mol-1

eV

1 K        =

1

0.69504

8.31451 x 10-3

1.98722 x 10-3

8.61739 x10-5

1 cm-1         =

1.43877

1

1.19627 x 10-2

2.85914 x 10-3

1.23984 x10-4

1 kJ mol-1   =

1.20272 x 102

8.35935 x 101

1

0.23901

1.03643 x10-2

1 kcal mol-1 =

5.03217 x 102

3.49755 x 102

4.18400

1

4.33641 x10-2

1 eV       =

1.16044 x 104

8.06554 x 103

9.64853 x 101

2.30605 x 101

1

a E. R. Cohen and B. N. Taylor, CODATA Bulletin 63, Pergamon Press , New York, (1986).

b F m -1 ≡ C2  m-1  J-1 ≡ C m-1 V-1

c Note that |c| is the pure number 29979245800(i.e., it equals the magnitude of the speed of

light in vacuum when it is expressed in cm  s-1 units).