Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

3-6

REFERENCE

DATA

FOR

ENGINEERS

and steradian, are given to the number

1

in

these two

cases

to

aid understanding, e.g., to indicate that a par-

ticular plane angle is expressed on the basis of arc

length divided by radius rather than on the basis

of

a

full circle divided into

360

degrees.

Decibels

and

Nepers

The decibel, symbol dB, represents the ratio of two

values of power. The number

n

of

decibels is

10

times

the logarithm to the base

10

of

the power ratio:

n(dB)

=

10

log,,

(P2/P1)

Where the power ratio is less than

unity,

it is

usual

to invert

the fi-action and express the answer as a loss

in

decibels.

In the electrical case of voltage

V,

current

I,

and

impedance Z (when

2

is a pure resistance):

P2/P1

=

(VZ/V,l2(Zl/Z2)

=

(12/~1)2(z2/z11

Thus,

n,(dB)

=

20

log,, (V2/V1)

+

10

loglo (Z1/Z2)

and

n,(dB)

=

20

log,,

(12/11)

+

10

log,, (Z2/Z1)

Only

in

the special case

of

matched impedances (Z2

=

2,)

does

Greek Alphabet

The neper, symbol Np, is a dimensionless unit for

expressing the ratio

of

two values

of

amplitude. The

number

n

of neper is the natural logarithm of the

amplitude ratio:

n(Np)

=

In

(A2/A1)

To convert decibels to nepers, multiply by

0.1 151.

Numerical Values

To

facilitate the reading

of

numbers, the digits may

be separated into groups of three, counting from the

decimal sign toward

the

left and the right. The groups

should be separated by a small space, but not by a

comma or a point.

In

numbers of four digits, the space

is

usually not necessary. For example:

2.141 596 73 772 7372 0.133 47

T

=

3.141 592 653 589

e

=

2.718 281

828

459

American-English documents use a period for the

decimal sign. British-English documents use a raised

dot

(.).

For all other languages, the recommended deci-

mal sign

is

a comma.

If the magnitude of a number is less than unity, the

decimal sign should be preceded by a zero.

The sign

of

multiplication

of

numbers is a cross

(x)

or a raised dot

(.).

Name

Capital Small Commonly Used to Designate

Alpha

Beta

Gamma

Delta

Epsilon

Zeta

Eta

Theta

Iota

Kappa

Lambda

Mu

Nu

Xi

Omicron

Pi

Rho

Sigma

Tau

Upsilon

Phi

Chi

Psi

A

B

r

A

E

Z

H

0

I

K

A

M

N

0

n

P

z

T

Y

cp

X

w

-

c

angles, coefficients, attenuation constant, absorption factor, area

angles, coefficients, phase constant

complex propagation constant (cap), relative density, angles, electrical conductivity,

increment or decrement (cap or small), determinant (cap), density, angles

permittivity, electric intensity

coordinates, coefficients

intrinsic impedance, efficiency, surface charge density, hysteresis, coordinates

angular phase displacement, time constant, reluctance, angles

unit vector

susceptibility, coupling coefficient, thermal conductivity

permeance (cap), wavelength, attenuation constant

permeability, amplification factor, prefix micro

reluctivity, frequency

coordinates

propagation constant

3.1416

(see more precise value in text)

resistivity, volume charge density, coordinates

summation (cap), surface charge density, complex propagation constant, electrical

conductivity, leakage coefficient, deviation

time constant, volume resistivity, time-phase displacement, transmission factor, density

scalar potential (cap), magnetic flux, angles

electrical susceptibility, angles

dielectric flux, phase difference, coordinates, angles

Omega

n

w

resistance in ohms (cap), solid angle (cap), angular velocity

Note: Small letter is used except where capital (cap) is indicated.

UNITS, CONSTANTS, AND CONVERSION FACTORS

3-7

The 1998 values replace the 1986 set. A detailed

description

of

the data and their analysis that led

to

the 1998 values is published

in

the

Journal

ofPhysi-

cal and Chemical Reference Data,

Vol.

28,

No.

6,

1999 and in the

Reviews of Modern Physics,

Vol.

72,

No.

2,2000.

That paper was prepared under the aus-

pices

of

the CODATA Task Group

on

Fundamental

Constants.

FUNDAMENTAL PHYSICAL

CONSTANTS

The

following

values

of

the fundamental physical

constants are recomended by the international

Cum-

mittee

on

Data for Science and Technology

(CODATA).

They are called “1998 CoDATA RecommendedValues.”

They are available

on

the World Wide Web at

the

URL:

http://www.physics.nist.gov/cuu/Constants/index.html.

Fundamental Physical Constants

-

Complete Listing

Quantity

speed

of

light in vacuum

magnetic constant

electric constant

1/poc2

characteristic impedance

of

vacuum

Ji&

=

poc

Newtonian constant

of

gravitation

Planck constant

ineVs

h/2n

Planck mass (h.c/G)’/’

Planck

length

h./mpc

=

(h.G/c3)’/’

Planck time

lplc

=

(tiG/~~)‘/~

elementary charge

magnetic flux quantum

h/2e

conductance quantum

2e2/h

Josephson constanta

2e/

h

van

Klitzing

constantb

inverse

of

conductance quantum

h/e2

=

fioc/2ci

Bohr

magneton

eh./2m,

in

eV

T-’

nuclear magneton

eh./2mp

in

eV

T-‘

fine-structure constant

e2/4nqhc

inverse fine-structure constant

-

Relative std.

Symbol Value Unit uncert.

u,

UNIVERSAL

C,

cg 299 792458

m

s-’

(exact)

lI0

4n 10-7

N A-’

=

12.566370614

...

x

loM7

NA-’

(exact)

EO

8.854187 817

...

x

lo-’’

F

rn-l

(exact)

zo

376.730313 461

...

c2

(exact)

6.673(10)

x

lo-”

m3 kg-’

s-~

1.5 10-~

G

Glkc 6.707(101

x

(GeV/c2)-’

1.5

x

h 6.62606876(52)

x

J

s

h.

1.054571 S96(82)

x

J

s

4.13566727(16)

x

eVs

6.582 118 89(26)

x

eV

s

mp

2.1767(16)

x

kg

IP

1.6160(12)

x

m

tP

5.3906(40)

x

S

ELECTROMAGNETIC

1.602 176462(63)

x

lo-’’

2.417 989 491(95)

x

2.067 833 636(81)

x

7.748 091 696(28)

x

lop5

12 906.403 786(47)

483597.898(19)

x

lo9

25 812.807572(95)

927.400899(37)

x

5.788 381 749(43)

x

13.99624624(56)

x

lo9

46.686 4521

(19)

0.671 7131(12)

5.050783 17(20)

x

lo-’’

3.152451238(24)

x

lo-’

7.622593 96(31)

2.542623 66(10)

x

lo-’

3.6582638(64)

x

ATOMIC AND NUCLEAR

General

ci

7.297 352533(27)

x

E-’

137.035 999 76(SO)

C

A

J-I

wb

S

c2

Hz

V-‘

c2

J

T-I

eV

T-’

Hz

T-’

K

T-l

,-l

T-1

J

T-’

eV

T-‘

MHz

T-’

,-I

T-1

K

T-I

7.8

x

7.8

x

3.9

x

10-8

3.9

x

10-8

7.5 10-4

7.5 10-~

7.5

10-4

3.9

x

10-8

3.9

x

10-8

3.9

x

10-8

3.7 10-~

3.7

x

10-~

3.9

x

10-8

3.7

x

10-~

7.3

4.0

x

4.0

x

lo-*

4.0

x

lo-’

1.7

x

4.0

x

4.0

x

10@

4.0

x

lo-’

1.7

x

7.6 10-9

3.7 10-~

3.7

10-~

3-8

REFERENCE

DATA

FOR ENGINEERS

Fundamental Physical Constants

-

Complete Listing

Relative std.

Quantity Symbol Value Unit uncert.

ur

Rydherg constant

ci2mec/2h

R,hc

in

eV

Bohrradius

ci/4nRx.

=

4Xeoh-'/m&2

Hartree

energy

e2/4n.zoao

=

2R,hc

=

ci2m,c2

in

eV

quantum of circulation

Fermi coupling constant'

weak mixing angled

Ow

(on-shell scheme)

sin2

=

s$

1

-

(mw/mz)'

electron mass

in

u,

me

=

Ar(e)

u

(electron

relative atomic mass times

u)

energy equivalent

in

MeV

electron-muon mass ratio

electron-tau mass ratio

electron-proton mass ratio

electron-neutron mass ratio

electron-deuteron mass ratio

electron to alpha particle mass ratio

electron charge

to

mass quotient

electron

molar

mass

NAme

Compton wavelength

h/m,c

hc/2rr

=

aao

=

ci2/4nR,

classical electron radius

a'ao

Thomson cross section

(8n/3)r:

electron magnetic moment

to Bohr magneton ratio

to

nuclear magneton ratio

electron magnetic moment

electron g-factor

-2(1

+

a,)

electron-muon

anomaly

IPeI/PB

-

1

magnetic moment ratio

R,

10973731.568549(83)

R,

c

R,hc

3.289 841 960368(25)

x

2.179 871 90(17)

x

IO-''

13.605 691 72(53)

ao 0.529 1772083(19)

x

lo-''

Eh

4.35974381(34)

x

lo-''

h/2m, 3.636947516(27)

x

h/me 7.273 895 032(53)

x

27.211 3834(11)

Electroweak

G~/(fic)~

1.16639(1)

x

sin'

&I

0.2224(19)

Electron, e-

me

9.109381 88(72)

x

5.485799 llO(12)

x

0.510998 902(21)

mec2

8.187 10414(64)

x

rn,/m,

4.836 332 lO(15)

x

me/m,

2.875 55(47)

x

m,/mp

5.446 170232(12)

x

10W4

me/mn 5.438 673 462(12)

x

rne/m,

1.3709335611(29)

x

-elm,

-1.758 820 174(71)

x

10"

M(e),

Me

5.485799 llO(12)

x

hC 2.426310215(18)

x

IO-''

XC

386.1592642(28)

x

re

2.817940285(31)

x

ne

Pe

-928.476362(37)

x

me/md

2.724437 1170(58)

X

0.665 245 854(15)

x

lo-''

pe//LB

-1.001 1596521869(41)

pLB/p~

-1

838.281 9660(39)

ae

1.159652 1869(41)

x

ge

-2.0023193043737(82)

m-'

HZ

J

eV

m

J

eV

m2

s-'

m2

s-'

GeV2

kg

U

J

MeV

C kg-'

7.6

x

lo-''

7.6

x

IO-''

7.8

x

IO@

3.9

x

10-8

3.7 10-~

7.8

x

lo-'

3.9

x

10-8

7.3

lop9

7.3

10-~

8.6

x

8.7 10-~

7.9

x

10-8

2.1 10-~

7.9

x

10-8

4.0

x

lo-'

3.0

x

lo-'

1.6 10-~

2.1 10-9

2.2

lop9

2.1 10-~

2.1

10-9

4.0

x

lo-'

kgmol-*

2.1

x

m

7.3 10-~

m

7.3

10-~

m

1.1

x

10-8

m2

2.2

x

10-8

JT-I

4.0

io-'

2.1

10-~

3.5 10-~

4.1

x

lo-''

4.1

x

pe/p,

206.766 9720(63)

3.0

x

lop8

UNITS, CONSTANTS, AND CONVERSION FACTORS

3-9

Fundamental Physical Constants

-

Complete Listing

Relative std.

Quantity Symbol Value Unit uncert.

ur

electron-proton

electron to shielded proton

magnetic moment ratio

pe/pp

-

658.2106875(66)

magnetic moment ratio

Pe/P;

-

658.227 5954(71)

(H20,

sphere,

25

"C)

electron-neutron

electron-deuteron

electron to shielded helione

magnetic moment ratio

pe/p,,

960.92050(23)

magnetic moment ratio

pe//Ld

-2 143.923 498(23)

magnetic moment ratio

pe/pLi,

864.058255(10)

(gas, sphere,

25

"C)

electron gyromagnetic ratio

2[p,

]/k

ye

ye/2n 28 024.9540(11)

Muon,

p-

1.760 859 794(71)

x

10"

muon mass

m,

1.883531 09(16)

x

0.113 428 9168(34)

in

u,

m,

=

A&)

u

(muon

relative atomic mass times

u)

energy equivalent

m,c2

1.69283332(14)

x

lo-"

in MeV

105.658 3568(52)

muon-electron mass ratio

m,/me

206.768 2657(63)

muon-tau mass ratio

m,/m,

5.94572(97)

x

muon-proton mass ratio

m,/mp

0.1126095173(34)

muon-neutron mass ratio

mp/mn

0.1124545079(34)

muon molar mass

NAm,

M(p).

M,

0.1134289168(34)

x

lop3

muon Compton wavelength

h/m,c

hc,,

muon magnetic moment

PLP

hc,,/2n

k.

I*

to Bohr magneton ratio

h/PB

to nuclear magneton ratio

P.l*/PN

muon magnetic moment anomaly

IPLPl/(eR/2m,)

-

1

a,

muon

g-factor

-2(1

+

aLP)

magnetic moment ratio

PWIPP

gLP

muon-proton

tau massf

m,

in

u,

m,

=

A,(r)

u

(tau

relative atomic mass times

u)

energy equivalent

m,c2

in MeV

11.734441 97(35)

x

lo-"

1.867594444(55)

x

lo@

-4.490448 13(22)

x

-4.841 97085(15)

x

lo-'

-8.890 597 70(27)

1.16591602(64)

x

-2.002331 8320(13)

-3.183 34539(10)

Tau,

t-

3.167 88(52)

x

1.90774(31)

2.847 15(46)

x

10-l'

1777.05(29)

1.0

x

10-8

1.1

x

10-8

2.4 10-~

1.1

x

10-8

1.2

x

10-8

s-l

T-1

4.0

x

lo-'

MHZ

T-'

4.0

x

kg

8.4

x

lo-'

U

3.0

x

lop8

MeV

4.9

x

10-8

J

8.4

x

3.0

x

lo-'

3.0

x

lo-'

3.0

x

lo-'

kg mol-'

3.0

x

10@

m

2.9

x

lo-'

m

2.9

x

1.6

10-~

JT-1

4.9

x

3.0

x

lo-'

3.0

x

5.5

10-~

6.4

x

10-l'

3.2

x

lo-'

kg

1.6 10-~

U

1.6

10-~

J

1.6

MeV

1.6 10-~

3-1

0

Fundamental Physical Constants

-

Complete Listing

Relative std.

Quantity Symbol Value Unit uncert.

ur

tau-electron mass ratio

tau-muon mass ratio

tau-proton

mass

ratio

tau-neutron mass ratio

tau molar mass

NAm,

tau Compton wavelength

h/m,c

k.,/2n

proton mass

in

u,

mp

=

A,@)

u

(proton

relative atomic mass times

u)

energy equivalent

in

MeV

proton-electron mass ratio

proton-muon mass ratio

proton-tau mass ratio

proton-neutron mass ratio

proton charge to mass quotient

proton molar mass

NAmp

proton Compton wavelength

h/mpc

proton magnetic moment

Ac.p/2n

to

Bohr

magneton ratio

to nuclear magneton ratio

proton g-factor

2pp//.LN

proton-neutron

shielded proton magnetic moment

magnetic moment ratio

(H20,

sphere,

2.5

"C)

to Bohr magneton ratio

to

nuclear magneton ratio

proton magnetic shielding

correction

1

-

pk/pp

(H20,

sphere,

25

"C)

proton gyromagnetic ratio

2w.,/h

shielded proton gyromagnetic

ratio

24/h

(H20,

sphere,

2.5

"C)

3 477.60(57)

16.8188(27)

1.89396(31)

1.891 35(31)

1.90774(31)

x

low3

0.69770(11)

x

0.111042(18)

x

Proton,

p

1.672621 58(13)

x

1.007 276466 88(13)

1.50327731(12)

x

lo-''

938.271 998(38)

1836.1526675(39)

8.880

24408(27)

0.527 994(86)

0.998 62347855(58)

9.578 83408(38)

x

lo7

1.00727646688(13)

x

1.321 409 847(10)

x

0.210308 9089(16)

x

1.410 606 633(58)

x

1.521 032203(15)

x

2.792 847 337(29)

5.585

694675(57)

-1.459 898 OS(34)

1.410 570 399(59)

x

1.520993 132(16)

x

2.792775 597(31)

25.687(15)

x

2.67522212(11)

x

lo8

42.577 4825(18)

2.675 15341(11)

x

lo8

42.576 3888(18)

Neutron,

n

1.6

10-~

1.6

10-4

1.6

10-~

m

1.6

10-4

m

1.6

10-~

1.6

x

kg

mol-'

1.6

x

kg

7.9

x

10-8

U

1.3

x

lo-''

J

7.9

x

10-8

MeV

4.0

x

2.1

10-~

3.0

x

1.6

x

5.8

x

10-10

C

kg-'

4.0

x

lo-'

kg

mol-'

1.3

x

lo-''

m

7.6 10-9

m

7.6

10-9

.IT-'

4.1

x

1.0

x

10-8

1.0

x

10-8

1.0

x

10-8

2.4 10-7

J

T-I

4.2

x

io-8

1.1

x

10-8

1.1

x

10-8

5.7 10-4

s-l

T-1

4.1

x

10@

MHz

T-'

4.1

x

s-l

T-l

4.2

x

lop8

MHz

T-'

4.2

x

UNITS, CONSTANTS, AND CONVERSION FACTORS

3-1

1

Fundamental Physical Constants

-

Complete Listing

Relative std.

Quantity Symbol Value Unit uncert.

ur

neutron mass

in

u,

m,

=

A,(n)

u

(neutron

relative atomic mass times

u)

energy equivalent

in

MeV

neutron-electron mass ratio

neutron-muon mass ratio

neutron-tau mass ratio

neutron-proton mass ratio

neutron molar mass

NAm,

neutron Compton wavelength

h/m,c

neutron magnetic moment

to Bohr magneton ratio

to nuclear magneton ratio

k.n/2n

neutron g-factor

2Pnlll.N

neutron-electron

magnetic moment ratio

neutron-proton

magnetic moment ratio

neutron to shielded proton

magnetic moment ratio

(H20,

sphere,

25

"C)

neutron gyromagnetic ratio

21pLnl/ti

deuteron mass

in

u,

md

=

A,(d)

u

(deuteron

relative atomic mass times

u)

energy equivalent

in

MeV

deuteron-electron mass ratio

deuteron-proton mass ratio

deuteron molar mass

NAmd

deuteron magnetic moment

to Bohr magneton ratio

to nuclear magneton ratio

deuteron-electron

deuteron-proton

magnetic moment ratio

m,

1.674927 16(13)

x

kg

7.9

x

10-8

1.008 664915 78(55)

U

5.4

x

10-10

m,c2

1.50534946(12)

x

lo-"

J

7.9

x

10-8

m,/m,

1 838.683 6550(40)

2.2 10-~

m,/m,

0.528 722(86j

1.6 10-4

939.565 330(38)

MeV

4.0

x

lo-'

mn/ml*

8.89248478(27)

3.0

x

mn/mp

1.001 37841887(58)

5.8

x

lo-''

M(n),M,

1.00866491578(55)

x

kgrnol-'

5.4

x

AC,,

1.319590898(10)

x

m

7.6

10-~

KC,,

0.2100194142(16)

x

m

7.6 10-~

P,,/E.LB

-1.041 875 63(25)

x

2.4

10-~

/.L~/FN

-1.913 04272(45j 2.4

10-7

gn

-3.826 085 45(90) 2.4 10-7

p,,/pe

1.04066882(25)

x

2.4

10-~

/L"//L~

-0.684979 34(16) 2.4 10-~

w,/wb

-0.68499694(16) 2.4

Yn

1.832471 88(44j

x

lo8

s-l

T-1

2.4 10-7

yn/2r

29.1646958(70)

MHZ

T-'

2.4

x

10-~

md

3.343 583 09(26)

x

kg

7.9

x

10-8

2.013 553 21271(35)

U

1.7

x

lo-''

mdC2

3.005 06262(24)

X

lo-''

J

7.9

x

10-8

mdlm,

3 670.4829550(78) 2.1 10-9

Pn

-0.96623640(23)

x

JT-I

2.4

x

Deuteron, d

1875.612762(75) MeV 4.0

x

lop8

md/mp

1.999 007 50083(41

j

2.0

x

10-10

M(d),

Ma

2.013 553 21271(35)

x

kg

mol-'

1.7

X

lo-''

Pd

0.433 073457(18)

x

J

T-'

4.2

x

lop8

/.Ld/kB

0.466 975 4556(50)

X

io-3

1.1

x

10-8

/J,d/Px 0.857 438 2284(94)

1.1

x

10-8

/.Ld//.Lc.e

-4.664 345 537(50)

X

io-4

1.1

x

10-8

pd/Pp

0.307 0122083(45) 1.5

x

lo-'

3-1

2

REFERENCE

DATA

FOR ENGINEERS

Fundamental Physical Constants

-

Complete Listing

Relative std.

Quantity Symbol Value Unit uncert.

ur

deuteron-neutron

magnetic moment ratio

helion masse

in

u,

mh

=

A,(h)

u

(helion

relative atomic mass times u)

energy equivalent

in

MeV

helion-electron mass ratio

helion-proton mass ratio

helion molar mass

NAmh

shielded helion magnetic moment

(gas, sphere,

25

"C)

to

Bohr

magneton ratio

to nuclear magneton ratio

magnetic moment ratio

shielded helion

to

proton

(gas, sphere,

25

"C)

shielded helion to shielded proton

magnetic moment ratio

(gas/HzO, spheres,

25

"C)

shielded helion gyromagnetic

ratio

2jpLl/tt

(gas, sphere,

25

"C)

alpha particle mass

in

u,

mu

=

A,((Y)

u (alpha particle

relative atomic mass times u)

energy equivalent

in MeV

alpha particle to electron mass ratio

alpha particle to proton mass ratio

alpha particle molar mass

NAm,

Avogadro constant

atomic mass constant

mu

=

&m("C)

=

1

u

=

kg

mol-'/NA

energy equivalent

in MeV

El.d/WLn

-0.44820652(11)

Helion, h

mh

5.006 41 1 74(39)

x

loMz7

3.01493223469(86)

2808.391 32(11)

mhC2

4.49953848(35)

x

lo-''

mh/m,

5495.885238(12)

mh/mp

2.993 152658 50(93)

M(h),

k'h

3.01493223469(86)

X

4l

-1.074552967(45)

x

&/p~

-1.158671474(14)

x

wk/fijy

-2.127497 718(25)

pk/pp

-0.761 766563(12)

/~k/pf,

-0.761 786 1313(33)

?J;

2.037 894764(85)

x

lo8

y;/2n 32.434 1025(14)

Alpha particle,

(Y

ma

6.644655 98(52)

x

4.001 506 1747(10)

mar

5.971 91897(47)

x

3 727.379 04(15)

malm,

7 294.299 508(16)

mu/mp

3.9725996846(11)

M(a),

M,

4.001 506 1747(10)

x

10W3

PHYSICO-CHEMICAL

NA,

L

mu

1.66053873(13)

x

6.022 141 99(47)

x

loz3

muc2

1.49241778(12)

x

93 1.494 013(37)

Faraday constantg

NAf2

F

96 485.3415(39)

2.4 10-7

kg

7.9

x

10-8

J

7.9

x

10-8

U

2.8

x

MeV

4.0

x

2.1

x

10-~

J

T-I

4.2

x

10-8

3.1

x

lo-''

kg

mol-'

2.8

x

lo-''

1.2

x

10-8

1.2

x

10-8

1.5

x

lop8

4.3 10-9

s-l

T-1

4.2

x

lop8

MHZT-'

4.2

x

10-8

kg

7.9

x

10-8

J

7.9

x

10-8

U

2.5

x

MeV

4.0

x

lop8

2.1

10-~

2.8

x

lo-''

kg

mol-'

2.5

x

mol-'

7.9

x

10-8

kg

7.9

x

10-8

J

7.9

x

10-8

MeV

4.0

x

10@

C mol-'

4.0

x

3-1

3

Ouantitv Svmbol

Fundamental Physical Constants

-

Complete Listing

-

molar Planck constant

molar gas constant

Boltzmann constant

R/NA

in eV

K-‘

molar volume of ideal gas

RTIp

T

=

273.15

K,

p

=

101.325

kPa

T

=

273.15

K,

p

=

100kPa

Vm

Loschmidt constant

NA/vm

no

Vm

Sackur-Tetrode constant

(absolute entropy constantP

Ti

=

1K:

po

=

100kPa

TI

=

1 K,

po

=

101.325kPa

$

+

lt1[(2~~m,kTi

/h2)3/2kT1

/pol

SoIR

Stefan-Boltzmann constant

(n2/60)k4/k3c2

U

first radiation constant

2rrhc2

c1

second radiation constant he/

k

first radiation constant for spectral radiance

2hc2

Wien displacement law constant

C~L

c2

-

Relative std.

uncert.

ur

Value Unit

3.990312689(30)

x

lo-’’

Js

mol-’

7.6

x

0.1

19 626 564 92(9 1)

J

m mol-’

7.6

x

8.314472(15)

J

mol-’

K-’

1.7

x

IO@

1.3806503(24)

x

JK-’

1.7

x

8.617342(15)

x

eV

K-’ 1.7

x

lop6

2.083 6644(36)

x

10”

Hz

K-’ 1.7

x

10@

1.7

x

69.50356(12)

K-1

22.413996(39)

x

m3

mol-’

1.7

x

2.686 7775(47)

x

loz5

m-3

1.7

x

lop6

22.710981(40)

x

m3 mol-’

1.7

x

10@

-1.151 7048(44)

-1.164 8678(44)

3.8

x

3.7

x

10-6

5.670400(40)

x

lo-*

W

mP2

K-4

7.0

x

lop6

3.741 771 07(29)

x

W

m2

7.8

x

lop8

1.191 042722(93)

x

W

m2

sr-’

7.8

x

lo-’

1.438 77S2(25)

x

m

K

1.7

x

10@

b

=

h,,T

=

~214.965 114231

...

b

2.897 7686(51)

x

m

K 1.7

x

a

See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the volt using the Joseph-

son effect.

See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the

ohm

using the quantum Hall

effect.

Value recommended by the Particle Data Group, Caso et al.,

Em.

Phys.

J.

C

3(1-4),

1-794 (1998).

Based on the ratio of the masses

of

the

W

and

Z

bosons

mwlrnz

recommended by the Particle Data Group (Caso et al., 1998). The value

for

sin2& they recommend, which is based on

a

particular variant of the modified minimal subtraction

(m

scheme, is sin2&(Mz)

=

0.231 24(24).

e

The helion, symbol h, is the nucleus of the 3He atom

This and all other values involving

m,

are based on the value of

mrc2

in MeV recommended by the Particle Data Group, Caso et

al.,

Eur. Phys.

J.

C

3(1-4),

1-794 (1998), hut with a standard uncertainty

of

0.29 MeV rather than the quoted uncertainty of -0.26 MeV, +0.29 MeV.

The numerical value of

F

to be used

in

coulometric chemical measurements is 96 485.3432(76) 17.9

x

lo-’]

when the relevant current is measured

in terms of representations of the volt and

ohm

based on the Josephson and quantum

Hall

effects and the internationally adopted conventional values

of the Josephson and von Klitzing constants

Kj-90

and

R~-90

given in the “Adopted values” table.

The entropy

of

an ideal monoatomic gas of relative atomic mass

Ar

is given by

S

=

Sa

+

$R

In

Ar

-

R ln(p/po)

+

{R ln(T/K).

CONVERSION FACTORS*

abampere

abcoulomb

abfarad

abhenry

abmho

abohm

I.***

***

El

I.***

***

*** ***

El

I.***

***

E9

I.***

***

E -9

I.***

***

E9

I.***

***

*** ***

***

E

-9

A

C

F

H

S

ohm

*These conversion factors

are

an extension of those found in Mechtly,

E.

A.

The Znternational System

of

Units-Physical Constants

and

Conversion Factors,

National Aeronautics and Space Administration

(1973),

Publication

SP-7012 (1973).

Washington,

D.C.

20402:

U.S. Government Printing Office.

Continued

on

next page.

To

Convert From

I

Multiply By

I

To

Get Unit

I

abvolt

acre

angstrom

are

astronomical unit

(IAU)

astronomical unit (radio)

atmosphere, standard

atmosphere, technical, kgf/cm2

bar

barn

barrel (petroleum,

42

gallons)

barye

board foot

(144

cubic inches)

Btu

(IST

before

1956)

Btu

(IST

after

1956)

Btu (mean)

B tu (thermochemical)

Btu

(39

OF)

Btu

(60

OF)

bushel

(US)

cable

caliber (0.01 inch)

calorie

(IST)

calorie (mean)

calorie (thermochemical)

calorie

(15

"C)

calorie

(20

"C)

calorie, kilogram

(IST)

calorie, kilogram (mean)

calorie, kilogram (thermochemical)

carat (metric)

centimeter of mercury

(0

"C)

centimeter of water

(4

"C)

chain (engineer or Ramden)

chain (surveyor or Gunter)

circular mil

clo

cord

cubit

curie

day (mean solar)

day (sidereal)

degree (angle)

denier (international)

dram (avoirdupois)

dram (troy or apothecary)

dram

(US

fluid)

dyne

electronvolt (eV)

emu of

xxx

(see ab---)

erg

esu of

xxx

(see stat---)

faraday (based on carbon

12)

faraday (chemical, before

1960)

faraday (physical, before

1960)

fathom

fermi (femtometer, fm)

fluid ounce

(US)

foot

foot (US survey)

CUP,

I.***

***

I.***

***

I.***

***

1.495 978 70-

---

1.495 978 9-

---

9.806 65*

***

I.***

***

I.***

***

1.589 873

---

I.***

***

*** ***

2.359 737 216

***

1.055 04-

___

4 046 9--

___

__-

---

1.013 25*

**e

e**

*e*

1 055 056

___ ___

___

1.055 87-

---

1.054 350

---

1.059 67-

---

_--

1 054 68-

___

3.523 907 016 688

***

2,194 56-

---

_--

_-_

2.54*

***

4.186

8**

***

*** ***

4.190 02-

___

4.184

***

*** ***

***

4,185

80-

---

--_

4.181 90-

-_-

_-_

___

4.186

8**

***

*** ***

4,190 02-

___

4.184

***

2.***

***

*** ***

1,333 22-

___ ___

___

3.048

***

2.011 684

---

5.067 074

8-

---

2.003 712

---

3.624 556 3-

---

4,572

___

2.365 882 365

---

3.7**

***

8.64*

***

*** ***

8.616 409

0--

---

1.745 329 251 994 3--

I.***

***

1.771 845 195 312 5**

3.887 934

6**

***

3.696 691

195

312

5**

I.***

***

1.602 189 2--

---

I.***

***

9.648 530 9--

---

9.806 38-

_--

--- _-_

9.649 57-

---

--_

___

9,652 19-

---

--_

1.828 804

---

1.***

***

*** ***

2.957 352 956 25*

***

3.048

***

120013937

***

3.048

006

096

---

E

-8

E3

E- 10

E2

E

11

E

11

E5

E4

E5

E-28

E -1

E -3

E3

E -2

E2

E

-4

EO

----

E3

E

-4

E3

El

E-10

E -1

E

-1

E -4

E 10

E4

E -2

E -7

E -3

E -6

E

-5

E-

19

E -7

----

E4

EO

E-

15

E

-5

E

-1

E -1

EO

V

mz

m

mz

m

Pa

m2

m3

Pa

m3

J

m3

m

J

Pa

m

m2

K.m21W

m3

m

m3

Bq

s

(mean solar)

s

(mean solar)

rad

kg/m

kg

m3

N

J

C mol-'

m

m3

m

UNITS, CONSTANTS, AND CONVERSION FACTORS

To Convert From

foot of water

(39.2

OF)

footcandle

footlambert

free fall (standard, g)

furlong

gal

gallon (Canadian liquid)

gallon (UK dry)

gallon (UK liquid)

gallon (US dry)

gallon (US liquid)

gamma

gauss

gilbert

gill (UK)

gill (US)

grad (angle)

grain

gram

hand

hectare

hogshead

(US)

horsepower (boiler)

horsepower (electric)

horsepower (metric)

horsepower (UK)

horsepower (water)

horsepower

(550

ft.lbf/s)

hour (mean solar)

hour (sidereal)

hundredweight (long)

hundredweight (short)

inch

of

mercury

(32

OF)

inch of mercury

(60

OF)

inch of water

(39.2

OF)

inch of water

(60

OF)

jansky

kayser

kilocalorie (IST)

kilocalorie (mean)

kilocalorie (thermochemical)

kilogram force (kgf)

kilopond

kip

knot (international)

lambert

langley

lbf (pound force, avoirdupois)

lb,

(pound mass, avoirdupois)

league

league (international)

league (US nautical)

light year

link (engineer or Ramden)

link (surveyor or Gunter)

liter

maxwell

meter (based on constant

c)+

Multiply By

E3

El

EO

E2

----

E -2

E -3

E

-3

E -3

E -9

E -4

E

-1

E -4

E

-1

E -2

E -5

E -3

E

-1

E4

E

-1

E3

E2

E3

El

E -2

E3

E2

E-26

E2

E3

EO

E3

E

-1

E4

E3

E4

EO

E

-1

E3

E 15

E

-1

E -1

E -3

E

-8

To Get Unit

Pa

lx

c&m2

m/S2

m

dS2

m3

T

A

m3

degree (angle)

rad

kg

m

m2

m3

W

w

s (mean solar)

s

(mean solar)

kg

m

Pa

W/(m2

Hz)

m-’

J

N

m/S

cd/m2

c&m2

J/m2

N

kg

m

m3

Wb

t

On October

20, 1983,

the

17th

CGPM adopted the following definition: “The meter is the length

of

the path traveled by light

in vacuum during a time interval of

1/299 792 458

of a second.” This new definition has the effect

of

giving a fixed value

to

the

speed of light in vacuum

of

c

=

299 792 458

m/s

exactly. (Metrologia,

Vol.

19,

p.

163,

1984.)

Continued on next page.

Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

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