Table 26. General Physjcal Constants According to Birge

48

T A B L E PB.-GENERAL

Part 3.-Additional



P H Y S I C A L CONSTANTS ACCORDING T O BlRGE

(continued)



quantities evaluated or used in connection with Part 1



..........



Ratio of esu to emu (direct).

c' = (2.99711 f 0.0001) X l(Yo cm'/' set"/' ohm'/*

= (2.9978, 2 O.OOOlo) X 10" cm/sec

Ratio of esu to emu (indirect). ...... .c' = c = (2.99776 f0.0004) X 10'' cm/ser

Average density of earth.. ............6 = 5.517 f0.004 p/cm'

Maximum density of water. ....am(H20) = 0.999S2 2 0.000002 g/cm'

Acceleration of gravity (standard). ... .go = 980.665 cm/sec'

Acceleration of gravity (45"). ........ g =

~ 980.616 cm/sec?

Density of oxygen gas (OOC, A ) .... .L1= 1.42897 f0.0003 g/liter

Limiting density of oxygen gas (OOC, A K )

L t i m = 1.427609 2 0.000037 g/liter

Factor converting oxygen (O'C, All)

to ideal gas.. ..................1 - a = l.OOO953s2 0.000009,

Specific gravity of H g (O'C, Ao) referred to air-free water at maximum

density ..........................

.po = 13.59542 f 0.00005

Density of Hg (0°C. A ) .............DO= 13.59504f 0.00005, g/cm8

Electrochemical equivalents (chemical

scale) :

Silver (apparent) .............EA, = (1.11800 -t0.00012) x 10-'g/int coul

(corrected) .............E A , = (1.11807 2 0.00012) x

g/abs coul

Iodine (apparent) ..............E I = (1.315026 fO.oooO25) x lo-*g/int coul

(corrected) ..............E I = (1.31535 f0.00014) x lo-* g/abs coul

Effective calcite grating space ( W C )

d"a = 3.02904 X lo-' cm

Siegbahn system

True calcite grating space (20°C). .. . # Z O = 3.029512 X 10.' cm

Siegbahn system

True calcite grating space (20°C). . . .dm = (3.0356742 0.00018) X 10-'cm

cgs system

Ratio of grating and Siegbahn scales of

wavelengths ...................X I / L = 1.002034 f0.000060

Density of calcite (20°C). ............. p = 2.71029 U0.00003 g/cm*

Structural constant of calcite (20°C). . = 1.09594 2 0.00001

Molecular weight of calcite (chemical

- - - - - - -. naos

- --.M = inn.091.f

scale) ...........................

Rydberg constant for hydrogen (HI). .RH = 109677.5812f 0.007, cm-' (LA. scale)

Rydberg constant for deuterium (H') . .RD= 109707.419af0.0076 cm-' (I.A. scale)

Rydberg constant for helium.. ......R I I ,= 109722.263 -C 0.012 cm-' (I.A. scale)

Rydberg constant for infinite mass. ...R, = 109737,303& 0.017 cm-' (LA. scale\

or f 0.05 cm-' (cgs system)



.*



SMITHSONIAN PHYSICAL TABLES



49

P H Y S I C A L C O N S T A N T S A C C OR D IN G T O B I R G E

(continued)



T A B L E 26.-GENERAL



list o f derived quantities



P art 4.-Partial



,= {



Planck's constant :



{



27r7Fs }1/3

R,No (e/+iz)



........... = (6.62422 0.002,)



R
}

.......



It/e



=



h/e'



= I t / ( e c ) = Rx N2r2F2

o ' ( C / tit)



1/3.



{



'I3



erg sec



X



z (4.134g02 0.00071)



x



lo-' erg sec abs emu-'



= (1.3793, 2 0.0002,)



x



lo-'' erg sec abs esu-'



Atomic weight of electron : ...........E = F / ( c / n z )

(Physical scale) ..................= (5.4862, 2 0.0017) X lo-,

(Chemical scale) ..................= (5.48175 f 0.0017) X lo-'

Band spectra constant connecting wave

number and moment of inertia :



1"(8*2r) =



..... = (27.98,,



{



2 O.Ol0) X lo-'' g c m



Boltzmann constant :



I< = Ro/.Vo= Y o A U / ( T o N o........

).

= (1.38047, 2O.ooO26) X lO-"'erg/deg



Charge in electrolysis of 1 gram of H



F/H = 9572.1,,



f 1.0



abs. emujg



Charge in electrolysis of one gram of

H' ...........................

c/M,,' = I; H' = 9573.5,f



1.0 abs emu/g



Compton shift at 90" :



Energy i n ergs of one abs volt-electron:

E o = 106c = 108F/Zio .............. = (1.60203, 2 0.00034) X lo-'* erg

Energy in calories per mole for one abs volt-electron per molecule:

F(abs coul/gram-equiv.)

........... = 23052.85 2 3.2 call:, mole-'

J15(absjoules/cal)

Fine structure constant :

a



{



= 2x(e')'/(hr) = 4aRxF(c'1r2'}

N O



= (7.2976, f 0.0008.) x lo-'

l / a = 137.030, & 0.016

'a = (5.3255 2 0.0013) X



Gas constant per mole:

Ro = I'oA,/T, . . . . . . . . . . . . . . . . . . . = (8.31436 f 0.00038) X 10' erg deg-' mole-'

RIo= K,, x 10-'/115 . . . . . . . . . . . . . . . = 1.98646, 2 0.00021 call:, deg-' mole-'

1 atm deg-' mole-'

R'Io= Iv',/To.....................

= (8.20544, & 0.00037) X

R"' - RolAu= V , / T , ............ = 82.0566; f 0.0037 cms atm deg-' mole-'

also :



ROTo= I'oA, .....................



= (2.27115"f 0.00006) X 10'" erg mole-'



Loschmidt number (O"C, A0)riu= hro/V0.= (2.6870,t

hfagnetic moment of one Bohr magneton :

p1



* 0.00050)X 10'" molecules/cm3



= (Iz/4a)(e/m) =

= (0.9273,,



2 O.CO03,) X lo-% erg/gauss



Magnetic moment per mole for one Bohr

magneton per molecule :



{



}



1 2 7 r ' ~ ~ F ~ ( ~ / i' Ii 3

i )......

~

= 5585.2, f 1.6 erg gauss-' mole-'

,u1!V0= 4n

Rr No'

Mass of a-particle. . M a = ( H e - 2E)/No = (6.61422 f 0.0012) X lo-'' g

(corttirlurd)

SMITHSONIAN PHYSICAL TABLES



50

T A B L E 26.-GENERAL



P H Y S I C A L CONSTANTS ACCORDING

(concluded)



TO BlRGE



Mass of atom of unit atomic weight,

Mo = 1/No = (1.66035 2 0.00031) X lo-" g

Mass of electron ;

m = e/(e/m) = (F/No)/(e/m) = (9.1066, f 0.0032) X lo-" g

Mass of H' atom.. ...... . M H =

~ H'/No = (1.673393 0.0031) X lo'" g

Mass of proton.. ... . M P = (H'- E)/No = (1.672482f 0.00031) X lo-" g



*



Ratio mass H' atom to mass electron:

MHl/m = (e/m)(H'/F) ........... = 1837.5,, f 0.5,

Ratio mass proton to mass electron :

M,/m = ( e / m (H') ( T E)

) . ........



= 1836.56, 2 0.56



First radiation constant. ....cl** = 8rhc = (4.9908 f 0.0024) X lo-'' erg cm

= hcP = (0.59542 f 0.0024) >( 10.' erg cm2 sec-'

=2 ~ h =

2 (3.7403 0.0024) x lo-' erg cm2 sec-'

Second radiation constant :

cz



{



= hc/k = -



*



2rF6



VoAo RmNo(elm)



= 1.43848 f 0.00034 cm deg



}1/3



Specific charge of a-particle :

2F

................. = 4522.3s 2 0.5, abs emu/g

2e/M aHe-2E

~



Specific charge of proton :



e/Mp =



F



................... = 9578.77 f 1.0 abs emu/g



Radiation density constant,



a = 8r6k'/(15c'hs)



=



4rraNoRm(e/m) ............ - (7.56942f0.004#) X lo-= erg cm-' deg-'



(?)

15c'F

Stefan-Boltzmann constant : t



VoA

......... = (*)



rsNoR,(e/m)

15( F C ) ~

= (5.67283f 0.003,) X 10.' erg cm-' deg-' sec-'

Wien's displacement-law constant. ... . A = c2/4.965114= 0.28971, 2 0.00007 cm deg

Wavelength associated with 1 abs volt.

ko = 10-'c2(h/e') = c2

2
= (12395.. 2 2 4 x lo-' cm abs volt

10' RmNo(elm)

Wave number associated with 1 abs volt :

SO = 1/)b = lo8 RmN'(e/m)}'/3

2*2FZ

= 8067.4, '-+ 1.4 cm/abs volt

u = a c / 4 = 2r6k4/(15cah8)



{



C2



4



>;,



{



Zeeman displacement per gauss ( e / m ) / ( 4 ~ c )= 4.669g1 f 0.0013) X lO-'cm/gauss

**.

may

I,be defined in several ways and this determines the value of cl. If J,dX gives the energy

density of unpolarized radiation in range dX, then c l = 8nhc. If J,dX gives the emission of linearly

polarized light, in range dX per unit solid angles perpendicular to the surface, then c1= hc'. If this

expression J,dX denotes the emission of radiation in range dX, per unit surface from one side i n all

directions (2n solid angle) then cl = 2ahcz. See Table 53.

t For 2a solid angle.



Part 5.-Birge's



1944 values o f 3 constants



e, Electronic charge.. .................. = (4.8021 f 0.0006) X lo-" abs esu

Nu, Avogadro number.. ................ = (6.02338 f 0.00043) X 10" molecules mole-'

(chemical scale)

F, Faraday constant.. .................. = 96487.7 f 10 abs coul

(chemical scale)



SMlTHSONlAN PHYSICAL TABLES



51

T A B L E 27.-TABLE

O F L E A S T S Q U A R E S A D J U S T E D O U T P U T V A L U E S OF

P H Y S I C A L C O N S T A N T S ( B Y D u M O N D A N D ASSOCIATES)



(November 1952)

Part 1.-Auxiliary



constants used



These auxiliary constants are quantities which are uncorrelated (observationally) with

the variables of the least-squares adjustment.

Rydberg wave number for infinite mass. RE= 109737.309 f 0.012 cm-'

Rydberg wave numbers for the light nuclei

RH= 109677.576 f 0.012 cm-'

RD = 109707.419 f 0.012 cm-'

RH=

, ~109717.345 f 0.012 cm-'

Rne4= 109722.267 f 0.012 cm-'

Atomic mass of neutron.. ............. n = 1.008982 f0.000003

Atomic mass of hydrogen.. ...........H = 1.008142 2 0.000003

Atomic mass of deuterium.. .......... D = 2.014735 f 0.000006

Gas constant per mole (physical scale). R, = (8.31662 f 0.0003S) X 10' erg mole-' deg-'C

Standard volume of a perfect gas

(physical scale) ...................Y o= 22420.7 f 0.6 cms atmos-' mole-'

Part 2.-Least-squares



adjusted output values



(The quantity following each f sign is the standard error by external consistei;cy)

Velocity of light.. .................... c = 299792.9 f 0.8 km sec-'

Avogadro's constant (physical scale). ..N = (6.02472 f 0.00036) X 10'' (molecules mot)-'

Loschmidt's constant (physical scale). . . .

Lo= N/V0 = (2.68713 f 0.00016) x 10'Dmoleculescm-'

Electronic charge ....................

. e = (4.80288 2 0.00021) X lO-'Oesu

e' = e / c = (1.60207 f0.00007) j (

emu

Electron rest mass. ...................m = (9.1085 f0.0006) X lo-" g

Proton rest mass. . . . . . . . . . . .mp = M,/N = (1.67243 2 0.00010) x lo-" g

Neutron rest mass.. ..........m, = ?1/N = (1.67474 f 0.00010) x lo-'' g

erg sec

Planck's constant .................... h = (6.6252 t 0.0005) X

erg sec

4i = h / ( 2 * ) = (1.05444 2 0.00009) x

Conversion factor from Siegbahn X-units

to milliangstroms .............. .Xl/h, = 1.002063 f 0.000034

Faraday constant (physical scale) I; = N e = (2.89360 f0.00007) X 10" esu (g mot)"

F' = N e / c = (9652.01 -C 0.25) emu (gm mot)-'

Charge-to-mass ratio of the electron. . e / m = (5.27299 2 0.00016) x 1O''esu g-'

e'/m = e / ( m c ) = (1.7588 2 0.00005) x lO'emu g-'

h / e = (1.37943 C 0.00005) X lo-'' erg sec (em)-'

Ratio h / e ..........................

Fine structure constant ...... a = e2/(%r)= (7.29726 t 0.00008) x

l / a = 137.0377 2 0.0016

a j 2 r = (1.161396 f 0.000013) X

a* = (5.32501 f0.00012) X

1 - (1 - a')? = (0.266254 2 0.000006) X



Atomic mass of the electron (physical

scale) ........................... N m = (5.48760 2 0.00013) X lo-'

Ratio of mass of hydrogen to mass of

proton a



H/H'=



[ 1 - N-(Hm



1 - $ a Z ) ] - l = 1.000544610 f 0.000000013



Atomic mass of proton.. ............H' = 1.007593 f0.000003

Ratio of proton mass to electron mass.. .

H+/Nni = 1836.13 C 0.04

Reduced mass of electron in hydrogen

atom .................... p = mH+/H = (9.1035 f 0.0006) X

Schrodinger constant for a fixed nucleus



g



2ndV = (1.63844 f 0.00016) x 10" erg-' cm-'

Schrodinger constant for the hydrogen

atom .........................

. 2 p / V = (1.63755 f 0.00016) x 10" erg-' cm-'

First Bohr radius.. ........ao = P/(me') = (5.29171 2 0.00006) X IO-'cm = a/(47rRE)

* T h e binding energy of the electron in the hydrogen atom has been included in the quantity. The

mass of the electron when f o u n d in the hydrogen atom is not m but more correctly m ( 1 - 1 / 2 a'+ ' .).



(continued)

SMITHSONIAN PHYSICAL TABLES



52

T A B L E 27.-TABLE



O F LEAST-SQUARES A D J U S T E D O U T P U T V A L U E S O F

P H Y S I C A L C O N S T A N T S (continued)



Radius of electron orbit in normal H',

referred to center of mass.. ..........

a' = ao(l - a')* = (5.29157 2 0.00006) X lo-' cm

Separation of proton and electron in norma1 H' ..............&" = &' R,/RII = (5.29445 2 0.00006) X 10-Ocm

Compton wavelength of the electron.. . . . .

X,. = h / ( m c ) = (24.2625 2 0.0006) X lo-" cm = a'/(2Rm)

X,. = h c , / ( 2 r ) = (3.86150 2 0.00009) X lO-"cm = a2/(4rRm)

Compton wavelength of the proton. .....

Xe, = h/m,c = (13.2139 f 0.0004) X lo-'' cm

X,, = AeP/(27r)= (2.10307 2 0.00007) X lo-'' cm

Compton wavelength of the neutron.. ...

Xc. = h / n w = (13.1958 f 0.0004) X lo-'' cm

X,. = X,./(ZR) = (2.10017 2 0.00007) X lO-"cm

Classical electron radius.. . .ro= e'/(mc') = (2.81784 -C 0.00010) X 10''scm = a3/(4rR,)

r0*= (7.9402 2 0,0005)

cm'

8

cm'

Thompson cross section.. ......... - ~ ~ =0 (6.65196

2

-C 0.0005) X

3

Fine structure doublet separation in

1

hydrogen ....................... AE - -Raa'

1

(85 - 5.946 a']

'I16

= 0.365869 -f. 0.000008 cm-'

= 10968.49 -C 0.25 Mc sec-'

Fine structure separation in deuterium.. .

A E D= AEII RD/RIi :

0.365969 0.000008 cm-'

= 10971.48 -C 0.25 Mc/sec-'

Zeeman displacement per gauss. ........

(c /m c )/(4~ c )= (4.66879 2 0.00015) X lO"cm-'gauss-'

Boltzmann's constant .........k = Ro/N = (1.38042 -C 0.00010) XlO-''ergs deg-'

k = (8.6164 2 0.0004) 10"ev deg-'

I l k = 11605.7 -C 0.5 deg ev-'

erg cm

First radiation constant. ......c1 = 8 R hc = (4.9919 2 0.0004) X

Second radiation constant. .....c2 = hc/k = (1.43884 -C 0.00008) cm deg

Atomic specific heat constant. .......c z / c = (4.79946 2 0.00027) X lo-'' sec deg

Wien displacement law constant '. .X,,.,T = cJ(4.96511423) = 0.28979 2 0.00005 cm deg

Stefan-Boltzmann constant . ,. ..........

u = (w2/60)(k'/Rc') = (0.56686 rfr 0.00005) X lo-' erg cm-' deg-' sec-'

5

Sackur-Tetrode constant ......... .So/Ro=2 1 n { (2rR0)"' h-' N-'1

- _ 5.57324 f 0.00011

So= - (46.3505 2 0.0017) X 1O'erg mole-' deg-'

Bohr masneton .......................

1

erg gauss-'

p3 7he/(4n mc) = - e X.. = (0.92732 2 0.00006) X

2

Anomalous electron moment correction. ..

1

- 2.973 a' = p./po = 1.001145356 C 0.000000013



x



[ + +



7)



*



x



+



[ +2



73

R



Magnetic moment of the electron. ..... p a = (0.92838 2 0.00006) X lo-" erg gauss-'

Nuclear magneton .....................

p. = hc/(4rmpc) =poNm/H+= 0.505038 -C 0.000036) X lo-= erg gauss-'

Proton moment .....................

. p = 2.79277 -C 0.00006 nuclear magnetons

= (1.41045 2 0.00009) X lo-" erg gauss-'

Gyromagnetic ratio of the proton in hydrogen (uncorrected for diamagnetism)

y' = (2.67520 k 0.00008)X 10' radians sec-' gauss-'

Gyromagnetic ratio of the proton (cor.y = (2.67527 -C 0.00008) X10' radians sec-' gauss-'

rected) ...........................

Multiplier of (Curie constant)* to give

(erg mole deg-')*

magnetic moment per molecule. (3k/N)4 = (2.62178 k 0.00017) X

b



The numerical constant 4.96511423 is the root of the transcendental equation



(continued)



SMITHSONIAN PHYSICAL TABLES



I=



5 (1



-e+).