Table 27. Table of Least-Squares Adjusted Output Values of Physical Constants

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+).



53

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

P HY S ICA L C O N S T A N T S (concluded)



OF



Mass-energy conversion factors. .....1 g = ( 5.60999 C 0.00025) X 10%Mev

1 electron mass = 0.510984 0.000016 Mev

1 atomic mass unit = 931.162 2 0.024 Mev

1 proton mais = 938.232 2 0.024 ?\lev

1 neutron mass = 939.526 0.024 lfev

Quantum energy conversion factors.. 1 ev = (1.60207 C 0.00007) X lO-''erg

E / i =T (1.98620 2 0.00016) X lo"* erg cm

E A, = (12397.8 f 0.5) X lo-' ev-cm

E A, = 12372.2 f 0.4 k volt-x units

E / v = (6.6252 f0.0005) X

erg sec

E / v = (4.13544 f 0.00015) X

ev-sec

C/E = (5.0347 2 0.0004) X lOI5 cm-' erg-'

;/E = ( 8065.98 C 0.30) cm-' ev-'

v/E = (1.50938 2 0.00012) X 10" sec'' erg-'

v / E = (2.41812 2 0.00009) x 10" sec-' ev-'

de Broglie wavelengths, AD of elementary

particles

Electrons .....................

. A D , = (7.27373 2 0.00016) cm2sec-'/v

= (1.55226 2 0.00008) x 10-13cm( e r g ) + / \ / x

= (1.226377 2 0.000032) X lo-' cm (ev)+/V E

Protons ......................

. A D , = (3.96145

0.00013) X lo-' cm' sec-'/v

= (3.62261 2 0.00020) X 10-"cm (erg)*/\/ E

= (2.86208 0.00012) X lO-'cm ( e v ) * / \ / x

. A D , = (3.95599 2 0.00013) X

cm' sec-I/v Neutrons .....................

= (3.62005 C 0.00020) X

cm (erg)+/\/ E

= (2.86005 f 0.00012) X 10-O cm ( e v ) * / \ / y

Energy of 2200 m/sec neutron. ......EZ1W = 0.0252977 2 0.0000006 ev

Velocity of 1/40 ev neutron.. ...... .VO.OU= 2187.017 0.028 m/sec

The Rydberg and related derived constants

R , = 109737.309 f 0.012 cm-'

R,c = (3.289847 -C 0.000008) X 10'' sec-'

R,hc = (2.17961 f 0.00018) X lo-" ergs

Rzhc2

lo: = 13.6050 C 0.0005 ev

Hydrogen ionization potential. ....... . I 0 = 13.5978 C 0.0005 ev

= R Hhc'

p[ 1

x lo-'



*

*



*



-



*



*



+ $+. . ]



c These formulas apply only to non-relativistic velocities.

If the velocity of the particle is not negligihle compared to the velocity of light, c. or the energy not negligible compared to the rest mass energy,

2 ) ]-I/' where XC i s the appropriate Compton wavelength and E is the kinetic

we must use XD = &[E(E

energy measured in units of the particle rest mass.



+



SMlTHMNlAN PHYSICAL TABLES



54

TABLE 28.-GENERAL



PHYSICAL CONSTANTS ACCORDING T O BEARDEN

A N D ASSOCIATES *



P a r t 1 t (atomic weights according t o the physical scale unless otherwise indicated)



Least-squares adjusted values of the fundamental atomic constants

Atomic mass of hydrogen .............H = (1.008142 f .000003)

Atomic mass of deuterium ............ D = (2.014735 f .000006)

Atomic mass of deuteron ..............d = (2.014186 f .000006)

Atomic mass of proton ...............M = (1.007593 .000003)

Atomic mass of electron ............ N m = (5.48756 f .00018) x lo-'

Electron mass ......................

.m = (9.10818 f .00079) x lo-= g

Reduced electron mass in hydrogen atom

# = (9.10322 f .00072) X lO-=g

Ratio proton mass to electron mass. .....

M / m N = (1836.139 2.054)

Ratio of Siegbahn X-unit to milliangstrom

A,/X, = (1.002058 f .000039)

Ratio of physical to chemical scales of

atomic weights .....................

r = ( 1.0002783 2 .0000005)

Faraday ............................

F = (9652.14 2 . 3 3 ) emu (g-equiv)-'

Electron charge .....................

.e = (4.80283 f ,00022) X lo-" esu

Specific electronic charge .......... . c / m = (5.27309 f.00024) X lo" esu g-'

Planck's constant ....................

h = (6.62509 .00059) X lo-" erg sec

erg sec

Planck's constant X 1/2 7r . . . . . . . . . . . . .d = (1.05442 f.00009) X

h / e = (1.37941 2 .00006) X lO-''erg sec (em)-'

h/m = (7.27377 2.00017) cm' sec-'

Avogadro's number .................N = (6.02487 .00045) X 10" molecules (g-mol)-'

Boltzmann's constant

..........k = (1.38039 f .OOOlO) X lO-'"erg deg-'

..........no = (2.68719 f .OOOZO) x 10'' molecules cm-a

Loschmidt's number .

Rydberg for infinite mass ............R, = (109737.311 k.012) cm-'

Rydberg for hydrogen ..............RH = (109677.578 & ,012) cm-'

Rydberg for deuterium ...............RD= (109707.419f ,012) cm-'

Gas constant per mole.. ..............R,= (8.31665 2 ,00034) X IO'erg mol-'deg-'

Molar volume ......................

V@= (2.23207 -C .00004) X lo' cms mol-'

Fine structure constant.. ............. .a = (7.29729 2 .oooO8)X lo4

l/a = (137.0371 2 ,0016)

Velocity of light. ....................

.c = (2.997925

.000008) X 10"' cm sec-'

. . . ..c, = ;4.99175 1:.00044) X lO-'"rg cm

First radiation constant. ....

.....cz = ( 1.43884 k .00004 cm deg

Second radiation constant. ..

Stefan-Boitzrnann constant ...........u = (5.66858 f .00053) X IO-'erg cm-'deg-' sec-'

Wien displacement law constant. . .A,,, T = (289789 .000009) cm deg

.fro = (.927313 2.000055) X lo-" erg gauss-'

Bohr magneton ......................

Theoretical magnetic moment of electron

p. = (.928375 f .000055) X lo-" erg gauss-'

.................ao= (5.29173 f .00006) X lO-'cm

Conversion factor for atomic mass units

to Mev ...........................

E , = (9.31145 2.0032) X lo2Mev (amu)-'

Conversion factor for grams to Mev.. .E, = (5.61003 2 .00026) X lomMev g-'

Wavelength associated with 1 ev.. ... . A 0 = (1.23976 f .00005) X lo-' cm

Wave number associated with 1 ev. ... .PO = (8.05611 f.00035) X lo3cm-' ev-'

_+



*



*



*



*



For reference see footnote 18a p. 46.

t Private comm;nication by J. .4'. Bearden. Data presented at May 1953 meeting of Physical Society

at Washington by Bearden, Earle, Minkowski, Thomsen, Johns Hopkins University.



Part 2$



Multiplier of (Curie constant)"' to&e

magnetic moment per molecule. V 3k/N = (2.62173 f .00009) X lo-" (erg mol deg-')*

Atomic specific heat constant. .......h/k = (4.79903 f .00023) X lo-" sec deg

Schrodinger constant for fixed nucleus. .

2m/hz = (1.638995 f .000045) X lon erg-' cm"

Schrodinger constant for H' atom. .29/hZ= (1.638103 f .000045) X lon erg-' cm-'

Energy associated with unit wave number ..............................

.El= (1.985698 i..000048) X 10-"erg

Speed of 1 ev electron., ..............VO= (5.931098 2 .000045) X IO'cm sec-'

(c o n t i w e d )



t For



reference, see footnote 18a, p. 46.



SMITHSONIAN PHYSICAL TABLES



55

T A B L E 28.-GENERAL



P H Y S I C A L C O N S T A N T S ACCORDING T O B E A R D E N

A N D ASSOCIATES (concluded)



Energy equivalent of electron mass.. .711C2 = (S10969 .000009) Mev

Energy associated with 1°K.. ..........

( R , / F ) X lo-'= (8.61632 2.00042) x lO-'ev

Temperature associated with 1 ev.. ...Tn = (11605.9 2 .6) deg K

Grating space calcite at 20°C. ....... .dm = (3.03567 2 .OOOOS) x lO-'cm

Density of calcite at 20°C. . . . . . . . . . . . . . p = (2.71030 2 .00003) g cm-'

Compton wavelength of electron.. . . h / r i i c = (2.426045 2 .00002S) X 10-lacm

Zeeman displacement per gauss c/(4rrirrc) = (4.668885 2 .00008) X 10-5cm-'gauss-'

Doublet separation in hydrogen. . . . . . . . . .

- R,r a' = (.3649900 k .0000037) cm-'

16



SMITHSONIAN PHYSICAL TABLES