Table 40 (continued) 95 



PROBABLE VALUES OF THE GENERAL PHYSICAL CONSTANTS 



off to 6.55±o.oi. Henning and Jaeger 1 discuss the most probable value and 

 adopt 6.55. 



(a) Bohr's formula for the Rydberg Constant. — Bohr's theory of the Hy- 

 drogen atom leads to the equation 



R a > = 2^e 5 /h 3 c 2 e/m (i) 



in which R* is the Rydberg constant for infinite mass (cnr* units), e, the 

 electronic charge (abs. cs units), and e/m is in em units. i?» is derived from 

 the observed R H by the equation 



R x =R H ( 1 + m/mu) =Rr\ I + F/(e/m) (H-m) - 109737.424 cm" 1 . (2) 

 The probable error in R* is about 0.06 cm" 1 . In absolute units R» • c 

 = (3.28988 + 0.00004) X io 15 sec." 1 . Substituting in (1) the spectroscopic 

 value of e/m, since we are dealing with spectroscopic data, 

 h = (6.547 ± 0.01 1 ) X io -27 erg • sec. 



After adopting a weighted mean value of h, ( 1 ) becomes a method for calcu- 

 lating, indirectly, the value of R<*>. Or, using the directly determined value 

 Rod, (i) becomes a means for calculating e/m. 



(b) Ionization potentials. — In 1919 Birge had available 13 values of ioniza- 

 tion and resonance potentials. Many more such potentials have been obtained. 

 The probable error in each is rather large. We have one really accurate de- 

 termination obtained with electrons of carefully controlled velocity. This is 

 Lawrence's value ' of the ionization potential of Hg. His final value equals 

 10.40 ±0.02 int. volts. 



The equation for obtaining h is hv = eV ; all quantities are in absolute units. 

 The observed potential (V) is always in int. volts. The potential in abs. es units 

 is then V=pqV'lO s /c. The spectral frequency v (in sec. -1 ) is obtained always 

 from the wave length X, in cm. Hence v'(cm _1 ) = i/A, and v—c/X. The above 

 equations lead to h/g= {pq y, 10 * )/{ ^ = (pqV ' Xl0 s )/c , (3 ) 



It seems quite customary to assume that V cs = V volts/300 and to write this 

 equation h/e=V'X/2>ooc. (4) 



This is equivalent to assuming c = $X io 10 cm • sec.' 1 , causing an error of 0.07 



per cent. Scarcely anyone uses c = 3Xio 10 cm • sec. -1 when reducing X to v, 



and thus in the same equation it is customary to use two different values of c. 



The " term " of Hg corresponding to the ordinary ionization potential is 



84178.5 cm -1 , whence , /£ . , N „ 



^' ° h= (6.56o±o.oi5) xio -27 . 



The probable error in V is 0.2 per cent and in e, 0.1 per cent. The errors of 

 the other factors are negligibly small. 



(c) X-ray continuous spectrum. — This method uses (3), A being measured 

 by means of acalcite crystal, i.e., X = 2d sin 6 where d is the grating space, and 6 

 the angle at which the given wave length shows constructive interference. 



h/e-pq 2d (V sin 6) io 8 /c 2 



Duane, Palmer, and Yeh 3 have carried out an accurate investigation. The 

 resulting value of h is (6.556^0.009) x io -27 . Another result for which equal 

 accuracy is claimed, is by Wagner. 4 Ladenburg 5 gives a complete list of 

 Wagner's experimental results. Ladenburg, using eq. (4), with c = 2.9985 

 X io 10 , gets 6.529 ±0.01. 



1 H.P., 2, 510. 2 Phys. Rev., 28, 947, 1926. 3 Proc. Nat. Acad. Sci., 7, 237, 1921. * Phys. 

 Zeit., 21, 621, 1920. 5 H. P., 23, 296. 



Smithsonian Tables 



