SOME coNTiiMroi^'.iRy ,ii>r.ixci:s i\ i-iiysics i.\ 65.i 



lori' rtjiMl to —\ e-fi a. and this is tlu- (|ii.intit\' to iii' f(|ii,iti'fl to the 



ol>siT\ i-d t'iHTn\-\.iliii's of iIk- sl.ilioii.iry states; ('(iii.tl ion ((>) i> 

 ri-pl.ut'd !>>■ 



-<-V 2(/= -Rh 11- . (1(1) 



rill' aiij;iilar moiiu'iitiim of the electron is nnui; tlie aiii;iii.ir mo- 

 incnluin of the nucleus is .1/ I'.l ; the angular niomeiituin of tiie atom, 

 for which I use the synih.jl />, is the sum of these: 



p = iiivti + M I VI = mva n. (11) 



1 leave it again to the reader to use the foregoing statements to arri\e 

 at the expression 



p = e\/ma (12) 



antl by combining (12) and (10), at the expression 



pn = ne-\^mn -IRIi (18) 



for the \alue />„ of the angular momentum of the atom, or rather of 

 our atom-model, in its «th stationary- stale. 



Thus the values of the angular momentum of tiie atom-model, in 

 the various states in which it has the prescribed energy-values —Rh, 

 — Rh A, and so forth, increase from the first of these states onward 

 in the ratios 1 :2:3:4 . . . They arc the consecuti\e integer multiples 

 of a fundamental quantity, the quantity 



pi = e-\/>nii/2Kli. (14) 



Now it happens that this fundamental quantity is equal, within the 

 limits of experimental error, to /» '27r — to 1 /2jr times that same con- 

 stant /; which has already figured in this discussion: 



pi = h 2-k; p„ = nh, 2Tr. (15) 



This occurs because the \alue of R is equal, within experimental 

 error, to the combination of ni, e, and /; on the riglit of this c(iuation: 



R = 2T^-nme\h\ (16) 



The atom-model which I have been describing at some length 

 could therefore be described in a few words by saying that the electron 

 is permitted to revolve only in certain circular orbits, determined by the 

 condition that the angular momentum of the atom shall be equal to an 

 integer multiple of h, 2n-. This condition is in fact sufficient to impose 

 the values given for the radii of the circular orbits in equations (10) 

 which values in turn entail the desired energy-values for the stationary 

 states. The reader can easily prove this by working backward 



