SOMF. CONTEMrOli.lRY .llfr.lXCFS fN PtlVSICS-IX 655 



electron is describing lliat orbit, liie energy of the atom iH)ssesses 

 just the vaUie appropriate to that Stationary State? And granting 

 that this is possil>le and accoiu|)lislied; ran it l)e shown that these 

 additional orbits are distinguished 1)\ sonic Italure resembling that 

 feature of the circular orbits which is described by ecpiation (1 "))!•' 

 Our condition laid upon the circular orbits, thai in each of them the 

 angular momentum of the electron is an integer nniltiple of // 'Iir - 

 this condition \alid for the limited case, can it be generalized into a 

 condition governing the Stationary States of the hydrogen atom 

 under all circumstances? Can orbits be described which account 

 for all of the Stationary States of h>-drogen under all circumstances, 

 and which are determined b\- a general condition of which the condi- 

 tion set forth in equation (1.5) is one particular aspect? If so, that 

 general condition might well be such a Principle as the one towards 

 which, as it was said in the last section, so many physicists aspire. 

 Thus the test to which this condition laid upon the angular momentum 

 must be submitted is this: can it be generalized^ 



Before trying to generalize it let us examine some other (list inctive 

 features of the circular orbits defined in (7) — I will call tlu-m lienci- 

 forth the "permissible" circular orbits, but we should remember that 

 perhaps it is only ourselves who are "permitting" them and forbidding 

 the others, and not Nature at all. Let us calculate the integral / of 

 the doubled kinetic energy- 2K of the atom over a complete re\<>lulion 

 of the electron (and nucleus) : 





2Kdl. (17) 



It is easy in this case, for K is constant in time, so that I = '2KT. Now 

 A' is equal to \mv- ' n, and T is equal to 2Tra/v = 2ir-md'/nK; which 

 expression the reader may reduce, by means of that equation K = 

 jC-M a which he was invited to derive, to 



T=ire'Vm^/2K^ (18) 



multipKing which by A', and using equation (10), we have 



I = 2irn-e'Vmn/Rh. (19) 



The reader will recognize the factor which appeared in (14) and was 

 there stated to be numerically equal, within the error of observation, 

 to h 2w. 



Therefore this atom-mrKlel could also be described by saying that 

 the electron is permitted to rrcolve only in certain circular orbits deter- 

 mined by the condition that I shall be equal to an integer multiple of h. 



