656 /*/?/•/- SVSTF.M TECHNICAL JOURNAL 



For future use I interpolate the remark that the factor ii is called 

 the total or principal quantum number; in German, Ilanptquantenzahl. 



The reader will think that this is not a new condition, but only a 

 futile way of rc-stating the condition laid upon the angular momentum. 

 So it might be, in this case. But when we come to the more complex 

 cases, we shall find that the two conditions diverge from one another. 

 Which of the two can be generalized, ij either? Only experience can show. 



I will describe one more distincti\e feature of the permissible orbits; 

 it may seem more impressive than either of the others. 



We have seen that the frequency of the radiation emitted, when the 

 hydrogen atom passes from one stationary state to another — say from 

 the state of energy — Rhn'- to that of energy — Rh/n"'- — is 



R R 



which maN' be written 



R 



n -n 



,Jn'-n"){n' + n"). (20) 



Suppose that «' — »"=!, that is, that the transition occurs between 

 two adjacent stationary states of the atom; and let h' and ii" increase 

 indefiniteh'. In tlu' limit we shall have 



Lin, .=?^. (21) 



Accepting the atom-model with the electron rexolving in a circular 

 orbit, we take from (18) the value for the period of the re\olution, 

 substitute for K by the aid of (10), and arri\e at this expression for the 

 frequency of the re\()lution: 



i^'=v/2Trr = V»R^'/2Tn"eWm^ (22) 



Comparing this expression for co' with the expression for Lim v in 

 (21), we see that they are iiKiiticil, if 



R = 2Tr-mtie\h^ 



and this will be recognized as being that very NaUie ol R wliich was 

 given in equation (13), as the value established by experiment. Thus 

 the experimental value of R is such that 



Lim 03 = Lim v. (23) 



In this equation the symbol w stands for the frequency of revolution 

 of the electron in its orbit, when the energy of the atom is —Rhn-. 

 It therefore stands for ilie fre(iiionc\- of the radiation wliich the atom 



