20 BIOLOGICAL EFFECTS OF RADIATION 



On computing the energy possessed by the atom when the electron is 

 in one or another of these various orbits, it is found that the energy values 

 agree precisely with those of the stationary states deduced from the 

 Balmer series and other series in the spectrum of hydrogen! The com- 

 puted energy value corresponding to the nth orbit (that for which the 

 angular momentum is n/i/27r) when reckoned from that of the first orbit 

 taken as zero of energy, is given by the formula,^ 



27rVwie'Yi 

 h^ \ n 



a 



Let us subtract the energy value for the second orbit from that for the nth 

 orbit, and divide the difference by h to get the frequency of that photon, 

 the absorption of which should transfer the electron from the second orbit 

 to the nth. We get: 



27r>me* 



V = 



¥ 



(■-*)-( 



1 - 





and now comparing this with Balmer's formula we see that they are 

 identical if the combination 2tt -iime'^/h^ is equal to the observational 

 constant R — and this turns out to be so! 



One immediately inquires: should there not also be a series corre- 

 sponding to transfers of the electron from the first orbit into the outer 

 orbits, given therefore by the formula: 



So there is ! It is the Lyman series, discovere.d much later than the Balmer 

 series for the sole reason that it lies far out in the ultra-violet, while that 

 described by Balmer's formula is very conveniently placed in the visible 

 spectrum. The Lyman series is the better of the two to keep in mind, 

 for its lines correspond to absorption by normal atoms — the case to which 

 I have hitherto restricted my exposition — whereas the Balmer lines 

 correspond to absorption by excited atoms. 



Were I to attempt to give even an inkling of the ways in which Bohr's 

 ideas were developed in order to interpret more complicated spectra — 

 developments in the course of which many other striking numerical 

 agreements between the theory and the data were discovered — the char- 

 acter of this essay would be entirely distorted. It must suffice to say 

 that the successes of the theory were such, that the word "orbit" has 

 become practically a synonym for "stationary state" in the common 

 language of physicists. Even theorists who in their own thinking make 



^ The symbol m stands for the mass of the electron, the symbol ju for the ratio 

 M/{M + m), where M represents the mass of the nucleus. 



