THE QUANTUM 
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4. The Quantum Theory of Spectral Series 
The application of the quantum theory to the study of 
spectra continues to excite very great interest. This work, 
which will always be associated with the name of the Danish 
physicist Niels Bohr,* is based on two fundamental ideas. The 
first is a natural extension of the principle involved in the photo 
electric effect. Bohr argued that when an atom emits mono 
chromatic radiation of frequency v, it must be because the atomic 
system has lost energy of amount hv. Thus 
hv = HL - H. 
i : 6 
where H a and H e are the values of the energy in the two states f 
of the atomic system under consideration. This relation, 
generally known as Bohr’s Frequency Condition, at once explains 
the Combination Law in connection with spectral series. This 
law states that the frequencies of the lines of a spectrum are 
given by the difference between pairs of terms of a sequence. 
But a second application of the quantum principle is required 
to fix the “ stationary states ” of the atomic system, that is 
to determine the permissible orbits by “ quantizing the orbits.” 
In the earlier work this was effected by employing the sugges 
tion of J. W. Nicholson that h may be regarded as a natural unit 
of angular momentum. The determination of the orbits is 
simple when a single electron is moving in the field of a positively 
charged nucleus. 
By the application of these hypotheses Bohr was successful 
in deducing Balmer’s and certain similar series emitted by 
hydrogen, and the enhanced spectrum of helium, i.e. the spec 
trum given by helium which has lost one electron so that there 
is a surplus positive charge. The same principles have also been 
employed in the explanation of the spectra of other elements. 
In particular we must notice the remarkable agreement 
between the value of the fundamental Rydberg constant of 
spectroscopy deduced by Bohr and that found as the result of 
observation. Bohr’s value for this fundamental frequency is 
2 n 2 me i 
h 3 
1:7 
where e is the charge in ordinary electrostatic units, m is the 
* Bohr, Phil. Mag., vol. 26, pp. 1, 476, 857, 1913. 
T is convenient to use the subscript letters a and e to distinguish 
e ween the initial (antecedent) state and the final (end) state of the 
system. v ’