# Introduction to The Quantum Theory Of Line-Spectra

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Bohr tries to develop a theory of line-spectra based on the fundamental ideas from:

- Planck in his theory of temperature radiation and
- Sir Ernest Rutherford in his atomic nucleus

His theory only explained the case of periodic systems, not the difference between the hydrogen spectrum and the spectra of other elements, or the effects on the hydrogen spectrum of external electric and magnetic fields.

Recently, Sommerfeld fixed this by:

- introducing a simple type of non-periodic motion
- taking into account the small variation of the mass of the electron with its velocity

These explained the fine-structure of the hydrogen lines which conform with the measurements.

Sommerfeld’s theory offered a clue to the interpretation of the more intricate structure of the spectra of other elements. Briefly afterwards, Epstein1 and Schwarzschild2, independent of each other adapted Sommerfeld’s ideas to the treatment of a more extended class of non-periodic systems.

They were able to explain the effect of an electric field on the hydrogen spectrum discovered by Stark.

Subsequently, Sommerfeld3 himself and Debye4 indicated an interpretation of the effect of a magnetic field on the hydrogen spectrum which is an important step towards a detailed understanding of this phenomenon.

In spite of the great progress involved in these investigations many difficulties of fundamental nature remained unsolved, not only as regards

The problems is the limited applicability of the methods used in calculating the frequencies of the spectrum of a given system, especially the polarisation and intensity of the emitted spectral lines.

These difficulties are intimately connected with the radical departure from the ordinary ideas of mechanics and electro

dynamics involved in the main principles of the quantum theory, and with the fact that it has not been possible hitherto to replace these ideas by others forming an equally consistent and developed structure. Also in this respect, however, great progress has recently been obtained by the work of Einstein1) and Ehrenfest.2

On this state of the theory it might therefore be of interest to make an attempt to discuss the different applications from a uniform point of view, and especially to consider the underlying assumptions in their relations to ordinary mechanics and electrodynamics.

Such an attempt has been made in the present paper, and it will be shown that it seems possible to throw some light on the outstanding difficulties by trying to trace the analogy between the quantum theory and the ordinary theory of radiation as closely as possible.

The paper is divided into four parts.

Part I contains a brief discussion of the general principles of the theory and deals with the application of the general theory to periodic systems of one degree of freedom and to the class of non-periodic systems referred to above.

Part II contains a detailed discussion of the theory of the hydrogen spectrum in order to illustrate the general

Part III contains a discussion of the questions arising in connection with the explanation of the spectra of other elements.

Part IV contains a general discussion of the theory of the constitution of atoms and molecules based on the application of the quantum theory to the nucleus atom.

Copenhagen, November 1917.