On the quantum theory of radiation and the structure of the atom E-Book

Bohr Niels

• Herausgeber: Balungi Francis
• Kategorie: Lebensstil
• Sprache: Englisch

Veröffentlichungsjahr: 2024

Beschreibung

IN a series of papers in this periodical the present writer has attempted to give the outlines of a theory of the constitution of atoms and molecules by help of a certain application of the Quantum theory of radiation to the theory of the nucleus atom. As the theory has been made a subject of criticism, and as experimental evidence of importance bearing on these questions has been obtained in the meantime, an attempt will be made in this paper to consider some points more closely.

Leseprobe

Table of Contents

XLII. On the Quantum Theory of Radiation and the Structure of the Atom.      5

§ 1. General assumptions.      9

§ 2. Spectra emitted from systems containing only one electron.      15

§ 3. Spectra emitted from systems containing more than one electron.      21

§ 4. The high frequency spectra of the elements.      28

FOOTNOTES:      30

XLII. On the Quantum Theory of Radiation and the Structure of the Atom.

By N. BOHR, Dr. phil. Copenhagen; p.t. Reader in Mathematical Physics at the University of Manchester[1].

@Bill stone services ltd2024

https://bit.ly/billstoneservicesltd

IN a series of papers in this periodical[2] the present writer has attempted to give the outlines of a theory of the constitution of atoms and molecules by help of a certain application of the Quantum theory of radiation to the theory of the nucleus atom. As the theory has been made a subject of criticism, and as experimental evidence of importance bearing on these questions has been obtained in the meantime, an attempt will be made in this paper to consider some points more closely.

§ 1. General assumptions.

According to the theory proposed by Sir Ernest Rutherford, in order to account for the phenomena of scattering of -rays, the atom consists of a central positively charged nucleus surrounded by a cluster of electrons. The nucleus is the seat of the essential part of the mass of the atom, and has linear dimensions exceedingly small compared with the distances apart of the electrons in the surrounding cluster. From the results of experiments on scattering of alpha rays, Rutherford concluded that the charge on the nucleus corresponds to a number of electrons per atom approximately equal to half the atomic weight. Concordant evidence from a large number of very different phenomena has led to the more definite assumption that the number of electrons per atom is exactly equal to the atomic number, i.e., the number of the corresponding element in the periodic table. This view was first proposed by van den Broek[3]. While the nucleus theory has been of great utility in explaining many important properties of the atom[4], on the other hand it is evident that it is impossible by its aid to explain many other fundamental properties if we base our considerations on the ordinary electrodynamical theory; but this can hardly be considered as a valid objection at the present time. It does not seem that there is any escape from the conclusion that it is impossible to account for the phenomena of temperature radiation on ordinary electrodynamics, and that the modification to be introduced in this theory must be essentially equivalent with the assumptions first used by Planck in the deduction of his radiation formula[5].

These assumptions are known as the Quantum theory. In my previous paper it was attempted to apply the main principles of this theory by introducing the following general assumptions:— A. An atomic system possesses a number of states in which no emission of energy radiation takes place, even if the particles are in motion relative to each other, and such an emission is to be expected on ordinary electrodynamics. The states are denoted as the “stationary” states of the system under consideration.

B. Any emission or absorption of energy radiation will correspond to the transition between two stationary states. The radiation emitted during such a transition is homogeneous and the frequency is determined by the relation

where is Planck’s constant and , and , are the energies of the system in the two stationary states.

C. That the dynamical equilibrium of the systems in the stationary states is governed by the ordinary laws of mechanics, while these laws do not hold for the transition from one state to another.

D. That the various possible stationary states of a system consisting of an electron rotating round a positive nucleus are determined by the relation

where is the mean value of the kinetic energy of the system, the frequency of rotation, and a whole number.

It will be seen that these assumptions are closely analogous to those originally used by Planck about the emission of radiation in quanta, and about the relation between the frequency of an atomic resonator (of constant frequency) and its energy. It can be shown that, for any system containing one electron rotating in a closed orbit, the assumption C and the relation (2) will secure a connexion between the frequency calculated by (1) and that to be expected from ordinary electrodynamics, in the limit where the difference between the frequency of the rotation of the electron in successive stationary states is very small compared with the absolute value of the frequency (see IV. p. 5). On the nucleus theory this occurs in the region of very slow vibrations. If the orbit of the electron is circular, the assumption D is equivalent to the condition that the angular momentum of the system in the stationary states is an integral multiple of . The possible importance of the angular momentum in the discussion of atomic systems in relation to Planck’s theory was first pointed out by J. W. Nicholson[6].

In paper I. it was shown that the above assumptions lead to an interpretation of the Balmer formula for the hydrogen spectrum, and to a determination of the Rydberg constant which was in close agreement with the measurements. In these considerations it is not necessary to make any assumption about the degree of excentricity of the orbit of the electron, and we shall see in the next section that it cannot be assumed that the orbit is always circular.

So far we have considered systems which contain only one electron, but the general validity of the assumptions A and B seems strongly supported by the fact that they offer a simple interpretation of the general principle of combination of spectral lines (see IV. p. 2).

This principle was originally discovered by Ritz to hold for the ordinary series spectra of the elements. It has recently acquired increased interest by Fowler’s work on the series spectra of enhanced lines emitted from many elements when subject to a powerful electric discharge. Fowler showed that the principle of combination holds for these spectra although the laws governing the numerical relation between the lines at an important point (see section 3) differed from those of the ordinary series spectra. There is also, as we shall see in section 4, some indication that the principle holds for the high frequency spectra revealed by interference in crystals. In this connexion it may also be remarked that the assumption A recently has obtained direct support by experiments of A. Einstein and J. W. de Haas[7], who have succeeded in detecting and measuring a rotational mechanical effect produced when an iron bar is magnetized. Their results agree very closely with those to be expected on the assumption that the magnetism of iron is due to rotating electrons, and as pointed out by Einstein and Haas, these experiments therefore indicate very strongly that electrons can rotate in atoms without emission of energy radiation.

When we try to apply assumptions, analogous with C and D, to systems containing more than one electron, we meet with difficulties, since in this case the application of ordinary mechanics in general does not lead to periodic orbits. An exception to this, however, occurs if the electrons are arranged in rings and rotate in circular orbits, and from simple considerations of analogy the following assumption was proposed (see I. p. 24).

E. In any atomic or molecular system consisting of positive nuclei and electrons in which the nuclei are at rest relative to each other, and the electrons move in circular orbits, the angular momentum of each electron round the centre of its orbit will be equal to in the “normal” state of the system, i.e. the state in which the total energy is a minimum.