N. Bohr, Philos. Mag. 26, 11913On the Constitution of Atoms and MoleculesN. Bohr,Dr. phil. Copenhagen(Received July 1913)IntroductionIn order to explain the results of experiments on scattering of α rays bymatter Prof. Rutherford1has given a theory of the structure of atoms.According to this theory, the atom consist of a positively charged nucleussurrounded by a system of electrons kept together by attractive forces fromthe nucleus; the total negative charge of the electrons is equal to the positivecharge of the nucleus. Further, the nucleus is assumed to be the seat ofthe essential part of the mass of the atom, and to have linear dimensionsexceedingly small compared with the linear dimensions of the whole atom.The number of electrons in an atom is deduced to be approximately equal tohalf the atomic weight. Great interest is to be attributed to this atom-model;for, as Rutherford has shown, the assumption of the existence of nuclei, asthose in question, seems to be necessary in order to account for the resultsof the experiments on large angle scattering of the α rays.2In an attempt to explain some of the properties of matter on the basisof this atom-model we meet, however, with difficulties of a serious naturearising from the apparent instability of the system of electrons: difficultiespurposely avoid in atom-models previously considered, for instance, in theone proposed by Sir. J.J. Thomson3According to the theory of the latterthe atom consist of a sphere of uniform positive electrification, inside whichthe electrons move in circular orbits.1E. Rutherford, Phil. Mag. XXI. p. 669 (1911)2See also Geiger and Marsden, Phil. Mag. April 1913.3J.J. Thomson, Phil. Mag. VII. p. 237 (1904).1The principal difference between the atom-models proposed by Thomsonand Rutherford consist in the circumstance that the forces acting on theelectrons in the atom-model of Thomson allow of certain configurations andmotion of the electrons for which the system is in a stable equilibrium; suchconfigurations, however, apparently do not exist for the second atom- model.The nature of the difference in question will perhaps be most clearly seen bynoticing that among the quantities characterizing the fist atom a quantityappears – the radius of the positive sphere – of dimensions of a length and ofthe same order of magnitude as the linear extension of the atom, while sucha length does not appear among the quantities characterizing the secondatom, viz. the charges and masses of the electrons and the positive nucleus;nor can it do determined solely by help of the latter quantities.The way of considering a problem of this kind has, however, undergoneessential alterations in recent years owing to the development of the theoryof the energy radiation, and the direct affirmation of the new assumptionsintroduced in this theory, found by experiments on very different phenomenasuch as specific heats, photoelectric effect, R¨ontgen-rays, & c. The result ofthe discussion of these questions seems to be a general acknowledgment ofthe inadequacy of the classical elecrtodynamics in describing the behaviourof system of atomic size.4Whatever the alteration in the laws of motion ofthe electrons may be, it seems necessary to introduce in the laws in questiona quantity foreign to the classical electrodynamics, i.e., Planck’s constant, oras it often is called the elementary quantum of action. By the introductionof this quantity the question of the stable configuration of the electrons inthe atoms is essentially changed, as this constant is of such dimensions andmagnitude that it, together with the mass and charge of the particles, candetermine a length of the order of magnitude required.This paper is an attempt to show that the application of the above ideasto Rutherford’s atom-model affords a basis for a theory of the constitutionof atoms. It will further be shown that from this theory we are led to atheory of the constitution of molecules.In the present first part of the paper the mechanism of the binding ofelectrons by a positive nucleus is discussed in relation to Planck’s theory. Itwill be shown that it is possible from the point of view taken to account ina simple way for the law of the line spectrum of hydrogen. Further, reasonare given for a principal hypothesis on which the considerations containedin the following parts are based.4See f. inst., “Theorie du ravonnement et les quanta.” Rapports de la rennion aBruxeless, Nov. 1911, Paris, 1912.2I wish here to express my thinks to Prof. Rutherford for his kind andencouraging interest in this work.Part I. – Binding of Electrons by Positive Nuclei.§ 1. General ConsiderationsThe inadequacy of the classical electrodynamics in accounting for the prop-erties of atoms from an atom-model as Rutherford’s, will appear very clearlyif we consider a simple system consisting of a positively charged nucleus ofvery small dimensions and an electron describing closed orbits around it.For simplicity, let us assume that the mass of the electron is negligibly smallin comparison with that of the nucleus, and further, that the velocity of theelectron is small compared with that of light.Let us at first assume that there is no energy radiation. In this case theelectron will describ e stationary elliptical orbits. The frequency of revolutionω and the major-axis of the orbit 2a will depend on the amount of energyW which must be transferred to the system in order to remove the electronto an infinitely great distance apart from the nucleus. Denoting the chargeof the electron and of the nucleus by – e and E respectively and the massof the electron by m, we thus getω =√2π·W3/2eE√m, 2a =eEW. (1)Further, it can easily be shown that the mean value of the kinetic energy ofthe electron taken for a whole revolution is equal to W . We see that if thevalue of W is not given, there will be no values of ω and a characteristic forthe system in question.Let us now, however, take the effect of the energy radiation into account,calculated in the ordinary way from the acceleration of the electron. In thiscase the electron will no longer describe stationary orbits. W will continu-ously increase, and the electron will approach the nucleus describing orbitsof smaller and smaller dimensions, and with greater and greater frequency;the electron on the average gaining in kinetic energy at the same time as thewhole system loses energy. This process will go on until the dimensions of3the orbit are