1913 N Bohr Philos Mag 26 1 On the Constitution of Atoms and Molecules N Bohr Dr phil Copenhagen Received July 1913 Introduction In order to explain the results of experiments on scattering of rays by matter Prof Rutherford1 has given a theory of the structure of atoms According to this theory the atom consist of a positively charged nucleus surrounded by a system of electrons kept together by attractive forces from the nucleus the total negative charge of the electrons is equal to the positive charge of the nucleus Further the nucleus is assumed to be the seat of the essential part of the mass of the atom and to have linear dimensions exceedingly small compared with the linear dimensions of the whole atom The number of electrons in an atom is deduced to be approximately equal to half 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 as those in question seems to be necessary in order to account for the results of the experiments on large angle scattering of the rays 2 In an attempt to explain some of the properties of matter on the basis of this atom model we meet however with difficulties of a serious nature arising from the apparent instability of the system of electrons difficulties purposely avoid in atom models previously considered for instance in the one proposed by Sir J J Thomson3 According to the theory of the latter the atom consist of a sphere of uniform positive electrification inside which the electrons move in circular orbits 1 E Rutherford Phil Mag XXI p 669 1911 See also Geiger and Marsden Phil Mag April 1913 3 J J Thomson Phil Mag VII p 237 1904 2 1 The principal difference between the atom models proposed by Thomson and Rutherford consist in the circumstance that the forces acting on the electrons in the atom model of Thomson allow of certain configurations and motion of the electrons for which the system is in a stable equilibrium such configurations however apparently do not exist for the second atom model The nature of the difference in question will perhaps be most clearly seen by noticing that among the quantities characterizing the fist atom a quantity appears the radius of the positive sphere of dimensions of a length and of the same order of magnitude as the linear extension of the atom while such a length does not appear among the quantities characterizing the second atom 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 undergone essential alterations in recent years owing to the development of the theory of the energy radiation and the direct affirmation of the new assumptions introduced in this theory found by experiments on very different phenomena such as specific heats photoelectric effect Ro ntgen rays c The result of the discussion of these questions seems to be a general acknowledgment of the inadequacy of the classical elecrtodynamics in describing the behaviour of system of atomic size 4 Whatever the alteration in the laws of motion of the electrons may be it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics i e Planck s constant or as it often is called the elementary quantum of action By the introduction of this quantity the question of the stable configuration of the electrons in the atoms is essentially changed as this constant is of such dimensions and magnitude that it together with the mass and charge of the particles can determine a length of the order of magnitude required This paper is an attempt to show that the application of the above ideas to Rutherford s atom model affords a basis for a theory of the constitution of atoms It will further be shown that from this theory we are led to a theory of the constitution of molecules In the present first part of the paper the mechanism of the binding of electrons by a positive nucleus is discussed in relation to Planck s theory It will be shown that it is possible from the point of view taken to account in a simple way for the law of the line spectrum of hydrogen Further reason are given for a principal hypothesis on which the considerations contained in the following parts are based 4 See f inst Theorie du ravonnement et les quanta Rapports de la rennion a Bruxeless Nov 1911 Paris 1912 2 I wish here to express my thinks to Prof Rutherford for his kind and encouraging interest in this work Part I Binding of Electrons by Positive Nuclei 1 General Considerations The inadequacy of the classical electrodynamics in accounting for the properties of atoms from an atom model as Rutherford s will appear very clearly if we consider a simple system consisting of a positively charged nucleus of very small dimensions and an electron describing closed orbits around it For simplicity let us assume that the mass of the electron is negligibly small in comparison with that of the nucleus and further that the velocity of the electron is small compared with that of light Let us at first assume that there is no energy radiation In this case the electron will describe stationary elliptical orbits The frequency of revolution and the major axis of the orbit 2a will depend on the amount of energy W which must be transferred to the system in order to remove the electron to an infinitely great distance apart from the nucleus Denoting the charge of the electron and of the nucleus by e and E respectively and the mass of the electron by m we thus get 2 W 3 2 eE 1 2a eE m W Further it can easily be shown that the mean value of the kinetic energy of the electron taken for a whole revolution is equal to W We see that if the value of W is not given there will be no values of and a characteristic for the 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 this case the electron will no longer describe stationary orbits W will continuously increase and the electron will approach the nucleus describing orbits of smaller and smaller dimensions and with greater and greater frequency the electron on the average gaining in kinetic energy at the same time as the whole system loses energy This process will go on until the dimensions of 3 the orbit are the same order of magnitude as the dimensions of the electron or those of the