The atom and the Bohr theory of its structure

by Helge Holst; Hendrik Anthony Kramers

Moreover, the terms (c[f. p. 59]) may often be approximately given by the Rydberg formula

K

(n + α) ²

where K has about the same value as in hydrogen, and α can take on a series of values α₁, α₂ ... αₖ, while n takes on integer values. Since we thus determine the different lines by assigning values to the two integers n and k in each term, we have in this respect something like the fine structure in the hydrogen spectrum, where the stationary states are determined by a principal quantum number and an auxiliary quantum number. The spectra of which we are speaking here, and for which the terms have the form given above, are often called arc spectra, because they are emitted particularly in the light from the electric arc or from the vacuum tube. We must expect that the similarity which exists in the law for the distribution of spectral lines will correspond to a similarity in the atomic processes of hydrogen and the other elements.

The hydrogen atom emits radiation corresponding to the different spectral lines when an electron from an outer stationary orbit jumps, with a spring of varying size, to an orbit with lower number, and at last finds rest in the innermost orbit in a normal state, where the energy of the atom is as small as possible. Similarly, we must assume that the electrons in other atoms, during processes of radiation, may proceed in towards the nucleus until they are collected as tightly as possible about the nucleus, corresponding to the normal state of the atom, where its energy content is as small as possible: “capture” of electrons by the nucleus. The region in space which, in the normal state, includes the entire electron system, must be assumed to be of the same order of magnitude as the dimensions of the atom and molecule which are derived from the kinetic theory of gases. This normal state may be called a “quiescent” state, since the atom cannot emit radiation until it has been excited by the introduction of energy from without. This excitation process consists of freeing one (or more) electrons, in some way or other, from the normal state and either removing it out to a stationary orbit farther away from the nucleus or ejecting it completely from the atom. Not all electrons can be equally easily removed from the quiescent state. Those moving in small orbits near the nucleus will be tighter bound than those moving in larger orbits farther from the nucleus. The arc spectrum is now caused by driving one of the most loosely bound electrons out into an orbit farther from the nucleus or removing it completely from the atom. In the latter case the rest of the atom, which with the loss of the negative electron becomes a positive ion, easily binds another electron, which, with the emission of radiation, corresponding to lines of the series spectrum, can approach closer to the nucleus.

Let us now assume, first, that this radiating electron moves at so great a distance from the nucleus and the other electrons that the entire inner system can be considered as concentrated in one point; then the situation is quite as if we had to deal with a hydrogen atom. If the atomic number is as high as 29 (copper), for instance, the nuclear charge will consist of twenty-nine elementary quanta of positive electricity; but since there are twenty-eight electrons in the inner system, the resultant effect is that of only one elementary quantum of positive electricity, as in the case of a hydrogen nucleus. The spectral lines which are emitted in the jumps between the more distant paths will be practically the same as hydrogen lines. But, since in the jumps between these distant orbits, very small energy quanta will be emitted, the frequencies are very small, the wave-lengths very great, i.e., the lines in question lie far out in the infra-red.

Fig. 29.—Different stationary orbits which the
outermost (11th) electron of sodium may describe.

When the electron has come in so close to the nucleus that the distances in the inner system cannot be assumed to be small in comparison to the distance of the outer electron from the nucleus, the situation is changed. The force with which the nucleus and the inner electrons together will work upon the outer electron will be appreciably different from the inverse square law of attraction of a point charge. The consequence of this difference is that the major axis in the ellipse of the electron rotates slowly in the plane of the orbit as described in case of the theory of the fine structure of the hydrogen lines ([cf. p. 146]), and even if the cause is different the result is the same; the orbit of the outer electron in the stationary states will be characterized by a quantum number n and an auxiliary quantum number k. If the electron comes still closer to the nucleus, its motion is even more complicated. When the electron in its revolution is nearest the nucleus it will be able to dive into the region of the inner electrons, and we can get motions like those shown in [Fig. 29] for one of the eleven sodium electrons. The inner dotted circle is the boundary of the inner system which is given by the nucleus and the ten electrons remaining in the “quiescent” state—little disturbed by the restless No. 11. In the figure we can see greater or smaller parts of No. 11’s different stationary orbits with principal quantum numbers 3 and 4. We shall not account further for the different orbits and the spectral lines produced by the transitions between orbits, but shall merely remark that the yellow sodium line, which corresponds to the Fraunhofer D-line ([cf. p. 49]), is produced by the transition 3₂-3₁, between two orbits with the same principal quantum number. The sketch shows to a certain degree how fully many details of the atomic processes can already be explained. The theory can even give a natural explanation of why the D-line is double.

We have restricted ourselves to the case where only one electron is removed from the normal state of the neutral atom. It may, however, happen that two electrons are ejected from the atom so that it becomes a positive ion with two charges. When an electron from the outside is approaching this doubly charged ion it will, at a distance, be acted upon as if the ion were a helium nucleus with two positive charges. The situation, in other words, will be as in the case of the false hydrogen spectrum ([cf. p. 142]), where the constant K in the formula for the hydrogen spectrum is replaced by another which is very close to 4K. But if the atom is not one of helium, but one with a higher atomic number, the stationary orbits of the outer electron which approach closely to the nucleus will not coincide exactly with those in the ionized helium atom, corresponding to the fact that the terms in the formula for the spectrum, instead of the simple form 4K/n², have the more complicated form 4K/(n + α)². Spectra of this nature are often called spark spectra, since they appear especially strong in electric sparks; they appear also in light from vacuum tubes, when an interruptor is placed in the circuit, making the discharge intermittent and more intense.

An atom with several electrons can, however, be much more violently excited from its quiescent state when an electron in the inner region of the atom is ejected by a swiftly moving electron (a cathode ray particle or a β-particle from radium) which travels through the atom. Such an invasion produces a serious disturbance in the stability of the electron system; a reconstruction follows, in which one of the outer, more loosely bound electrons takes the vacant position. In the transitions, in which these outer electrons come in, rather large energy quanta are emitted. The emitted radiation has therefore a very high frequency; monochromatic X-rays are thus emitted. Since these have their origin in processes far within the atom, it can be understood that the different elements have different characteristic X-ray spectra, which can give very valuable information about the structure of the electron system ([cf. p. 91]).