The atom and the Bohr theory of its structure

by Helge Holst; Hendrik Anthony Kramers

The one electron of hydrogen will, upon being captured, first be at “rest” when it reaches the 1₁-path, and we might perhaps be led to expect that in the atoms with greater nuclear charges the electrons in the normal state also would be in the one quantum orbit 1₁, because to this corresponds the least energy in hydrogen. This assumption formed actually the basis of Bohr’s work of 1913 on the structure of the heavier atoms. It cannot be maintained, however. Considerations of theoretical and empirical nature lead to the assumption that the electrons which already are gathered about the nucleus can make room only to a certain extent for new ones, moving in orbits of the same principal quantum number. Those electrons which are captured later are kept at an appropriate distance; they are, for instance, prevented from passing from a 3-quantum orbit to a 2-quantum one, if the number of electrons moving in 2-quantum orbits has reached a certain maximum value. When it is said that the captured electrons end in the stationary state which corresponds to the least energy, it must, therefore, mean, not the 1-quantum orbit, but the innermost possible under the existing circumstances. The final result will be that the electrons are distributed in groups, which are characterized each by their quantum numbers in such a way that passing from the nucleus to the surface of the atom, the successive groups correspond to successive integer values of the quantum number, the innermost group being characterized by the quantum number one. Moreover, each group is subdivided into sub-groups corresponding to the different values which the auxiliary quantum number may take.

That the electrons first collected keep the latecomers at an appropriate distance must be understood with reservations; a new electron moving in an elongated orbit can very well come into the territory already occupied; in fact, it may come closer to the nucleus than some of the innermost groups of electrons. In case an outer electron thus dives into the inner groups, it makes a very short visit, travelling about the nucleus like a comet which at one time on its elongated orbit comes in among the planets and perhaps draws closer to the sun than the innermost planet, but during the greater part of its travelling time moves in distant regions beyond the boundaries of the planetary system. It is a very important characteristic of the Bohr theory of atomic architecture that the outer electrons thus penetrate far into the interior of the atom and thus chain the whole system together.

Such a “comet electron” has, however, a motion of a very different nature from that of a comet in the solar system. Let us suppose that the nuclear charge is 55 (Caesium), that there already are fifty-four electrons gathered tightly about the nucleus, and that No. 55 in an orbit consisting of oblong loops moves far away from the nucleus, but at certain times comes in close to it. Then, for the greater part of its orbit, this electron will be subject to approximately the same attraction as the attraction towards one single charge, as a hydrogen nucleus; but when No. 55 comes within the fifty-four electrons it will for a very short time be influenced by the entire nuclear charge 55. Together with the nearness of the nucleus, this will cause No. 55 to acquire a remarkably high velocity and to move in an orbit quite different from the elliptical one it followed outside. Moreover, the great velocity of the electron during its short visit to the nucleus is in a considerable degree determinative of its principal quantum number; this will be higher than would be expected from the dimensions of the outer part of the orbit if we supposed the motion to take place about a hydrogen nucleus (cf. Figs. 27 and 29).

After these general remarks we shall try in a few lines to sketch the Bohr theory of the structure of the atomic systems from the simplest to the most complicated. We shall not examine the entire periodic system with its ninety-two elements, but here and there we shall bring to light a trait which will illustrate the problem—partly in connection with the schematic representations in the atomic diagrams at the end of the book.

Description of the Atomic Diagrams.

The curves drawn represent parts of the orbital loops of the electrons in the neutral atoms of different elements. Although the attempt has been made to give a true picture of these orbits as regards their dimensions, the drawings must still be considered as largely symbolic. Thus in reality the orbits do not lie in the same plane, but are oriented in different ways in space. It would have been impracticable to show the different planes of the orbits in the figure. Moreover, there is still a good deal of uncertainty as to the relative positions of these planes. On this account the orbits belonging to the same sub-group, i.e., designated by the same quantum numbers, are placed in a symmetric scheme in the sketch. For groups of circular orbits the rule has been followed to draw only one of them as a circle, while the others in the simpler atoms are drawn in projection as ellipses within the circle, and in the more complicated atoms are omitted entirely. The two circular orbits of the helium atom are both drawn in projection as ellipses. Further, for the sake of clearness, no attempt has been made to draw the inner loops of the non-circular orbits of electrons which dive into the interior of the atom. In lithium only, the inner loop of the orbit of the 2₁ electron has been shown by dotted lines.

In order to distinguish the groups of orbits with different principal quantum numbers two colours have been used, red and black, the red indicating the orbits with uneven quantum numbers, as 1, 3, 5, the black those with even quantum numbers, as 2, 4, 6. Wherever possible the nucleus is indicated by a black dot; but in the sketches of atoms with higher atomic numbers the 1-quantum orbits are merged into one little cross and the nucleus has been omitted. It should be noticed that the radium atom is drawn on a scale twice as great as that for the other atoms.

We shall begin with the capture of the first electron. If the nucleus is a hydrogen nucleus the hydrogen atom is completed when the electron has come into the 1₁ orbit, a circle with diameter of about 10⁻⁸ cm. (cf. the diagram). If the nucleus had had a greater nuclear charge the No. 1 electron would have behaved in the same way, but the radius of its orbit would have been less in the same ratio as the nuclear charge was greater. For a lead nucleus, with charge (atomic number) 82, the radius of the 1₁ orbit is ¹/₈₂ that of the hydrogen 1₁ orbit. Since atoms with high atomic numbers thus collect the electrons more tightly about them it is understandable that, in spite of their greater number of electrons, they can be of the same order of magnitude as the simpler atoms.

Let us now examine the helium atom. The first electron, which its nucleus (charge 2) catches, moves as shown in a circle 1₁, but with a smaller radius than in the case of the hydrogen atom. Electron No. 2 can be caught in different ways, and the closer study of the conditions prevailing here, which are still comparatively simple since there are only two electrons, has been of greatest importance in the further development of the whole theory. We cannot go into it here, but must content ourselves with saying that the stable final result of the binding of the second electron consists in the two electrons moving in circular 1-quantum orbits of the same size with their planes making an angle with each other (cf. the diagram). This state has a very stable character, and the helium atom is therefore very disinclined to interplay with other atoms, with other helium atoms as well as with those of other elements. Helium is therefore monatomic and a chemically inactive gas.

In all atomic nuclei with higher charges than the helium nucleus the first two orbits are also bound into two 1-quantum circular orbits at an angle with each other; this group cannot take up any new electron having the same principal quantum number. It takes on an independent existence and forms the innermost electron group in all atoms of atomic number higher than 2.