The Distribution of Electrons among Atomic Levels

Edmund C. Stoner
Philosophical Magazine October 1924
Series 6, Volume 48, No. 286
p. 719 - 736

Communicated by R.H. Fowler, M.A.


1. Introduction.

The scheme for the distribution of electrons among the completed sub-levels in atoms proposed by Bohr* is based on somewhat arbitrary arguments as to symmetry requirements; it is also incomplete in that all the sub-levels

* Bohr, Zeit. f. Phys. ix p. 1 (19220 or 'The Theory of Spectra and Atomic Constitution,' Essay III. (Cambridge, 1922).


known to exist are not separately considered. It is here suggested that the number of electrons associated with a sub-level is connected with the inner quantum number characterizing it, such a connexion being strongly indicated by the term multiplicity observed for optical spectra. The distribution arrived at in this way necessitated no essential change in the process of atom-building pictured by Bohr; but the final result is somewhat different, in that a greater concentration of electrons in outer sub-groups is indicated, and the inner sub-groups are complete at an earlier stage. The available evidence as to the final distribution is discussed, and is not unfavorable to the scheme proposed.

2. Classification and number of X-ray Levels.

The X-ray at mic levels may be conveniently classified by means of three quantum numbers -- n (total), k (azimuthal), and j (inner), as shown in Table I.

Table I. -- Classification of X-ray Levels.
["Relativity doublet" terms are bracketed.]
Level K L M
Optical term 1s 2s 2p2 2p1 3s 3p2 3p1 3d2 3d1

[N.B. In the original Table I., there appear three curly brackets, one each placed above the following groupings of two terms in the "Sub-level" row: LII and LIII; MII and MIII; MIV and MV.]

This classification has been put foward by Landé*. In contradistinction to the older schemes, such as that of Sommerfeld, it gives a satisfactory selection principle (k changes by 1, j by 1 or 0), and at the same time brings out clearly the analogy between X-ray and optical spectra. The sub-levels may, in fact, be regarded as corresponding to typical doublet-series terms, as for alkali metal arc spectra, in the way indicated in the lst row of the table.

The main criticism to be advanced against the classification

* Zeit. f. Phys. xvi. p. 391 (1922).


is that it invalidates the interpretation of terms such as LII-LIII as simple relativity doublets, although their separation is given accurately by Sommerfeld's formula. Bohr*, however, has shown that though LI-LIII was to be regarded as a relativity + screening doublet, the further subdivision into separate relativity (LII-LIII) and screening doublets (LI-LII) was not justifiable. De Broglie and Danvillier**, who adopt a scheme somewhat similar to the above, but with a larger number of subgroups point out that the "relativity doublet" separation increases in a similar way to that of the optical doublet with increase in atomic number. Landé***, in two recent papers, has traced out the anaolgy in quantitative detail. He shows that the relativity in optical doublet separations can both be represented by the same general formula and places beyond doubt that the two types of doublet are essentially similar in origin.

Now, observations on the anomalous Zeeman effect show that the optical doublets must have a magnetic origin; and although the magnetic explanations are as yet inadequate, it is justifiable to apply those ideas, which have coordinated the optical, to the case of X-rays -- in particular in the assignment of inner quantum numbers, as in the above scheme.

De Broglie and Dauvillier postulate a larger number of sublevels (6M, 10N...) in order to account for certain weak X-ray lines observed; the necessity for this, however, is not admitted by most workers, and it is undoubted that not more than 5M absorption discontinuities have been directly observed.**** The work of Robinson***** on excited electrons, moreover, seems to prove conclusively that there are only 5M, and probably 7N, levels. The experiments thus support the view that for Röntgen spectra, as for optical doublet series, the number of sublevels characterized by different j's into which a given k subdivides is restricted to two.

* Bohr and Coster, Zeit. f. Phys. xii p. 342 (1923).
** Journ. de Phys. VI. v. p. 1 (1924).
*** Zeit. f. Phys. xxiv. p. 88 (1924) and xxv. p. 96 (1924).
**** Cf. Coster, Phys. Rev. xix. p. 20 (1922); Ross, Phys. Rev. xxii. p. 221 (1923).
***** Proc. Roy. Soc. civ. p. 455 (1923).


3. Suggested Distribution of Electrons

In the classification adopted, the remarkable feature emerges that the number of electrons in each completed level is equal to double the sum of the inner quantum numbers as assigned, there being K, L, M, N, levels, when complete, 2, 8, (2 + 2 + 4), 18 (2 + 2 + 4 + 4 + 6), 32 ... electrons. It is suggested that the number of electrons associated with each sublevel separately is also equal to double the inner quantum number. The justification for this is discussed below. A summarized periodic table (Table II) is given, which shows the nature of the distribution suggested. In the table, the number of electrons in the sublevels of the atom named on the left is given by the whole of the part of the table above and to the left of the thick line which begins under the atom. Krypton, for example, has 2K, 8L, 18M, and 8N electrons.

Table II.- Suggested Distribution of Elections.

[The distribution of electrons in the atoms is given by the part
of the table above and to the left of the thick lines.]

Element Atomic
Level (n) Sub-levels (k, j)
1, 12, 12, 23, 23, 34, 34, 4

[N.B. the (6 8) at the end of the Kr row is shown with dashed parenthesis. Stoner refers to this on p. 724.]

4. Comparison with Bohr's Distribution.

A summarized Bohr's periodic table (Table III) is given for purposes of comparison. This, and also Table II., should be referred to in conjunction with a more complete table. The Bohr distribution cannot be easily put in the form of Table II., owing to the way in which the sub-groups undergo further development after reaching a first pseudocompleteness; but the relation betwen the two tables will be obvious on inspection.

Table III. -- Distribution of Electrons in Atoms,
according to Bohr.

Element Atomic
Sub-Levels, (n, k)

[N.B. - Each arrow in Table III is intended to terminate just above and to the right of the parenthesis it is pointing at. In addition, the third arrow, from (6 6 6) to (8 8 8 8 ) is the only dashed arrow of the four. Stoner refers to this on p. 724.]

It can be seen at once that the distribution proposed is equally in harmony with the essential features of the development process pictured by Bohr as his own; which means that it is equally in accord with chemical considerations which are so beautifully covered by Bohr's scheme, especially in his attribution of the similarity in chemical properties of such sequences as the rare earths to the development of underlying groups of electrons.

A question which arises is whether the Bohr (n, k) levels are to be regarded as corresponding to the (n, k) or the (n, j) in the alternative scheme; for example, whether Bohr's (2, 1) level corresponds to LI or LI + LII. The latter might seem reasonable in that (2, 2, 1) and (2, 1, 1) levels are more alike in certain respects, notably in energy


value, than (2, 2, 1) and (2, 2, 2); but the former is the direct and usual interpretation, and will be assumed here for the present. There is then a considerable difference in the assignment of electrons to (n, k) levels, the numbers running (2, 6), (2, 6, 10), and (2, 6, 10, 14) for the L, M, and N (n, k) sub-groups in place of (4, 4), (6, 6, 6), and (8, 8, 8, 8). If, however, Bohr's (n, k), for this purposes, should be taken to correspond with our (n, j) levels, the numbers to compared with Bohr's are (4, 4), (4, 8, 6), and (4, 8, 12, 8).

As to the process of up-building, analogous sequences of elements correspond exactly on both schemes to analogous developments in the number and distribution of electrons; but the reorganization of underlying groups occurs in a much simpler manner in the scheme proposed. Beginning at Sc (21), 10 electrons complete the M group (noticeably beginning when there are 2, not 4, electrons in the N group); on our view these simply fill up the vacant (n3, k3) levels, precisely 10 electrons being required; on Bohr's view the change also involves addition of electrons to the inner sub-levels -- in fact, a complete reorganization of the whole M groups. The added electrons referred to are bracketed in Table II., and the corresponding development on Bohr's scheme is indicated by the arrow in Table III. A similar process, probably beginning at Y (39), occurs when the 10 (n4, k3) electrons are added, and again, beginning at Lu (71), for the 10 (n5, k3) electrons. The (n4, k4) level requires 14 electrons, and the adding of these corresponds to the rare earth sequence; on the Bohr view, a complete reorganization of the M group occurs. The dotted brackets and dotted arrow indicate this development. [See N.B.s above.]

The present scheme, then, accounts well for the chemical properties; it differs from Bohr's in the final distributions suggested, and in the fact that inner sub-groups are completed at an earlier stage, subsequent changes being made by simple addition of electrons to outer sub-levels without reorganization of the groups as a whole.

5. Significance of Inner Quantum Numbers.

From a physical point of view, the real significance of inner quantum numbers, especially when applied to inner X-ray atomic levels, is very problematical. Evidence based on the analogous optical spectra, however, provides strong justification for the idea of the numbers of electrons


in a sub-group being related to the inner quantum number in the way assumed.

The case of the doublet series of the alkali methods only need be considered. In the atoms there is one electron external to a core composed of a completed system of electronic groups. Observations on the Zeeman effect can be correlated by assigning inner quantum numbers k and (k-1) to the atom with the electron in a k level. For p terms (k=2), j=1 or 2, giving p2 and p1, for d terms (k=3), j=2 or 3. There is actually a certain degree of arbitrariness as to the absolute value given to j ; for instance, values 1/2 and 3/2 for p2 and p1 ; 3/2 and 5/2 for d2 and d1 can be made to fit the facts equally well*. This difficulty, however, is irrelevant, for the reason given below. The inner quantum number is usually interpreted as giving the magnetic moment of the atom as a whole, and the number of possible energy states of the atom in a weak external magnetic field, in which core and light electron are no separately affected, is attributed to the number of possible orientations of the atom in virtue of space-quantization.

The actual number of possibilities is given by the multiplicity of terms in the anomalous Zeeman effect, and can be deduced very straightforwardly (in simple cases at least) from observations on the behaviour of the lines. The point which it is desired to emphasize here is that, however the inner quantum numbers are interpreted, if they are give the values used above (k and k-1), twice the inner quantum number does give the observed term multiplicity as revealed by the spectra in a weak magnetic field. (Thus in a weak magnetic field there are 2s, 2p2, and 4p1 terms.) In other word, the number of possible states of the (core + electron) system is equal to twice the inner quantum number, these 2j states being always possible and equally probable, but only manifesting themselves separately in the presence of the external field.

At present it is not clear whether the number of equally probably states indicates that the atom as a whole is always the same as concerns relative orientation of core and outer electron orbit, and can take up 2j different orientations relative to the (weak) field; or that the core takes up a definite orientation relative to the field, and the outer electron orbit can take up 2j different orientations relative

*For a fuller discussion of this whole subject, see Sommerfeld, 'Atombau und Spektrallinien,' and recent papers by Sommerfeld and Landé, e.g. Sommerfeld, Ann. der Phys. lxx. p. 32 (1923), lxxiii. p. 39 (1924) ; Landé, Zeit. f. Phys. xix. p. 112 (1921).


to the core*. (The mutual influence becomes of less relative importance as the strength of the field increases, so that ultimately the field affects electron and core separately, and the Paschen-Back effect is obtained.) There may be some quite different interpretation.

The spectral term-values themselves, in so far as they are altered by external fields, would seem to depend primarily on the outer electron orbit itself (and not so much on electron + core, as do the magnetic properties of the atom) ; and remembering this, it seems reasonable to take 2j as the number of possible equally probably orbits.

Without laying too much stress on any definite physical interpretation, or pressing the analogy too far, it may be suggested that for an inner sub-level, in a similar way, the number of possible orbits is equal to twice the inner quantum number, these orbits differing in their orientation relative to the atom as a whole. Electrons can enter a group until all the possible orbits are occupied, when the atom will possess a symmetrical structure.

That the inner quantum number are analogous to those for the alkali metals, is presumably connected with the fact that the building-up can always be regarded as occurring on a sub-structure of the inert gas atom type with completed group systems. The complicated optical multiplet series occur when there are light-electrons moving externally to incompleted group.

In brief, then, it is suggested that, corresponding roughly to the definite indication in the optical case, the number of possible states of the atom is equal to 2j ; so, for the X-ray sub-levels, 2j gives the number of possible orbits differing in orientation relative to the atoms as a whole; and that electrons can enter a sub-level until all the orbits are occupied.

6. Statistical Weight of Electrons bound in Atoms.

If electrons in the atom are distributed according to the present scheme, the interesting point is suggested that all electrons bound in the atom forming constituents of completed groups are to be regarded as having the same statistical weight, namely unity (or h3) ; for there is then one electron in each possible equally probably state.

* This general questions and the allied on of the orientation of the inert gas atoms in a magnetic field are discussed by Bohr, Ann. der Phys. lxxi. p. 228 (1923).


7. Evidence as to Electron Distribution

Unfortunately there are few properties which depend solely on the number of electrons in levels and not also on the type of level and its energy value; so that, in the present state of theory, a definite test of the merits of different distributions proposed is difficult. Some evidence, however, is available from which a few comclusions may be drawn; and the general lines of evidence on which the question must finally be decided are briefly considered.

(a) Intensities of X-ray lines.

The intensity of X-ray lines will depend in part on the number of electrons in levels between which transitions occur; a simple relation between the relative numbers of electrons in two sub-levels and the relative intensities of the lines corresponding to transitions from these to the same final level would only be expected to hold when the sub-levels are close together, so that the energy associated with each transitions is approximately the same, and when the sub-levels are of the same nk type. It has been shown for optical multiplets that the probability of possible transitions is not then dependent on the inner quantum number characterizing the terms concerned*. In the optical case, however, the outer electron switches over to a lower level, and no disturbing factors enter owing to the presence of intervening electrons between the levels concerned. For the X-ray case, on the other hand, transitions occur between levels across intervening occupied electronic orbits, which may modify the probability of transition from different j types of k orbit. -- Simple relations would only be expected for transitions between contiguous levels such as L--->K, M--->L. A straightforward theoretical interpretation of observed relative intesities is thus only possible for a few cases.

From an experimental point of view, the relative intensity of different X-ray lines is difficult to determine, except when the lines are fairly close, so that corrections otherwise necessary, which cannot at present be accurately calculated, need not be applied. In one case very accurate measurements have been made, namely for Ka1 (LIII--->K) and Ka2 (LII--->K). The result are as follows:--

a2 / a1......499.512.500.52.50

* Ornstein and Burger, Zeit. f. Phys. xxiv. p. 41 (1924).


The first three, due to Siegbahn and Zacek*, are the means of a large number of photometric measurements, agreeing closely among themselves; the last two, obtained from ionization measurements, are due to Duane and Patterson, and Duane and Stenström.

The ratio a1 / a2 is thus practically constant and equal to 2 / 1 from Fe (26) to W (74).

This result can at once be explained on the assumption that there are twice as many electrons in the LIII as in the LII sub-level. Now, in Bohr's scheme four electrons are assigned to the (2, 2) level, so that 4 electrons have to be divided between LII and LIII -- a ratio 3 / 1 or 1 / 1 for the a lines would be expected, certainly not 2 / 1.

For the Lb group, Duane and Patterson** gave for tungsten b1, b2, b3, b4 as 100, 55, 15, 9. (See Table IV for transitions involved.) The b3/b4 value again suggests the 2/1 ratio for the number of electrons assigned to the MIII and MII sub-levels. g1, g2, g3, g4 have relative intensities 100, 14, 18, 6. g2 and g3 correspond to transitions from N to L across the M group, and disturbing factors may come in, so that the g3/g2 value is not inconsistent with a 2/1 electron ratio.

The importance of disturbances due to intervening electrons must be stressed; for it should be noted that the relative intensities of components of doublets such as b3b4 and g3g4 change considerably with the atomic number, even after all the levels directly concerned are completed, the two components approaching equality for high atomic numbers.

As to switches from the same initial level to different final L levels, Coster*** states that "for all elements l is 2-3 times as strong as h, and b6 2-3 times as strong as g5," supporting the conclusion that LIII has twice as many electrons as LII (so that it is twice as likely to lose an electron by ionization).

The very meagre results available as to line-intensities are practically exhausted in the above account; much further experimental (and theoretical) work is necessary. The results, however, do give definite support to the allocation of 2 electrons to the II sub-levels, and 4 to the III sub-levels, in the L, M, and probably N groups.

* Data used, along with references to the original papers, will be found in Siegbahn, 'Spektroskopie der Rontgenstahlen' (Berlin, 1924), pp. 96, 97, 106.
** Proc. Nat. Acad. Sci. vi. p. 518 (1920).
*** Phil. Mag. xiiii. p. 1088 (1922)


TableIV. -- Showing Transitions corresponding to K and L lines.

Level (n)K (1)L (2)M (3)N (4)
k, j1, 11, 12, 12, 21, 12, 12, 23, 23, 31, 12, 12, 23, 23, 3
number of electrons22242214622446
K seriesK  a2a1 b3b1   b2  
. . . . .LI     b3b4   g2g3  
L series . . . . .LII    h  b1 g5 g1  
. . . . .LIII    l  a2a1b6   b2
[N.B. The b2 in the K series row has, in the original, a curly bracket just above it, linking it to the 2 and 4 above it in the "number of electrons" row. The "L series," in the original, has a curly bracket to the right which links it to the LI, LII and LIII.]


Two other matters concerned with X-ray lines may be briefly noticed. Firstly, new lines would be expected to appear for the same atomic number on both Bohr's and the present scheme, as they are exactly similar as regards points of origin of group development. Secondly, if the appearance of "anomalous" longer wave-length satellites to lines is connected with the development of the corresponding, or associated, sub-groups, it might be possible to decide whether development occurs simply by addition of electrons to outer sub-groups, or also by reorganization of inner sub-groups. Coster gives some examples, but the data are insufficient as yet to make further discussion useful; it may be mentioned, however, that no irregularities are observed at all for b6 and g5 during the development of the N group.

(b) Absorption of X-rays.

The relative absorption of X-rays by different sub-groups of electrons, as the relative intensities of lines corresponding to switches from them, will depend in part on the number of electrons they contain. Theories of absorption, as yet very incomplete, indicate that the part ap of the characteristic atomic absorption due to a level P containing Np electrons may be written:

where Np is the corresponding total quantum number.

Kramers* does not consider the relative absorption for different subgroups (e.g. LI, LII, LIII), but gives as an approximate expression for the groups as wholes:

where ap is the statistical weight of the electrons in the group. De Broglie,** semi-empirically, derives the expression:

lp being the critical wave-length for the level concerned.

* Kramers, Phil. Mag. xliv. p. 836 (1923).
** De Broglie, Journ. de Phys. VI. iii. p. 33 (1922).


As far as measurements on the relative K and L absorptions go, there is little to choose between the formulae, though neither is adequate.

For orbits of a similar type, not too widely separated, it may, however, be anticipated that relative absorption, like relative emission, will depend primarily on relative numbers of electrons.

Owing to experimental difficulties, data as to relative absorption by different subgroups are meagre, Dauvillier's for gold being the only direct ones available*. From his curves based on ionization measurements on absorption in the L region of Au, he deduces for the relative absorption, for l = lLI :

(M + N + O . . .) : LIII : LII : LI = 42 : 62 : 41 : 35,

and applying de Broglie's expression, obtains

NLII / NLIII = .495, NLI / NLII = .78,

a conclusion which may be taken to support the 2, 2, 4 distribution of electrons.

In the M region, photographic methods only have been used. All that can be said is that the greater contrast corresponding to transitions from the outer sub-levels (see, for example, the photographs of Ross** for Th) suggests that they contain a greater number of electrons, as in the 2, 2, 4, 4, 6 distribution proposed.

The most powerful method of investigating the relative absorption by different subgroups, however, is by investigating the secondary corpuscular rays ejected from them, as in the work of Robinson.*** Using homogeneous X-rays, the electrons emitted from a secondary radiator are bent round in a magnetic field, and fall on a photographic plate. The relative intensities of the lines (really heads of bands) corresponding to electrons from the different levels, when these are fairly close, give a rough estimate of the actual relative numbers of electrons ejected. Using copper Ka-rays, Robinson gives the following visually estimated intensities (on a 1-6 scale) for the lines corresponding to

* Dauvillier, Comptes. Rendus, clxxviii. p. 476 (1924)
** Ross, Phys. Rev. xxii. p. 221 (1923).
*** Robinson, Proc. Roy. Soc. civ. p. 455 (1923)


electrons ejected from the L sub-levels: --

 Ba.I. Sn.Ag.Mo.Sr.Cu.

The remarkable fact appears that the relative absorption by the different sub-levels varies with the difference between the critical wave-lengths and the incident wave-length in a manner quite unforeseen by any theories hitherto put forward. This is also observed by Ellis and Skinner* with g-rays. Over a wide range, however, in which the frequency is not too widely removed from the critical frequencies, and these themselves are not too close together, the run of intensities is exactly of the kind to be expected from a 2, 2, 4 distribution of electrons in the L subgroups; and in the view of the strong evidence in favour of this distribution from other sources, it seems justifiable to consider the M intensities in a similar manner in the light of this. Robinson gives the following estimates: --


[N.B. In the original, there are two right-handed curly brackets. One is located to the right of the two 6s in the Ba column and other to the right of the two 6s in the W column.]

Here, again, the general run of the figures in the range in which, from the L results, anomalies would be least expected, is in accord with the 2, 2, 4, 4, 6 distribution. (The MI, MIII, MIII intensities show progressive change of the same type as the LI, LII, LIII, as would be anticipated from their respective kj values being the same.) The N sub-levels of bismuth give:

Bi . . . . . .234453-4
[N.B. In the original, there is a curly bracket pointed downward. It is below the NVI and NVII, pointing at the 3-4.]

Too much stress must not be placed on the evidence here brought forward as favouring the distribution proposed.

* Ellis and Skinner, Proc. Roy. Soc. cv p. 186 (1924)


The estimate of intensities is arbitrary, and it is difficult to say how far the estimated values correspond to actual numbers of ejected electrons. It has scarcely been sufficiently emphasized that the lines are really heads of bands; the number of electrons required is the total number in the band, and this number may diverge widely from that suggested by the line-intensity, particularly if the heads are close together. The inadequacy of theories of absorption, moreover, comes out most strongly in the very experimental results being considered. If, however, for sub-groups of similar energy relative absorption does not depend largely on relative numbers of electrons under comparable conditions of excitation - and unless disturbing factors enter, it is difficult, physically, to imagine an alternative to this, -- then the Robinson results do point definitely to a concentration of electrons in the outer sub-levels to an extent greater than it seems possible to account for on the basis of the Bohr numbers.

(c) Magnetic Properties

[N.B. The charges on the ions which follow are subscripted in the original.]

The ionic paramagnetism of the third-period elements only will be briefly considered here. The development of ions from K+ or Ca++ (with 18 electrons) to Cu+ (with 28 electrons) is brought about, on our view, by the simple addition of electrons to the MIV and MV sub-levels in 10 (4 + 6) orbits of the same nk type (3, 3).

Sommerfeld, taking into account spatial quantization, has shown that** the number of Bohr magnetons associated with the ions increases regularly by steps of 1 from 0 to 5 (attaining this maximum value for Mn++ and Fe+++ with 23 electrons), and then decreases regularly to 0 (for Cu+) with increasing numbers of electrons.

While the deeper meaning of this may be obscure, especially in that unit magnetic moment has apparently to be associated with (3, 3) orbits, such a beautiful regularity is in agreement with the development of the M group by the simple addition of 10 similar (n, k) orbits; the presence of x electrons in the (MIV and MV) levels, superposed on completed groups, may be expected (by a sort of Babinet principle!) to produce the same paramagnetic properties as (10 - x) electrons, for with the latter number the group diverges from non-paramagnetic completeness in the absence of x electrons. On the Bohr scheme, the

* Robinson discusses this question l. c. p. 473.
** Sommerfeld, Zeit. f. Phys. xix. p. 221 (1923).


development occurs by a complete reorganization of the whole M group from a (4, 4) to a (6, 6, 6) arrangement. While the general nature of the cdhange might be the same, the essential and striking feature -- the regularity -- would certainly not be anticipated.

(d) Chemical Properties

Chemical properties depend mainly on the number of electrons in outer I, II, III sub-groups. The distribution proposed is primarily concerned with completed groups rather than their course of development ; but a few rather suggestive features of the new scheme, where it diverges from Bohr's, may be mentioned. The course of development strongly indicated for the L (Li-Ne), M (Na-A), N (Cu-Kr), O (Ag-Xe), P (Au-Nt) sub-groups is shown in Table V.

TABLE V. -- Number of Electrons in Outer Sub-groups.

Column of Periodic Table and Typical Element.
II  122222
III    1234

A consideration of the electrovalency of the elements as indicated by the halides, for example, provides considerable evidence for a subdivision of electrons among the levels in this way. Thus P is 5-valet, corresponding to all the five outer electrons in PCl5, but also trivalent in PCl3, corresponding to the three more loosely-bound (MII + MIII) electrons. (Similarly, the analogous Sb.) S forms SF6, SCl4, and SCl2. (There are analogous Se and Te compounds.) Si and the analogues C, Ge, Sn, Pb all form tetrachlorides, and Sn and Pb dichlorides. I forms ICl3 and IF5, and also compounds in which it acts as a heptavalent.


The development of underlying groups occurring from Sc-Ni, Y-Pd, and Lu-Pt involves the addition of 4 and 6 electrons in IV and in V sub-groups. (See Table III.) The problem of coordination compounds and "residual affinity" is undoubtedly linked up with these underlying groups, and in this connexion the prevalence of 6 as the number of groups surrounding the central atom in the ion of many complex compounds seems very significant as indicating 6 as the number of electrons to be associated with the outermost of the underlying sub-groups (V) when complete. As examples may be given the cyanides such as H4[Fe(CN)6], H4[Ru(CN)6], H4[Os(CN)6], and the ammines such as [Co(NH3)6]Cl3, [Pt(NH3)6]Cl4. The number 6 also occurs in the Bohr scheme in a somewhat similar manner, and the chemical evidence has already been discussed in this connexion*.

It seems undesirable here to enter more fully into chemical considerations, though they raise many important questions. The evidence is favourable, and the scheme seems to possess some new inherent possibilities for coordinating chemical facts.

A final remark may be made on the question of atomic symmetry as exemplified in carbon. According to Bohr, carbon has 4 (2, 1) electrons, whose orbits are taken to be tetrahedrally aranged. On the present view there are 2 (2, 1) and 2 (2, 2) electrons. The tetrahedral symmetry, therefore, is probably not to be attributed to the four outer electrons the atom possesses, but to the four "vacant places" which would have to be filled up for it to attain a complete configuration. Somewhat similar considerations may apply to the six-fold symmetry characteristic of coordination compounds of the type referred to above.

(e) Optical Spectra.

The relation between optical spectra and distribution of outer electrons has been (and is being) very fully considered by Bohr himself and others. Here it is only necessary to note the relevant fact that the doublet spectrum of ionized carbon (C II) ** can at once be explained if C+ has 2 (2, 1) electrons and 1 (2, 2) ; whereas it cannot be fitted easily into a 4 (2, 1) scheme for neutral carbon. The spectra of silicon in various stages of ionization fit in with the scheme propsed, as also the recently analysed oxygen spectrum***.

* Sidgwick, Journ. Chem. Soc. cxxiii. p. 725 (1923).
** Fowler, Proc. Roy. Soc. cv. p. 299 (1924).
*** Hopfield, Phys. Rev. xxi. p. 710 (1923).


The correlation of the types of spectra with electronic structure, however, presents many unsolved problems for the future.

This section may be briefly summarized. The X-ray emission-line intensities seem to provide conclusive evidence for the presence of 2 and 4 electrons in LII and LIII as inner atomic sub-levels over a wide range of atomic numbers, a subdivision also indicated for MII and MIII. The absorption measurements confirm this, and suggest a distribution of the 2, 2, 4, 4, 6 type for the 5M and the first 5N sub-levels. The chemical evidence is strongly in support of the up-building of the I, II, III, L, M, ... P sub-levels as suggested by the final 2, 2, 4 distribution, and this is confirmed in an important case by the optical spectra. The chemical properties also indicate strongly the number 6 as characterizing the M, N, and O V sub-groups, and magnetic considerations suggest 10 as the number of electrons in the completed MIV and MV sub-levels.

While evidence based on experiment is inadequate to provide quantitative proof of the correctness of the whole system of electronic distribution propsed, it seems conclusive as to the simpler sub-groupings, and collectively does lend strong support to a scheme in itself simple and consistent.


A distribution of electrons in the atom is proposed, according to which the number in a sub-group is simply related to the inner quantum number characterizing it. A formal justification of the connexion is given. The suggested numbers of electrons in the sub-levels of the completed K, L, M . . . groups are (2), (2, 2, 4), (2, 2, 4, 4, 6) . . . respectively. The scheme is compared with that of Bohr. It enables all the essential features involved in Bohr's picture of atom-building to be retained, and so is equally in accord with general chemical and spectroscopic evidence; but it differs in the distribution in the completed groups, and in indicating a somewhat simpler mode of development. Evidence based on considerations of intensities of X-ray lines, absorption of X-rays, chemical and magnetic properties, and optical spectra is discussed and shown to give considerable support to a distribution of the kind put forward.

I would like to thank Mr. R. H. Fowler for helpful criticism and discussion.

Cavendish Laboratory,
July 1924.

For Further Reading

  1. Cantor, G. "The making of a British theoretical physicist -- E. C. Stoner's early career." British Journal for the History of Science. 27, p. 277-290 (1994).
  2. Heilbron, J. L. "The origins of the exclusion principle." Historical Studies in the Physical Sciences. 13, 2, p. 261-310 (1983).