Examination of the periodic classification at once reveals that the most basic or alkali-forming atoms have electrons which are most easily detached, and that, in general, basic character is pro portional to electron mobility. Take, for example, the thallium atom : it posseses a single most feebly attached electron responsi ble for the powerful alkalinity of its hydroxide in which the valency is unity ; it further possesses two more firmly attached electrons by which it becomes trivalent and yields an oxide of relatively feeble basicity. It is evident that the electrons in an atom are not all equally firmly bound, but that there is a pro gressive increase in firmness of binding as more and more elec trons are disclosed by increase of valency. If different atoms are compared, this rule of increase of firmness of electron binding with valency increase is still found to hold true, bivalent magnesium, for example, being less basic and having more firmly bound elec trons than univalent sodium. This general feature is abundantly evident in the abridged classification (Table I.) in which basic or alkali-forming character decreases steadily in each period from group I. to group VIII.
The maximum firmness of binding of electrons observable in the elements of group VIII. in each period, leads to curious re sults. Helium of atomic number 2 and with 2 electrons is chemi cally inert. The next element, lithium, of atomic number 3 and with 3 electrons, is definitely only univalent and thus possesses 2 electrons which resemble the helium 2 in being unavailable for chemical combination by valency. From lithium, valency and firmness of electron binding increase to a new maximum in neon, which is chemically inert like helium. In each period the same cir cumstances are observable, leading to the conclusion that the inert gases represent specially stable arrangements of electrons. This arrangement is obviously one of 2 electrons for helium, and 8 for all the other inert gases.
The fact that each period begins with a univalent alkali metal, following an inert gas of the previous period, involves that each alkali metal contains the stable structures of all the preceding inert gases, and similarly for every other element in the classification. The bivalent group II. element radium, for example, must contain the structures of the inert gases radon, xenon, krypton, argon, neon and helium, and must, therefore, contain the seven electron groupings, 2, 8, 8, 8, 8, 8, 2 in order of decreasing firmness of electron binding, that is, from the atomic nucleus outwards, the last 2 being the valency electrons. The number of elec tron groups is 7, radium being in the 7th period. In Bohr's theory of atomic structure, based on spectral evidence, these groups of electrons are referred to as quantum groups and are characterized by quantum numbers from I to 7, which are identical with the ordinal numbers appropriate to the various chemical periods. This description of electron groups by quantum numbers is con venient to avoid confusion between the facts of periodic classi fication and those of electronic structure.
Law of Uniform Atomic Plan.-It has been indicated that the elements in each chemical period fall into three classes, an alkaline, an amphoteric, and a non-alkaline class, consisting of 2,2 and 4 ele ments respectively per period. It has further been indicated that valency variation occurs only by two units, that a bivalent ele ment can never be univalent, a quadrivalent element never trival ent. This involves that 2 valency electrons in an atom are most
firmly bound, 2 less firmly bound and any remaining least firmly bound. Sulphur, with 6 electrons, for example, can be bivalent with 2 weakly bound electrons, quadrivalent with a further 2 more firmly bound, and sexavalent with a further 2 still more firmly bound. Hence, the inert gas octet of electrons comprises three sub-groups, the first with 2 electrons most firmly bound, the second also with 2 but less firmly bound, and the third with 4 electrons least firmly bound. This 2, 2, 4 sub-grouping is discerni ble throughout all the periods shown in the abridged classification and is thus present in each quantum group of electrons in all atoms.
In the 4th chemical period, ten elements intervene between groups II. and III. and form a transition series, and it can be shown that none of the ten transition elements possesses more than 2 electrons of the 4th quantum group, and that all the io more firmly bound electrons are proper to the 3rd quantum. Examina tion of the transition classification shows that it is divisible into two classes (see Table II.), the first consisting of 4 elements with high natural valencies and the second of 6 elements with low natural valencies. This division of the transition period corres ponds with a division of the ten electrons into two sub-groups of 4 more firmly and 6 less firmly bound. This sub-grouping is gen eral throughout all the transition series and leads to the conclu sion that the 3rd, 4th and 5th quantum groups can be extended from the 2, 2, 4 sub-grouping of the inert gases to 2, 2, 4, 4, 6 discernible onwards from univalent copper, silver and gold, respectively.
In the 6th chemical period, 14 elements intervene between groups III. and IV. of the transition classification and form a transition sub-series. It can be shown that the firmness of binding of the 14 electrons concerned relates them to the 4th quantum group. This sub-series can further be shown on various grounds to be divisible into two classes, the first comprising the six cerium earths and the second the eight lutecium earths (usually referred to as the "yttrium earths"). This division of the sub-series corres ponds with a division of the 14 electrons into two sub-groups of 6 electrons more firmly and 8 less firmly bound. The 4th quantum group is thus extended from the sub-grouping 2, 4, 4, 6 to 2, 2, 4, 4, 6, 6, 8.
From the foregoing group and sub-group schemes, the structure of the heaviest atom, uranium with 92 electrons, may be deduced to contain the groups 2, 8, 18, 32, 18, 8, 6, comprising the sub groups 2; 2, 2, 4; 2, 2, 4, 4, 6; 2, 4, 4, 6, 6, 8; 2, 2, 4, 4, 6; 2, 2, 4; 2, 2, 2. The precise form of the law of uniform atomic plan is now evident. The maximum numbers of electrons in main groups are equal to twice the squares of the natural numbers, 8, 18, 32 ; the number of sub-groups in a main group is equal to one less than twice the natural number char acterizing the group, the 4th group having 2X4-1=7 sub-groups; the numbers of electrons in the sub-groups of a main group are equal to twice the natural numbers taken in duplicate, the last sub-group being unduplicated and equal to twice the natural num ber characterizing the main group, the 4th group having the sub groups, 2(1, I, 2, 3, 3, 4, 4, 6, 6, 8. This law of uni form atomic plan discloses clearly the inner meaning of the pe riodic law of chemistry in terms of the arrangement of electrons within atoms.