THE STRUCTURE OF THE ATOM AND THE CHEMICAL PROPERTIES OF THE ELEMENTS
Introduction.
We have hitherto restricted ourselves mainly to those applications of
the Bohr theory which have a direct connection with the processes of
radiation. We have shown how fertile the theory has proved to be, how
many problems, previously inexplicable, have been solved, and what
exact agreement has been established between experiment and theory in
this comprehensive field. We may now ask how the theory accounts for
the chemical behaviour of the different elements. As early as 1913,
Bohr, in connection with his researches on spectral phenomena, had
considered the chemical properties of the elements and had pointed out
interesting possibilities.
[Illustration: FIG. 33.—Early representation of the formation of a
hydrogen molecule (Bohr, 1913).]
The Combination of Atoms into Molecules.
In his discussion of hydrogen, Bohr suggested a model for the structure
of its molecule, which we shall give here, because, by a simple
example, it illustrates how two neutral atoms may form a molecule
(cf. p. 13). In Fig. 33, _a_, _K₁E₁_ and _K₂E₂_ are
two neutral hydrogen atoms which are approaching each other with the
orbits of the two electrons parallel. The nucleus _K_₁ and the
electron _E_₂ then attract each other as do the nucleus _K_₂
and the electron _E_₁. The two electrons repel each other as do
the two nuclei; but when the electrons are in opposite positions of
their orbits, the forces of attraction outweigh the effect of the
forces of repulsion. Calculation shows that when the atoms are allowed
to approach each other the positions of the atoms will be as is shown
in Fig. 33, _b_, where the orbits are closer to each other than
the nuclei. Finally, for small distances of the two nuclei, the two
orbits will be merged into one, as is shown in Fig. 33, _c_.
This orbit will be slightly larger than the original ones. The two
hydrogen atoms may, in this way, combine into one molecule. In fact,
an equilibrium position can be found for which the nuclei are held
together, in spite of their mutual repulsion, by the attractive forces
existing between them and the electrons which are moving in their
common orbit. It must, however, be assumed, for reasons which cannot
be given here, that the hydrogen molecule is, in reality, constructed
somewhat differently; probably the orbits of the electrons make an
angle with each other.
The formation of a hydrogen molecule may also be supposed to occur
when a positive hydrogen ion, _i.e._, a hydrogen nucleus, and
a negative hydrogen ion, _i.e._, a hydrogen nucleus with two
electrons, are drawn together by their mutual attractions. The forces
of attraction would be much stronger than in the first example given,
and the formation of a neutral molecule would not take place in the
same way. More energy would also be released, but the final result will
be the same.
Just as in the case of the hydrogen molecule, other molecules may be
formed from atoms belonging to the same or to different elements. The
method of formation of molecules varies according as it is a union
of neutral molecules in the normal state, or a union of positive and
negative ions. Conversely, by chemical decomposition a molecule can be
separated either into neutral parts or into ions. If, for instance,
common salt (sodium chloride, NaCl) is dissolved in water, the salt
molecules are, under the influence of the water molecules, decomposed
in Na-ions with one positive charge and Cl-ions with one negative
charge, corresponding to the monovalent electropositive character of
sodium and the monovalent electronegative character of chlorine.
The possibilities are, however, far from being exhausted by these two
methods of composition and decomposition. An atom may exist not only
in the normal state where it has its complete number of electrons
collected as tightly as possible about the nucleus, and in the ionized
state with one or more too many or too few electrons; but in a neutral
atom one or more of the outer electrons may be in a stationary orbit
at a greater distance from the nucleus than corresponds to the normal
stationary state. It is easy to understand that an atom in such an
“excited” or (as it is called in chemistry) _active_ state often
finds it easier to act in concert with other atoms than when it is in
the normal state; in this latter state the atom is often more like a
little compact lump of neutral substance than in the active state.
It will, in any case, be understood that the interplay between the
atoms, which reveals itself in the chemical processes or reactions
between different elements, offers many opportunities for the Bohr
theory to give in the future a more detailed explanation than was
possible to the earlier theories of chemistry. We must also mention
the fact that it has become possible to elucidate in main features
the phenomena, hitherto unexplained, of the chemical effects of
light, as on a photographic plate (_photochemistry_) and of
_catalysis_, which consists in bringing about, or accelerating,
the chemical interaction between two substances by the presence of a
third substance which does not itself enter in the compound, and often
needs only to be present in very small quantities. It must, however, be
emphasized that at present we do not yet possess a detailed theory of
molecular constitution comparable with our knowledge of the structure
of the atoms.
The Periodic System.
Instead of inquiring how the chemical processes may take place, we
shall now study the general correlation between the chemical properties
and the atomic numbers of the elements, a correlation which has found
its empirical expression in the natural or periodic system of the
elements (cf. p. 23). The explanation of the puzzles of this system
must be said to be one of the finest results which Bohr has obtained,
and it constitutes a striking evidence in favour of the quantum theory
of atoms.
There is nothing new in the idea of connecting the arrangement of
the elements in the periodic system with an arrangement of particles
in the atom in regular _groups_, the character of which varies,
so to say, periodically with increasing number of particles. In the
atom model of Lord Kelvin and J. J. Thomson (cf. p. 86), with the
positive electricity distributed over the volume of the whole atom,
Thomson tried to explain certain leading characteristics of the
periodic system by imagining the electrons as arranged in several
circular rings about the centre of the atom. He pointed out that the
stability of the electronic configurations of this type varied in a
remarkable periodic way with the number of electrons in the atom. By
considerations of this nature Thomson was able to enunciate a series of
analogies to the behaviour of the elements in the periodic system as
regards the tendency of the neutral atoms to lose one or more electrons
(electropositive elements) or to take up one or more electrons
(electronegative elements). But, setting aside possible objections to
his considerations and calculations, the connection with the system
was very loose and general, and his theory lost its fundamental
support when his atomic model had to give way to Rutherford’s. With
Bohr’s theory the demand for a stable system of electrons was placed in
an entirely new light.
In his treatise of 1913, Bohr tried to give an explanation of the
structure of the atom, by thinking of the electrons as moving in a
larger or smaller number of circular rings about the nucleus. His
theory did not exclude the possibility of orbits of electrons having
different directions in space instead of lying in one plane or being
parallel. The tendency of the considerations was to attain a definite,
unique determination of the structure of the atom, as is demanded by
the pronounced stability of the chemical and physical properties of
the elements. The results were, however, rather unsatisfactory, and it
became more and more clear that the bases of the quantum theory were
not sufficiently developed to lead in an unambiguous way to a definite
picture of the atom. Nowadays the simple conception of the electrons
moving in circular rings in the field of the nucleus is definitely
abandoned, and replaced by a picture of atomic constitution of which we
shall speak presently.
In the following years the general conception of the group distribution
of the electrons in the atom formed the basis of many theoretical
investigations, which in various respects have led to a closer
understanding of chemical and physical facts. The German physicist,
Kossel, showed that the characteristic X-ray spectra of the elements,
which are due to a process of reconstruction of the atom subsequent to
the removal of one or more of the innermost electrons (cf. p. 161),
give a most striking support to the assumption that the electrons are
distributed in different groups in which they are bound with different
strength to the atom.
The connection between the electron groups and the chemical valence
properties of the atoms, to which Thomson had first drawn attention and
which also played an important part in Bohr’s early considerations,
was further developed in a significant way by Kossel, as well as
by Lewis and by Langmuir in America. These chemical theories had,
however, little or no connection with the quantum theory of atomic
processes; even the special features of the Rutherford atom, which are
of essential importance in the theory of the hydrogen spectrum and of
other spectra, played only a subordinate part.
In 1920 Bohr showed how, by the development of the quantum theory
which had taken place in the meantime, and the main features of which
consisted in the introduction of more than one quantum number for the
determination of the stationary states and in the establishment of the
correspondence principle, the problem of the structure of the atom had
appeared in a new light. In fact, he outlined a general picture of
atomic constitution, based on the quantum theory, which in a remarkable
way accounted for the properties of the elements. In order to decide
doubtful questions, he has often had to call to his aid the observed
properties of elements, and it must be readily admitted that the
finishing touches of the theory are still lacking. But from his general
starting-point he has been able to outline the architecture of even
the most complex atomic structures and to explain, not only the known
regularities, but also the apparent irregularities of the periodic
system of the elements.
The method Bohr used in his attempt to solve the problem was to study
_how a neutral normal atom may gradually be formed by the successive
capturing and binding of the individual electrons in the field of
force about the nucleus of the atom_. He began by assuming that he
had a solitary nucleus with a positive charge of a given magnitude.
To this nucleus free electrons are now added, one after the other,
until the nucleus has taken on the number sufficient to neutralize the
nuclear charge. Each individual electron undergoes a “binding” process,
_i.e._ it can move in different possible stationary orbits about
the nucleus and the electrons already bound. With the emission of
radiation it can go from stationary states with greater energy to
others with less energy, ending its journey by remaining in the orbit
which corresponds to the least possible energy. We may designate
this state of least energy as the normal state of the system, which,
however, is only a positive atomic ion, so long as all the electrons
needed for neutralization are not yet captured.
From the exposition in the preceding chapter it will be seen that
the ordinary series spectra (arc spectra) may be considered as
corresponding to the last stage in this formation process, since the
emission of each line in such a spectrum is due to a transition between
two stationary states in each of which N-1 electrons are bound in their
normal state, _i.e._ as tight as possible, by the nucleus, while
the Nth electron moves in an orbit mainly outside the region of the
other electrons. In the same way the spark spectra give witness of the
last stage but one of the formation process of the atom, since here
N-2 electrons are bound in their normal state while an N-1th electron
moves in an orbit large compared with the dimensions of the orbits
of the inner electrons. From these remarks it will be clear that the
study of the series spectra is of great importance for the closer
investigation of the process of formation of the atom outlined above.
Furthermore, the general ideas of the correspondence principle, which
directly connects the possibility of transition from one stationary
state to another with the motion of the electron, has been very useful
in throwing light on the individual capturing processes and on the
stability of the electronic configurations formed by these. In what
follows we cannot, however, reproduce Bohr’s arguments at length; we
must satisfy ourselves with some hints here and there, and for the rest
restrict ourselves to giving some of the principal results.
Before going farther we shall recall what has previously been said
about the quantum numbers. In the undisturbed hydrogen atom, the
stationary orbits can be numbered with the principal quantum numbers
1, 2, 3 ... _n_. But to each principal quantum number there
corresponds not one but several states, each with its auxiliary quantum
number 1, 2, 3 ... _k_, _k_ at the most being equal to the
principal quantum number. In a similar way, the stationary orbits of
the electrons in an atom containing several electrons can be indicated
by two quantum numbers, the 3₂ orbit, for instance, being that with
principal quantum number 3 and auxiliary quantum number 2. But while
in the hydrogen atom the principal quantum number _n_, in the
stationary orbits which are slowly rotating ellipses, is very simply
connected with the length of the major axis of the ellipse, and
_k_: _n_ is the ratio between the minor and major axes,
still in other atoms with complex systems of electrons the significance
of the principal quantum number is not so simple and the orbit of
an electron consists of a sequence of loops of more complicated
form (cf. Fig. 29). We must satisfy ourselves with the statement
that a definition of their significance can be given, but only by
mathematical-physical considerations which we cannot enter into here.
It may, however, be stated that, if we restrict ourselves to a definite
atom, the rule will hold that, among a series of orbits with the same
auxiliary quantum number but different principal quantum numbers, that
orbit in which the electron attains a greater distance from the nucleus
has the higher number. Another rule which holds is, that an orbit with
a small auxiliary quantum number in comparison with its principal
quantum number (as 4₁ for instance, cf. Fig. 29), will consist of very
oblong loops with a very great difference between the greatest and
least distances of the electron from the nucleus, while the orbit will
be a circle when the two quantum numbers are the same as for 1₁, 2₂,
3₃. Although each orbit has two quantum numbers, we often speak simply
of the 1-, 2-, 3- ... _n_-quantum orbits, meaning here the orbits
with the principal quantum numbers 1, 2, 3 ... _n_.
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.
Electron No. 3 will accordingly not be bound in the same group with
1 and 2. It must be satisfied with a 2-quantum orbit, 2₁, which
consists of oblong loops, and, when nearest the nucleus, comes into the
territory of the 1-quantum orbits. It is but loosely bound compared
to the first two electrons, and the lithium atom, which has only
three electrons, can therefore easily let No. 3 loose so that the
atom becomes a positive ion. _Lithium_ is therefore a strongly
electropositive monovalent metal. The element _beryllium_ (No. 4)
will probably have two electrons in the orbits 2₁; it will therefore be
divalent. But during the short visit of these electrons to the nucleus
they are subject to a greater nuclear charge than in lithium. The 2₁
electrons are therefore, in beryllium, more firmly bound than in
lithium, and the electropositive character of beryllium is therefore
less marked.
We have something essentially new in the _boron_ atom (atomic No.
5) where the two electrons No. 3 and No. 4 are taken into 2₁ orbits,
but where No. 5 will very probably be bound in a circular 2₂ orbit.
How the conditions will be in the normal state of the following atoms
preceding neon is not known with certainty. We only know that the
electrons coming after the first two will be captured in 2-quantum
orbits, the dimensions of which get smaller, according as the atomic
number increases.
The _neon_ atom (compare the diagram) has a particularly stable
structure, both “closed” and symmetric, which besides two 1₁-orbits
contains four electrons in 2₁ orbits and four electrons in 2₂
orbits. As regards the four electrons in 2₁ orbits, they do not have
symmetrical positions at every moment or move simultaneously either
towards or away from the nucleus; on the contrary, it must be assumed
that the electrons come closest to the nucleus at different moments at
equal intervals of time.
The name of inert or inactive gases is given to the entire series
of helium (2), neon (10), argon (18), krypton (36), xenon (54) and
niton (86), the O-column in the periodic system given in the table
on p. 23. All these elements are monatomic and quite unwilling to
enter into chemical compounds with other elements (although there is
about 1 per cent. of argon in the air about us this element has, on
this account, escaped the observation of chemists until about 1895,
when it was discovered by the English chemist, Ramsay). This complete
chemical inactivity is explained by the fact that the atoms of all
these elements have a nicely finished “architecture” with all the
electrons firmly bound in symmetrical configurations. They may be said
to form the mile posts of the periodic system, and to be the ideals
towards which the other atoms aspire. The table shows how the electrons
in the atoms of these gases are divided among the types of orbits
corresponding to the different quantum numbers.
TABLE SHOWING THE DISTRIBUTION OF THE ELECTRONS OF
DIFFERENT ORBITAL TYPES IN THE NEUTRAL ATOMS OF THE
INACTIVE GASES.
-------+------+---------------------------------------+
| | Quantum Numbers. |
|Atomic+---+---+---+---+---+---+---+---+---+---+
|Number| 1₁| 2₁| 2₂ | 3₁| 3₂| 3₃| 4₁| 4₂ | 4₃| 4₄|
-------+------+---+---+---+---+---+---+---+---+---+---+
Helium | 2 | 2 | | | | | | | | | |
Neon | 10 | 2 | 4 | 4 | | | | | | | |
Argon | 18 | 2 | 4 | 4 | 4 | 4 | - | | | | |
Krypton| 36 | 2 | 4 | 4 | 6 | 6 | 6 | 4 | 4 | - | - |
Xenon | 54 | 2 | 4 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | - |
Niton | 86 | 2 | 4 | 4 | 6 | 6 | 6 | 8 | 8 | 8 | 8 |
? | 118 | 2 | 4 | 4 | 6 | 6 | 6 | 8 | 8 | 8 | 8 |
-------+------+---+---+---+---+---+---+---+---+---+---+
-------+------+------------------------------------------------------+
| | Quantum Numbers. |
|Atomic+---+---+---+---+---+---+---+---+---+---+---+---+---+--+
|Number| 5₁| 5₂| 5₃| 5₄ | 5₅| 6₁| 6₂| 6₃| 6₄| 6₅| 6₆| 7₁ | 7₂| 7₃|
-------+------+---+---+---+---+---+---+---+---+---+---+---+---+---+--+
Helium | 2 | | | | | | | | | | | | | | |
Neon | 10 | | | | | | | | | | | | | | |
Argon | 18 | | | | | | | | | | | | | | |
Krypton| 36 | | | | | | | | | | | | | | |
Xenon | 54 | 4 | 4 | - | - | - | | | | | | | | | |
Niton | 86 | 6 | 6 | 6 | - | - | 4 | 4 | - | - | - | - | | | |
? | 118 | 8 | 8 | 8 | 8 | - | 6 | 6 | 6 | - | - | - | 4 | 4 | -|
-------+------+---+---+---+---+---+---+---+---+---+---+---+---+---+--+
The elements _fluorine_, _oxygen_ and _nitrogen_ can
attain the ideal neon-architecture by binding respectively one, two
and three additional electrons. Naturally they do not become neon
atoms, but merely negative atomic ions with single, double or triple
charge; and their tendency in this direction appears in their character
of monovalent, divalent and trivalent electronegative elements
respectively. If we return to carbon it can probably not become a
tetravalent negative ion by binding four free electrons; but in the
typical carbon compound, methane (CH₄), the neon ideal is realized
in another manner. In fact, it is reasonable to assume that the four
electrons of the hydrogen atoms together with the six of the carbon
atom give approximately a neon-architecture. The four hydrogen nuclei
naturally cannot be combined with the carbon nucleus; the mutual
repulsions keep them at a distance. They will probably assume very
symmetrical positions within the electron system which holds them
together. The nitrogen atom may in a similar way find completion in
a neutral molecule with neon-architecture, if it unites with three
hydrogen atoms to form ammonia NH₃; but the three hydrogen nuclei,
although having symmetrical positions, will not lie in the same plane
as the nitrogen nucleus. The electric centre of gravity for the
positive nuclei will therefore not coincide with the centre of gravity
for the negative electron system. The molecule obtains thus what might
be called a positive and a negative pole, and this dipolar character
appears in the electrical action of ammonia (its dielectric constant).
Something similar holds true for the water molecule, where, in a
neon-architecture of electrons, in addition to the oxygen nucleus in
the centre there are two hydrogen nuclei which are not co-linear with
the oxygen nucleus.
If we go on from neon in the periodic system we come to _sodium_
(11). When the sodium nucleus captures electron No. 11, this cannot
find room in the neon-architecture formed by the first ten electrons.
Since the eleventh electron thus cannot find a place in either a 2₁ or
a 2₂ orbit, it is bound in a 3₁ orbit (cf. Fig. 29 and diagram at the
end). The atom then has a character like that of the lithium atom, and
we can therefore understand the chemical relationship between the two
elements, which are both monovalent electropositive metals.
We shall not dwell longer upon the individual elements of the atomic
series. If we pass from neon through sodium (11), magnesium (12),
aluminium (13), etc., to _argon_ (18), we get what is essentially
a repetition of the situation in the series from lithium to neon. We
first get two orbits of the 3₁ type in magnesium, a 3₂ orbit is for
the first time added in aluminium, and for the atomic number 18, eight
3-quantum orbits, together with the eight orbits of the inner 2-quantum
group and the two of the innermost 1-quantum group, give the symmetric
architecture of _argon_ (cf. table on p. 196, and diagram at the
end).
The architecture of the argon atom is in a certain sense less complete
than that of the neon atom. In argon there are indeed four orbits of
the 3₁ type and four of the 3₂ type, but the third kind of 3-quantum
orbit, the circular 3₃ one, is missing. Nor does it appear in the next
element, _potassium_ (19). The electron No. 19 prefers, instead
of the 3₃ orbit, the 4₁ orbit, which consists of oblong loops and
which gives a firmer binding because it dives in among the electrons
bound earlier, while the circle 3₃ would lie outside them all. We
thus obtain an atom of type similar to the lithium and sodium atoms.
But the slighted 3₃ path lies, so to speak, on the watch to steal a
place for itself in the neutral atom, and this has grave results for
the subsequent development. Even in _calcium_ (20), after the
first eighteen electrons are bound in the argon architecture, both the
nineteenth and the twentieth go into a 4₁ orbit, and the behaviour of
calcium is like that of magnesium. But since the increasing nuclear
charge means for the electron No. 19 a decrease in the dimensions and
an increase in the binding of the orbits corresponding to the quantum
number 3₃, a point will finally be attained where the 3₃ orbit of the
nineteenth electron lies within the boundaries of what may be called
the argon system, _i.e._, the architecture corresponding to
the first eighteen electrons, and corresponds to a stronger binding
than a 4₁ orbit would do. In _scandium_ (21) the 3₃-type orbit
occurs for the first time in the neutral atom and will not only come
into competition with the 4₁ type, but will also cause a disturbance
in the 3-quantum groups, which in the following elements must undergo
reconstruction. As long as this lasts the situation is very complicated
and uncertain. When the reorganization is almost completed, we come to
the blotting out of chemical differences, particularly known from the
triad, _iron_, _cobalt_ and _nickel_. Moreover, there
comes a fluctuation in the valency of the elements. Iron can, as has
been said, be divalent, trivalent or hexavalent. This oscillation in
valency begins in _titanium_.
We should perhaps expect that the reconstruction would be completed
long before nickel (28) is reached, because even with twenty-two
electrons we could get four orbits of each of the 3-quantum types
(3₁, 3₂ and 3₃); but from the chemical facts we are led to assume
that in a completed group of 3-quantum orbits there can be room for
six electrons in each sub-group. At first sight we should, then,
expect the end of the reconstruction with nickel, which has indeed
eighteen electrons more than neon where the group of 2-quantum orbits
was completed. We might expect that nickel would be an inert element
in the series with helium, neon, and argon. On the contrary, nickel
merely imitates cobalt. This is explained by the fact that the group of
eighteen 3-quantum orbits, although it has a symmetric architecture,
is weakly constructed if the nuclear charge is not sufficiently large.
The binding of this group is too weak for it to exist as the outer
group in a neutral atom. In _nickel_ the electrons, in a less
symmetrical manner, will probably arrange themselves with seventeen
3-quantum orbits and one 4-quantum orbit.
The group of eighteen 3-quantum orbits becomes stable, however, when
the nuclear charge is equal to or larger than 29, in which case it
can become the outer group in a positive ion. In this we find the
explanation of the properties of the atom of _copper_. The
neutral copper atom has its twenty-ninth electron bound in a 4₁ orbit
consisting of oblong loops (cf. diagram at the end); this electron
can easily be freed and leaves a positive monovalent copper ion with
a symmetrical architecture. Even under these circumstances, although
possessing a certain stability, the ion is not very firmly constructed.
Thus the fact that copper can be both monovalent and divalent, must be
explained by the assumption that for a nuclear charge 29, the 3-quantum
group still easily loses an electron.
When we come to _zinc_ (30) the group of eighteen is more firmly
bound; zinc is a pronounced divalent metal which in its properties
reminds us of calcium and magnesium. From zinc (30) to krypton (36) we
have a series of elements which in a certain way repeat the series from
magnesium (12) to argon (18).
In Fig. 34 is shown Bohr’s arrangement of the periodic system in which
the systematic correlation of the properties of the element appears
somewhat clearer than in the usual plan (cf. p. 23). It shows great
similarity with an arrangement proposed nearly thirty years ago by the
Danish chemist, Julius Thomsen. The elements from scandium to nickel,
where, in the neutral atom, the electron group of 3-quantum orbits is
in a state of reconstruction, are placed in a frame; the neutral
oblique lines connect elements which are “homologous,” _i.e._,
similar in chemical and physical (spectral) respect.
[Illustration: FIG. 34.—The periodic system of the elements.
The elements where an inner group of orbits is in a stage of
reconstruction are framed. The oblique lines connect elements which in
physical and chemical respects have similar properties.]
In _krypton_ (36) we again have a stable architecture with an
outer group of eight electrons, four in 4₁ orbits and four in 4₂
orbits. Owing to the appearance of 4₃ orbits in the normal state of the
atoms of elements with atomic number higher than 38, there follows in
the fifth period of the natural system a reconstruction and provisional
completion of the 4-quantum orbits to a group of eighteen electrons,
which shows a great simplicity with the completion of the 3-quantum
group in the fourth period. In Fig. 34 the elements where the 4-quantum
group is in a state of reconstruction are framed. The 4-quantum group
with eighteen electrons is of more stable construction than the group
of eighteen 3-quantum orbits in the elements with an atomic number
lower by eighteen. This is due to the fact that all the orbits in the
first-mentioned group are oblong and therefore moored, so to say, in
the inner groups, while in the complete group of 3-quantum orbits there
are six circular orbits. This is the reason why silver, in contrast to
copper, is monovalent.
The next inactive gas is _xenon_ (54), which outside of the
4-quantum group has a group of eight electrons in 5-quantum orbits,
four in 5₁ orbits and four in 5₂ orbits. We notice that in xenon the
group of 4-quantum orbits still lacks the 4₄ orbits. On the theory
we must, therefore, expect to meet a new process of completion and
reconstruction when proceeding in the system of the elements. The
theoretical argument is similar to that which applies in the case
of the completion of the 3-quantum group which takes place in the
fourth period of the natural system. In fact, in the formation of
the normal atoms of the elements next after xenon, caesium, 55,
and barium, 56, the fifty-four electrons first captured will form a
xenon configuration, while the fifty-fifth electron will be bound in
a 6₁ orbit, consisting of very oblong loops, which represents a much
stronger binding than a circular 4₄ orbit. Calculation shows, however,
that with increasing nuclear charge there must soon appear an element
for which a 4₄ orbit will represent a stronger binding than any other
orbit. This is actually the case in _cerium_ (58), and starting
from this element we meet a series of elements where, in the normal
neutral atom, the 4-quantum group is in a state of reconstruction.
This reconstruction must occur far within the atom, since the group of
eighteen 4-quantum orbits in xenon is already covered by an outer group
of eight 5-quantum orbits. The result is a whole series of elements
with very slight outward differences between their neutral atoms, and
therefore with very similar properties. This is the _rare earths_
group, which in such a strange way seemed to break down the order
of the natural system (cf. p. 21), but which thus finds its natural
explanation in the quantum theory of the structure of the atom.
The elements in which the 4-quantum group is in a state of
reconstruction are, in Fig. 34, enclosed in the inner frame in the
sixth period. Moreover, in the outer frame all elements are enclosed
where the group of 5-quantum orbits is in a state of reconstruction,
which started, even before cerium in lanthanum (57), where the
fifty-fifth electron in the normal state is bound in a 5₃ orbit. The
element _cassiopeium_, with atomic number 71, which is the last
of the rare earths, stands just outside the inner frame, because
in the normal neutral atom of this element the 4-quantum group is
just completed; this group, instead of eighteen electrons with six
electrons in each sub-group, consists now of thirty-two electrons with
eight electrons in each sub-group. The theory was able to predict that
the element with atomic number 72, which until a short time ago had
never been found, and the properties of which had been the subject of
some discussion, must in its chemical properties differ considerably
from the trivalent rare earths and show a resemblance to the
tetravalent elements zirconium (40), and thorium (90). This expectation
has recently been confirmed by the work of Hevesy and Coster in
Copenhagen, who have observed, by means of X-ray investigations,
that most zircon minerals contain considerable quantities (1 to 10
per cent.) of an element of atomic number 72, which has chemical
properties resembling very much those of zirconium, and which on this
account had hitherto not been detected by chemical investigation. A
preliminary investigation of the atomic weight of this new element, for
which its discoverers have proposed the name _hafnium_ (Hafnia =
Copenhagen), gave values lying between 178-180, in accordance with what
might be expected from the atomic weight of the elements (71) and (73).
(Cf. p. 23.)
The further completion of the groups of 5- and 6-quantum orbits, which
in the rare earths had temporarily come to a standstill, is resumed
in hafnium and goes on in a way very similar to that in which the 4-
and 5-quantum groups in the fifth, and the 3- and 4-quantum groups in
the fourth period underwent completion. Thus the reconstruction of
the 5-quantum group which began in lanthanum, and which receives a
characteristic expression in the triad of the platinum metals, has come
to a provisional conclusion in _gold_ (79), gold being the first
element outside the two frames which, in Fig. 34, appear in the sixth
period. The neutral gold atom possesses, in its normal state—besides
two 1-quantum orbits, eight 2-quantum orbits, eighteen 3-quantum
orbits, thirty-two 4-quantum orbits and eighteen 5-quantum orbits—one
loosely bound electron in a 6₁ orbit.
In _niton_ (86), finally, we meet again an inactive gas, the
structure of the atom of which is indicated in the table on p. 196.
In this element the difference between nuclear and electron properties
appears very conspicuously, since the structure of the electron system
is particularly stable, while that of the nucleus is unstable. Niton,
in fact, is a radioactive element which is known in three isotopic
forms; one of these is the disintegration product of radium, the
so-called radium emanation; it then has a very brief life. In the
course of four days over half of the nuclei in a given quantity of
radium emanation will explode.
In the diagram at the end of the book, as an example of an atom with
very complicated structure, there is given a schematic representation
of the atom of the famous element _radium_, on a scale twice
as large as the one used in the other atoms. It follows clearly
enough, from what has been said in Chap. IV., that the structure of
the electron system has nothing to do with the radioactivity. All
the remarkable radiation activities are due to the nucleus itself.
There has not even been room in the figure to draw the nucleus; the
1-quantum orbits consist only of a small cross, and in the other groups
we have contented ourselves with summary indications. The electron
system, with its eighty-eight electrons, is, however, in itself very
interesting, with its symmetry in the number of electrons in the
different groups. In the different quantum groups from 1 to 7 there are
found respectively two, eight, eighteen, thirty-two, eighteen, eight
and two electrons. The last group is naturally of a very different
nature from the first; they are “valence electrons,” which easily
get loose and leave behind a positive radium ion with stable niton
architecture. Radium then belongs to the family of the divalent metals,
magnesium, calcium, strontium and barium.
Four places from radium is _uranium_ (92) and the end of the
journey, if we restrict ourselves to the elements which are known to
exist. One could very well continue the building-up process still
further and discuss what structure would have to be assumed for the
atoms of the elements with higher atomic numbers. That they cannot
exist is not the fault of the electron system but of the nuclei, which
would become too complicated and too large to be stable. In the table
on p. 196 there is shown the probable structure of the atom of the
inert gas following niton; it must be assumed to have one hundred and
eighteen electrons distributed in groups of two, eight, eighteen,
thirty-two, thirty-two, eighteen and eight among the quantum groups
from 1 to 7.
As has been said, in all this symmetrical structure of the atoms
of the elements, Bohr has in many cases had to rely upon general
considerations of the information that observation gives about the
properties of the individual elements. It must, however, not be
forgotten that the backbone of the theory is and remains the general
laws of the quantum theory, applied to the nucleus atom in the same
way as they originally were applied to the hydrogen atom, leading
thereby to the interpretation of the hydrogen spectrum.
We have, further, a most striking evidence as to the correctness of
Bohr’s ideas in the fact that not only do the pictures of the atoms
which he has drawn agree with the known chemical facts about the
elements, but they are also able to explain in the most satisfactory
manner possible the most essential features of the characteristic X-ray
spectra of the different elements, a field we shall not enter upon here.
In all that has been said above we have been considering the Bohr
theory simply as a means of gaining a deeper understanding of the laws
which determine activities in the atomic world. Perhaps we shall now be
asked if we can “utilize” the theory, or, in other words, if it can be
put to practical use.
To this natural and not unwarranted question we may first give the
very general answer, that progress in our knowledge of the laws of
nature always contributes sooner or later, directly or indirectly, to
increase our mastery over nature. But the connection between science
and practical application may be more or less conspicuous, the path
from science to practical application more or less smooth. It must be
admitted that the Bohr theory, in its present state of development,
hardly leads to results of direct practical application. But since
it shows the way to a more thorough understanding of the details
in a great number of physical and chemical processes, where the
peculiar properties of the different elements play parts of decided
importance, then in reality it offers a wealth of possibilities for
making predictions about the course of the processes—predictions
which undoubtedly in the course of time will be of practical use in
many ways. In this connection the discovery of the element hafnium,
discussed on p. 204, may be mentioned. It must be for the future to
show what the Bohr theory can do for technical practice.
Below is given an explanation of the different symbols which occur
at various places in the book; also the values of important physical
constants.
1 m. = 1 metre; 1 cm. = 1 centimetre = 0·394 inches.
1 μ = 1 micron = 1/1000 of a millimetre = 0·0001 cm. = 10⁻⁴ cm.
1 μμ = 1/1,000,000 of a millimetre = 10⁻⁷ cm.
1 cm.³ = 1 cubic centimetre.
1 g. = 1 gram; 1 kg. = 1 kilogram = 2·2 pounds.
1 kgm. = 1 kilogrammetre (the work or the energy required to lift 1 kg.
1 m.).
1 erg = 1·02 × 10⁻⁸ kgm. = 7·48 × 10⁻⁸ foot-pounds.
λ represents wave-length.
ν represents frequency (number of oscillations in 1 second).
ω represents frequency of rotation (number of rotations in 1 second).
_n_ represents an integer (particularly the Bohr quantum numbers).
The velocity of light is _c_ = 3 × 10¹⁰ cm. per second = 9·9 × 10⁸
feet per second.
The wave-length of yellow sodium light is 0·589 μ = 589 μμ = 2·32 ×
10⁻⁵ inches.
The frequency of yellow sodium light is 526 × 10¹² vibrations per
second.
The number of molecules per cm.³ at 0° C. and atmospheric pressure is
about 27 × 10¹⁸.
The number of hydrogen atoms in 1 g. is about 6·10²³.
The mass of a hydrogen atom is 1·65 × 10⁻²⁴ g.
The elementary quantum of electricity is 4·77 × 10⁻¹⁰ “electrostatic
units.”
The negative electric charge of an electron is 1 elementary quantum (1
negative charge).
The positive electric charge of a hydrogen nucleus is 1 elementary
quantum (1 positive charge).
The mass of an electron is ¹⁄₁₈₃₅ that of the hydrogen atom.
The diameter of an electron is estimated to be about 3 × 10⁻¹³ cm.
The diameter of the atomic nucleus is of the order of magnitude 10⁻¹³
to 10⁻¹² cm.
The diameter of a hydrogen atom in the normal state (the diameter of
the first stationary orbit in Bohr’s model) is 1·056 × 10⁻⁸ cm.
The Balmer constant K = 3·29 × 10¹⁵.
The Planck constant _h_ = 6·54 × 10⁻²⁷.
An energy quantum is E = _h_ν.
The Balmer-Ritz formula for the frequencies of the lines in the hydrogen
spectrum is
( 1 1 )
ν = K ( ------ - -------)
( _n″_² _n′_² )
[Illustration: DIAGRAMS OF SPECTRA AFTER BUNSEN AND KIRCHHOFF]
[Illustration: STRUCTURE OF THE RADIUM ATOM]
[Illustration: MAIN LINES OF THE ATOMIC STRUCTURE OF SOME ELEMENTS]