in experiments on positive rays (Phil. Mag., 24, 253 (1912)).
We have now to consider the mechanism whereby a molecule of
hydrogen is formed from its constituents. We shall restrict ourselves
to the union of two neutral hydrogen atoms. Suppose that two such
* This expression obtained by Bohr is obviously the same as that found by Haber
in igri and referred to in the following chapter.
RUTHERFORD-BOHR ATOM-MODEL 117
atoms are approaching one another at a rate which is sufficiently slow
that the dynamical equilibrium of the electrons for every position of
the nuclei is the same as if the latter were at rest. Suppose that the
electron of atom i is rotating in the same plane as that of atom 2, the
difference in phase being one-half of a revolution. During the ap-
proach, the direction of the planes of the orbits of the electrons and
the difference in phase will be unaltered. The planes of the orbits
will, however, at the beginning of the process approach each other at
a higher rate than do the nuclei, for two electrons rotating in the same
direction attract one another. Finally, at a certain distance of the
nuclei apart the electron planes will coincide, the two electrons being
now arranged in a single ring. During the further approach of the
nuclei the ratio between the diameter of the electron ring and the
distance apart of the nuclei will increase, 1 and the system will pass
through a configuration in which it will be in equilibrium without the
application of extraneous forces on the nuclei. That is, a permanent
neutral hydrogen molecu'e is formed.
Now let us suppose that we are dealing with two helium atoms, i.e.
systems consisting of a nucleus of charge 2<? surrounded by a ring of
two electrons, and let us imagine the above process repeated. Assume
that at the beginning the helium atoms are orientated to each other like
the hydrogen atoms, with the exception that the electrons in the helium
atoms differ by one-quarter of a revolution instead of one-half. The
planes of the electrons will again approach one another at a higher rate
than do the nuclei, and for a certain position of the latter the planes
will coincide. During the further approach of the nuclei, the 4 elec-
trons will be arranged at equal angular intervals in a single ring. As
in the former case it may be shown that at any moment during this
operation the system will be stable for a displacement of the electrons
perpendicular to the plane of the ring. Contrary, however, to what
took place in the case of hydrogen, the extraneous forces to be applied
to the nuclei in order to keep the system in equilibrium will always be
in a direction to diminish the distance apart of the nuclei, and the
system will never pass through a position of equilibrium. The helium
atoms will in fact repel one another and no molecule will be perman-
As regards molecular systems containing a considerable number of
electrons the treatment becomes much more complicated. Bohr
attempts to deal with such cases, and for details his paper must be
consulted. It may be mentioned that, following an approximate
method of calculation, Bohr is led to expect an absorption band in the
infra-red spectrum of hydrochloric acid gas at v = 13*7 x io 13 whilst
the observed band lies at v = 8*5 x io 13 .
Bohr regards the water molecule as consisting of an oxygen nucleus
surrounded by a ring of four electrons, and the two hydrogen nuclei
situated on the axis of the ring at equal distances apart from the oxygen
1 Of course the actual diameter of the electron ring diminishes but not so fast as
does the distance between the nuclei.
n8 A SYSTEM OF PHYSICAL CHEMISTRY
nucleus and kept in equilibrium by two rings of greater radius than the
one just mentioned, each of these two rings containing 3 electrons ; the
latter rotate in parallel planes round the axis of the system and are
situated relatively to each other in such a way that the electrons in the
one ring are opposite the intervals between the electrons in the other.
If we imagine such a system broken up by slowly removing the hydro-
gen nuclei we should obtain two positively charged hydrogen atoms
and an oxygen atom with a double negative charge in which the outer-
most electrons will be arranged in two rings of three electrons each, the
two rings being parallel to one another.
Parson's Magneton and the Structure of the Atom.
Hitherto, in dealing with the problem of atomic structure, we have
regarded the electron as a minute discrete particle of electricity or
matter, assumed to be spherical, and capable of movement " inside "
the atom in certain orbits, the velocity of movement being relatively
small compared with the velocity of light. A new concept has been
introduced, however, in Connection with the electron which must be
very briefly discussed. According to this view the electron itself is a
tiny ring or annulus carrying a negative charge. The ring is regarded
as rotating continuously with a peripheral velocity which is of the same
order as that of light. This is equivalent to a circuit current, analogous
to the Ampere currents assumed to account for magnetism, and conse-
quently such a structure possesses magnetic properties. For this reason,
A. L. Parson, to whom this concept of the electron is due (Smithsonian
Inst. Pub., 65, No. n, 1915), substitutes the word magneton in place of
The term magneton was first introduced by Weiss in 1911 (cf. N.
Campbell's Modern Electrical Theory], On the basis of the electron
theory of paramagnetism an expression has been deduced for the sus-
ceptibility according to which this quantity should be proportional to
M' 2 /T, where M is the magnetic moment of a molecule and T is the
absolute temperature. Weiss observed that in the case of magnetite
over a certain temperature range the curve connecting the susceptibility
with the reciprocal of the temperature was not a straight line through
the origin, as it should have been, but consisted of a series of lines
separated by definite differences in the value of the susceptibility.
This was ascribed by Weiss to abrupt, discontinuous variations in the
value of the molecular magnetic moment M, and Weiss further showed
that the various observed values were all even multiples of a certain
quantity to which he gave the name the magneton. The magnitude
(i.e. the moment) of the magneton is the same as that which would be
produced by a rotating electron revolving in an orbit of radius io~ 8 cm.
with a frequency of io 14 per second approximately. Weiss of course
kept to the classical concept of the electron.
In the case of Parson's ring electron or circuit current the radius of
the ring is estimated to be about 1-5 x io~ 9 cm., that is a quantity
PARSON'S A TOM-MODEL 1 1 9
somewhat -less than the accepted value for the diameter of an atom.
Parson's theory of atomic structure based upon the magneton hypothesis
may be summarised as follows :
The positive charge in the neutral atom, which must be present to
balance the negative charges of the magnetons is regarded as a sphere
of uniform positive electrification possessing a volume which is pro-
portional to the number of magnetons which it contains. That is, the
distribution of the positive charge is once more treated as in the
original theory of atomic structure first advanced by Sir J. J. Thomson
(cf. Chap. I., Vol. I.). This positive sphere is regarded as having the
properties of an elastic solid and " is surrounded by an atmosphere or
envelope of very low charge density which is also elastic ". Given this
distribution, Parson shows that a group of eight magnetons may be
airanged symmetrically round the sphere so as to give a stable configura-
tion ; and even with atoms possessing a larger number of magnetons,
a similar distribution of eight is assumed. Such an arrangement ob-
vi3usly recalls the Abegg-Bodlander theory of valency, according to
waich the natural number of valencies is eight, though all these are not
effective as far as another atom is concerned. To explain the existence
of the long periods in the period classification as well as the properties
of certain elements contained therein, it is necessary to assume a certain
" hindrance " to the formation of the normal number of eight magnetons.
On the basis of these assumptions Parson discusses the single mag-
netic attraction between two such magnetons, the tendency to form the
group of eight, the residual valency effect and the electrical polarisation
set up by a magneton of the above type. On the basis of this atomic
structure Parson has made a rough calculation of the heat of dissocia-
tion of hydrogen, obtaining the value 135,000 cals. per gram- molecule;
Langmuir's value being of the order 80,000 cals.
One of the most obvious advantages of the Parson magneton is that
it affords a rational basis for the assumption made by Bohr, viz. that
an electron rotating in a stable orbit does not radiate. A rotating
electron as hitherto envisaged suffers an effective inward acceleration
in rotating, and hence, on the basis of the classical electromagnetic
theory, it should emit radiation continuously, its orbit becoming smaller
until it falls into the centre of the atom. On the basis of the classical
electromagnetic theory it is also known that the greater the number of
electrons rotating in a ring the less the radiation from the ring. The
Parson ring magneton is equivalent to a continuous series of charges,
and consequently such a ring, howsoever great its velocity, will not
radiate at all. This carries out Bohr's idea of the absence of radiation
from an electron in an orbit.
On the other hand one of the most obvious disadvantages of Parson's
theory of atomic structure lies in the assumption of a uniform positive
sphere of electricity, for on such a basis it is quite impossible to account
for the large angle scattering of a rays observed by Rutherford. The
point is therefore whether we can retain the advantage of the ring
electron or magneton and at the same time get rid of the hypothesis of
120 A SYSTEM OF PHYSICAL CHEMISTRY
the positive sphere, by substituting for it the nucleus idea of Rutherford.
The difficulty, as already pointed out, consists in the fact that an atom
consisting of a nucleus surrounded by an atmosphere of magneton?
would be an unstable system. The problem has been discussed in a
preliminary manner by D. L. Webster (/ Amer. Chem. Soc., 40, 375,
From what has been said it will be obvious that the magneton
theory of atomic structure as developed by Parson is still in a rudiment-
ary stage. Its advantages, however, are such, particularly in regard to
its applicability to chemical phenomena, that it cannot be discarded
without a serious attempt being made to overcome the main difficulty
of the scattering of the a particles.
High Frequency Spectra of the Elements. Moseley's Relation,
By the high frequency spectrum is meant the X-ray spectrum which
is obtained from a substance by bombarding the substance with /3-rays.
It has been pointed out in Vol. I., Chap. II., that the investigation of the
structure of crystals by means of their X-ray spectra affords a means of
determining with precision the wave-length of any homogeneous X-ray
employed. X-rays only differ from light in possessing very much shorter
wave-lengths (of the order io~ 8 cm.). The substance to be used as a
source of X-rays forms the anticathode in a vacuum tube, and the beam
of X-rays emitted as a result of bombardment by the cathode rays is
characteristic of the substance forming the anticathode. In general
the X-rays thus excited are not homogeneous. They consist of two
or more wave-lengths which can be analysed and measured by means
of the crystal acting as a grating. As a rule, however, one frequency
is more prominent than the others, that is, the intensity of the result-
ing spectrum is greatest for one type, and for the sake of simplicity we
shall consider these single frequencies as characteristic of the X-rays
emanating from the substance examined. When the anticathode is
of nickel, the characteristic wave-length of the X-ray produced is
i -io x io~ 8 cm. It follows, therefore, that a single quantum hv of
this type contains energy in amount 178 x io~ 8 ergs. It is of in-
terest to compare this quantity with the energy of the electron of the
cathode stream which gave rise to the X-ray. Whiddington (Proc.
Camb. Phil. Soc., 1910) has shown that an electron of the cathode
stream will not excite X-ray radiation unless its velocity exceeds a
certain critical value, which varies with the nature of the material
composing the anticathode. If the latter be of nickel the limiting
velocity of the electron striking it is 6 -17 x io 9 cm. per sec., or about
one-fifth of the speed of light. Taking the mass of the electron to be
0-9 x io~ 27 gram, the kinetic energy of the electron possessing the
limiting speed is 1*7 x io~ 8 erg, a quantity which is very nearly the
same as the energy in a single quantum of the X-ray produced.
Further, the investigation of the reverse process, i.e. the emission of an
HIGH FREQ UENC Y SPECTRA 1 2 1
electron by means of X-rays, has shown that the kinetic energy of the
electron is approximately equal to that of the cathode ray which
excited the X-ray in the first instance. As Bragg remarks " we are
justified in assuming that these processes are actual examples of the
give-and-take of radiant energy with which Planck's hypothesis is con-
Whiddington has also found that the limiting velocity of an electron
just necessary to excite an X-ray from a particular element is proportional
to the atomic weight of the element. Now we have seen that the
frequency v of the X-ray is proportional to the kinetic energy of the
electron producing the ray. Hence the frequency of the X-ray is pro-
portional to the square of the velocity of the electron and therefore to
the square of the atomic weight. This serves as a useful guide in the
choice of a substance for the anticathode which will produce an X-ray
of a given kind.
In 1913 van den Broek (Physikal. Zeitsch., 14, 3 2) suggested, that in
comparing elements with one another, the atomic number, that is,
number which represents the position of the element in the periodic
table is a far more fundamental quantity than the atomic weight itself.
As a matter of fact the atomic number of an element is approximately
one-half of the atomic weight, so that any quantity proportional to
the atomic weight is likewise proportional to the atomic number.
The connection between the nature of an element and the frequency
of the X-ray produced from it has been systematically studied by
Moseley (Phil. Mag., [vi.], 26, 1024 ; ibid., 27, 73 (1914))- On plotting
the square root of the frequency of the X-ray produced from a given
element against the atomic number of the element, for a whole series
of elements, Moseley found that a simple linear relation connected the
two quantities. This was true both for the K and L types of X-rays,
types which differ from one another in intensity, the K type being pro-
duced from a "hard" bulb (high vacuum), the L type being pro-
duced from a "soft" bulb. It is evident that the atomic number is
not simply an ordinal but possesses some actual physical significance.
The Rutherford atom-model, already discussed, suggests what this signi-
The measurements of Rutherford and Geiger showed that the magni-
tude of the positive charge on the nucleus was N* where e is identical
with the magnitude of the charge on an electron, and N is a number
approximately one-half the atomic weight. N is in fact a number
identical with the atomic number. It is probable that the elements
differ from one another in the magnitude of the nuclear charge, and it is
reasonable to suppose that successive elements in a table of elements vary
by the amount e on the nuclear charge. Regarding the nuclear charge of
hydrogen atom as e itself, the succeeding elements will possess 2<?, 3^, and
so on, or in other words, the atomic number indicates the magnitude of
the nuclear charge. If this be so, the various relations, found between
atomic number and other quantities serves to relate these quantities to
the magnitude of the nuclear charge. The simplest form of Bohr's
A SYSTEM OF PHYSICAL CHEMISTRY
relation, already discussed, between the frequency of emitted radiation
and electronic charge involves the square of the latter. In other words,
the square root of the frequency emitted is proportional to e itself.
Bohr's relation, in fact, is capable of predicting the characteristic X-ray
radiation from an element of high atomic weight with considerable
exactness. In this connection it may be pointed out (cf. Millikan
Physical Review, Aug., 1917) that the orbit of the innermost electron
is inversely proportional to the atomic number or nuclear charge, i.e.
the greater the charge on the nucleus the smaller the radius of circular
path followed by the innermost electron.
Characteristic Infra-red Frequency and Atomic Number.
An interesting relationship has been pointed out by Allen (Proc.
Roy. Soc., A, 94, ioo (1917)) between the atomic number and the infra-
red frequency which accounts approximately for the atomic heat of the
element. Writing N for the atomic number and v for the frequency of
a given element, Allen's relationship is
Nv = nv^
where n is an integer called the frequency number, and V A is a funda-
mental constant the same for all elements. The mean value for V A is
2 1 '3 x i o 12 . The following table illustrates the above relation. The
experimental values of v for the various elements (obtained from atomic
heat measurements of Nernst, Griffiths, and Keesom-Onnes) have
been multiplied by the atomic number N.
Nv x IO
5 x 21-6
5 x 21-4
10 X 20*9
10 x 20-9
9 x 213
9 x 21-9
9 X 21'2
9 x 21-3
7 x 20-6
7 x 20-6
7 x ao'6
IO X 21'2
TO X 21*1
IO X 2I'I
8 X 2I'I
8 X 2I'I
8 X 20'2
8 X 2O'2
7 X 22'2
7 x 22-5
7 x 21*6
7 X 22'O
The above relationship is empirical and its full significance has not
yet been determined. It may be pointed out, however, that Biltz has
shown the characteristic infra-red frequency v of the elements to be a
periodic function of the atomic weight, and therefore of the atomic
number. Since V A is a constant it follows that n must likewise vary in
a periodic manner with the atomic weight or number. This is not the
same thing, however, as explaining the significance of n.
(Systems not in equilibrium) Quantum theory and the photo-electric effect
Photochemical reactions Einstein's Law of the photochemical equivalent
Thermal reactions Reaction velocity from the standpoint of the quantum
THE PHOTO-ELECTRIC EFFECT.
HALLWACHS in 1888 was the first to show that a body carrying a charge
of negative electricity loses its charge on being exposed to ultra-violet
light ; on the other hand a positively charged body is not discharged.
Later, Hallwachs and Righi showed, independently, that an insulated
metal exposed to ultra-violet light acquires a positive charge. That is
to say, negatively charged particles, electrons, are emitted from the
metal under the action of ultra-violet light. This phenomenon is
known as the photo-electric effect. Certain metals, such as the alkali
metals and zinc and aluminium, exhibit this effect even under the in-
fluence of ordinary " visible ' ' light, the effect being greatest in the case
of the alkali metals. It is essential in all these cases that the surface
should be fresh and clean ; if a layer of oxide forms, the effect is greatly
weakened. This is known as photo-electric fatigue.
This emission of electrons is bound up with an absorption of the
light. The periodic electric force in the radiation sets the electrons on
the surface into more violent vibration, so that some of them are ejected
from the metal into the neighbouring space. If v is the velocity
possessed by an ejected electron, its kinetic energy is ^mv 2 , where m
is the mass of the electron. If the surface be charged positively to a
potential of V volts, which potential is just able to prevent the escape
of the electron, it follows that W, where e is the charge on the electron,
is just equal to ^mv 2 , i.e. the kinetic energy which the electron would
have had if no potential had existed.
Experiment has shown that the photo-electric effect really comprises
two phenomena, apparently distinct from one another. These are
known as the normal photo-electric effect and the selective photo-electric
effect respectively. We shall consider the normal effect in the first
The photo-electric current, produced by the moving electrons which
have been set free from the surface, depends upon two factors, (i) the
number of electrons emitted in unit time, and, (2) the speed of these
electrons. If the intensity of the light be increased, without altering
the colour or quality (i.e. without altering the vibration frequency), it
A SYSTEM OF PHYSICAL CHEMISTRY
has been found that the photo-electric effect increases proportionally
to this intensity, because the number of electrons emitted increases in
the same proportion. As long, however, as the frequency of the light
is maintained constant, the velocity of the electrons is also constant.
On the other hand, working with constant intensity of light but varying
the quality or frequency it has been found that, on increasing the
frequency of the light, the photo-electric effect increases, because the
speed of the electrons is now increased. According to Lenard and
Ladenburg, when the wave-length is thus shortened (at constant in-
tensity), the velocity of the electrons emitted increases proportionally
to the frequency. It is now known that the square of the speed is
proportional to the frequency of the incident light. Below a certain
wave-length or frequency, known as the threshold wave-length, the
normal photo-electric effect is not observable. That is, with wave-
lengths longer than a certain value A. characteristic of the substance
under examination no electrons are emitted. Hughes has determined
the value of X for a number of substances, using fresh surfaces, obtained
by distillation of the substance in vacua. These values are given in
the following table :
NORMAL PHOTO-ELECTRIC EFFECT. THRESHOLD WAVE-LENGTHS (\o).
The values obtained by Richardson and Compton with freshly scraped
surfaces correspond to somewhat longer wave-lengths than those given.
Starting from the above threshold wave-lengths and diminishing the
wave-length, the photo-electric effect increases in virtue of an increase
in the velocity of the electrons. According to Richardson and Compton
this goes on until a certain limiting value, corresponding to an ex-
tremely short wave-length is attained, beyond which the normal photo-
electric effect no longer increases.
One of the most striking features of the photo-electric effect is the
fact that the speed of the electrons is the same for a given quality
(frequency) of light quite independent of the intensity of the light.
Further, on keeping the intensity constant and varying the quality of
the light, the speed of the electrons increases as the frequency increases.
These two facts have found a satisfactory explanation on the basis of
the quantum hypothesis, in which the light is regarded as " hetero-
geneous". The following statements indicate the view held by Sir
J. J. Thomson in regard to the point under consideration (Proc.
THE PHOTO-ELECTRIC EFFECT 125
Camb. Phil. Soc., 14, 421, 1908): The [radiant] energy travelling
outwards [from the radiating source] with the wave is not spread
uniformly over the wave front, but is concentrated on those parts of
the front where the pulses are travelling along the lines of force ; 1
these parts correspond to the bright specks, the rest to the dark
ground. . . . The energy of the wave is thus collected into isolated
regions, these regions being the portions of the lines of force occupied,
by the pulses or wave motion. In fact, from this point of view, the
distribution of energy is very like that contemplated on the old emission,