THE INNER REGIONS 165
INDEX 187
CHAPTER I: _Units and Notation_
ATOMS AND ELECTRONS
Chapter I
_Units and Notation_
_Dimensions._—All physical magnitudes are measured in terms of the
three fundamental quantities, Length, Mass, Time. When we wish to
particularise, we denote these fundamental magnitudes by the letters
_L_, _M_, and _T_ respectively. Any magnitude which is not simply a
length or a mass or a time is derived from them. Thus an _area_ is
a length multiplied by a length. If we wish to express this fact we
say that the Dimensions of an Area = _L_ × _L_ = _L_^{2}. Similarly, a
velocity is a length divided by a time. Its dimensions are _L_/_T_. An
acceleration is the rate of increase of a velocity. A stone falling to
the earth has an acceleration, since it is moving faster and faster.
An acceleration is a velocity divided by a time, and therefore
its dimensions are _L_/_T_^{2}. A momentum is a mass multiplied by a
velocity. Its dimensions are therefore _ML_/_T_. These examples suffice
to illustrate the general idea.
_Metric System._—Throughout all civilised countries scientific men use
the metric system of units. The fundamental units are: for length, 1
centimetre; for mass, 1 gramme; for time, 1 second. This is called
the centimetre-gramme-second system or, as it is usually written,
the C.G.S. system. For those not used to measuring quantities in
centimetres and grammes, it may be useful to see how they compare
with English units. A centimetre is about 0·39 of an inch; a gramme
is about 0·035 of an ounce. The unit of velocity, on this system, is
one centimetre per second. The unit of momentum would be one gramme
moving with a velocity of one centimetre per second. A very useful
notion in science is the notion of _force_. This term has a perfectly
precise meaning. The force acting on a mass is measured by the velocity
imparted to that mass in the unit of time. On the C.G.S. system, unit
force is that force which gives to a mass of 1 gramme a velocity of
1 centimetre per second in a second. This unit of force is called a
_dyne_.
In the metric system, a very convenient system of prefixes is used
which play the part of multipliers or dividers. Thus the prefix “mega”
in front of some unit, such as a dyne or a gramme, means a million
dynes or grammes. The prefix “milli,” on the other hand, divides the
unit by a thousand. Thus a milligramme is a thousandth of a gramme. We
append a table of these prefixes.
mega is equivalent to multiplying the unit by 1,000,000
myria " " " " " " 10,000
kilo " " " " " " 1,000
hecto " " " " " " 100
deka " " " " " " 10
deci " " dividing " " " 10
centi " " " " " " 100
milli " " " " " " 1,000
micro " " " " " " 1,000,000
A centimetre, therefore, as its name denotes, is the hundredth part of
a metre. A kilogramme is a thousand grammes. And so on.
_Electrostatic and Electromagnetic Units._—The reader of this book
will notice that quantities of electricity are sometimes expressed in
what are called electrostatic units and sometimes in electromagnetic
units. Both systems of units are constantly employed in physics, and
they exist because there are two radically different ways of measuring
electric magnitudes. The reader probably knows that there are two
kinds of electricity, positive and negative. Two electric charges of
the same kind repel one another; if of unlike minds, they attract one
another. It is on this property of attraction or repulsion that the
electrostatic system is based. The electrostatic definition of a unit
quantity of electricity is as follows: The unit quantity of electricity
is that which, when concentrated at a point at unit distance in air
from an equal and similar quantity, is repelled with unit force. On the
C.G.S. system the unit distance is one centimetre and the unit force
one dyne. The unit magnetic charge, or magnetic pole, as it is called,
is defined in a similar way.
The electromagnetic system, on the other hand, starts with the
dynamic, not the static, properties of electricity. A wire conveying
an electric current produces a magnetic field. The lines of magnetic
force exist as circles round the wire. If we imagine the wire itself
to form a circle, we see that there will be a certain magnetic force
at the centre of this circle. This leads us to the electromagnetic
definition of the unit quantity of electricity. We proceed in two
steps. We first define the unit current as such that, if it is flowing
in a circular arc 1 centimetre in length where the circular arc
forms part of a circle having a radius of 1 centimetre, then it will
exert a force of 1 dyne on a unit magnet pole placed at the centre
of the circle. This defines the unit current. We get to the unit
quantity of electricity by saying that it is the quantity conveyed by
the unit current in 1 second. The electromagnetic unit of quantity
is enormously greater than the electrostatic unit. It is thirty
thousand million times bigger. The ratio of the electromagnetic to the
electrostatic unit is, in fact, equal to the velocity of light. This
is no mere meaningless coincidence. Maxwell showed that this ratio
gave the velocity of propagation of electromagnetic waves, and this
velocity is precisely the velocity of light. This was one of the chief
points confirming the theory that light itself is an electromagnetic
phenomenon.
_Large and Small Numbers._—Physicists often have to express very large
and very small quantities, and to that end they have adopted a useful
and simple convention. A large number like ten million is not written
10,000,000 but as 10^{7}. The figure 7 shows how many 0’s are to be
written after the 1. If the number had been thirty million it would
have been written 3 × 10^{7}. Thus 100 = 10^{2}; 1,000 = 10^{3}; 10,000 =
10^{4}; and so on. Such numbers as 10^{24} or 3·5 × 10^{24} would be
tedious to write out, and they are of frequent occurrence.
Similarly, very small numbers are expressed much more conveniently in
this way. But the minus sign is prefixed to the figure above the 10.
Thus one millionth is 10^{-6}. One million millionth is 10^{-12}. Seven
one hundred-thousandths is 7 × 10^{-5}. Thus 1/10 = 10^{-1}; 1/100 =
10^{-2}; 1/1000 = 10^{-3}; 1/10000 = 10^{-4}; and so on. So that when
we say that the weight of a hydrogen atom is 1·65 × 10^{-24} gramme,
the quantity we express in this way is
1·65/1,000,000,000,000,000,000,000,000
of a gramme. Similarly, when we say that the velocity of light is 3
× 10^{10} centimetres per second, the number we are expressing is
30,000,000,000 centimetres per second.
CHAPTER II: _Atoms and Molecules_
Chapter II
<i>Atoms and Molecules</i>
§ 1. _The Atom_
The theory that any piece of matter may be divided up into small
particles which are themselves indivisible was a speculation familiar
to the ancient Greeks. It is a theory which, unless it be enunciated
with some care, has been found by some people to be ambiguous. For
the indivisibility attributed to the ultimate particle or _atom_ may
have reference either to practical or to mental operations. There are
philosophers who have worried themselves as to how it is possible
to conceive any particle of matter, however small, as ultimately
indivisible. For, they argue, if the small particle exists at all it
must occupy space and have a shape. Something still smaller, therefore,
something occupying only half the space, could be imagined: the atom
could be pictured as divided into halves or quarters and so on. And
yet, although it seems impossible for thought to stop at any point
in the process of dividing up a piece of matter, it is also very
difficult, as can be shown by ingenious arguments, for thought to go
on with the process indefinitely. And so an interesting _impasse_ is
arrived at.
Now it must be clearly understood from the beginning that this is
not the sort of indivisibility with which science is concerned.
The scientific use of the term has reference purely to practical
scientific methods. The indivisibility ascribed to the atom was merely
an enunciation of the fact that smaller particles than atoms were
not found to occur in any of the processes known to science. Nothing
whatever was asserted about any supposed “inherent indivisibility” of
the atom. An atom of a substance was merely the smallest part of that
substance which took part in any known chemical processes. The whole
conception of the atom was first made really definite and fruitful by
John Dalton in 1803. He asserted that every irreducible substance, or
“element,” was composed of atoms indivisible in the sense described
above. All the atoms of every given element were precisely similar,
and, in particular, had the same weight. The atoms of different
elements were different and, in particular, had different weights. But
besides the chemical elements, that is, substances which cannot be
dissociated into other substances, there are chemical compounds. The
atoms of the elements constituting a compound unite with one another in
a perfectly definite way, and Dalton gave the laws according to which
these combinations are effected.
The Atomic Theory of Dalton was a tremendous success. The whole of
chemistry since his time has been based on it. To describe even a
small part of the consequences of the atomic theory would be beyond
our scope, but we must here call attention to one very important
classification to which the atomic theory led. By very careful
measurements, undertaken by many men and extending over many years,
the weights of the atoms of all the different primary substances,
or elements, known to science have been determined. The weights, as
usually given, are, of course, relative weights. If we denote the
weight of an atom of oxygen by 16, then helium, for example, will
have the atomic weight 4, copper will be 63·57, and hydrogen will be
a little greater than unity, viz., 1·008. The heaviest element known,
uranium, has an atomic weight of 238·2.
Now when all the elements known are arranged in order of increasing
atomic weight the highly interesting fact emerges that their
properties are not just chaotically independent of one another. They
fall into similar groups, recurring at definite intervals. These
relations, although they are not of mathematical definition, are quite
unmistakable, and show that there is a connection between chemical
properties and atomic weights. Such a connection is quite inexplicable
if each atom is regarded as a perfectly simple and irreducible
structure having no essential relations to the atoms of any other
elements. If the atom be regarded as something possessing a structure,
then the similarities between different elements may be attributed to
similarities in their atomic structures, the heavier atoms being, as it
were, more complicated versions of the same ground plan. We shall see
that there is much truth in this view.
Even as early as 1815 the idea had been put forward by Prout that
all the chemical elements were really combinations of one primordial
substance. Prout supposed this primordial substance to be hydrogen.
On comparing different atomic weights he was led to the conclusion
that they were all whole multiples of the atomic weight of hydrogen,
so that if the weight of hydrogen be represented by 1, then all the
other atomic weights would be whole numbers. Every atom, in this case,
could be considered as built up from a definite number of hydrogen
atoms. The determinations of atomic weights in Prout’s day were not
sufficiently accurate to warrant this conclusion, and when more
accurate measurements showed that a large number of atomic weights are
not whole multiples of hydrogen, Prout’s hypothesis was abandoned. But
recent work, as we shall see, has shown that Prout’s hypothesis is much
closer to reality than had been supposed.
§ 2. _Elements and Compounds_
The theory that all matter is built up out of atoms was invented, as
a scientific theory, to explain certain phenomena which belong to the
science of Chemistry. The universe of the chemist is, at first sight,
a very bewildering universe. He is concerned to find out what he can
about the properties of all the substances that exist. Now there are
hundreds of thousands of such substances. Gold, lead, iron, table
salt, air, water, gum, leather, etc., etc., is the mere beginning of
a list that it would take months simply to write down. The chemist is
concerned with every one of these substances. And if he found that all
these substances were quite independent of one another, that there were
no relations between them, then he would probably give up his task in
disgust. For, in that case, he could do nothing but draw up a gigantic
catalogue which would, at most, be of some practical use, but which
would possess no scientific interest. But even before the rise of a
true science of chemistry, men had become aware that all the different
substances on earth are not wholly unrelated to one another. The old
alchemists, chiefly by mixing different substances together and then
heating them, found that they could change some substances into others.
Some of their results were perfectly genuine; they did affect some of
the transformations they claimed to have effected. In other cases,
they were either mistaken or else imposing on the credulity of their
disciples. Many of them claimed, for instance, that certain “base”
metals, on being mixed with other substances and then heated, could be
turned into gold. We know that this is impossible. But one main idea
emerged from their work. They learned to distinguish between the simple
substance and the compound substance. It is true that this idea emerged
in a very curious form; they did not think so much of simple substances
as of primary principles, such as maleness and femaleness, which were
somehow incorporated in different substances in different degrees. But
the idea of the simple and compound substance, although in a vastly
different form, is the basis of the science of chemistry.
Out of all the substances known to exist, the chemist distinguishes
a certain number as being “elements.” An element is a substance which
cannot be decomposed into anything else. It happens that there are
remarkably few of them. Nearly every one of the hundreds of thousands
of substances known can be decomposed into other substances. When
this decomposition is carried as far as it will go, we find that the
substance in question is really built up out of a certain number of the
substances called elements. There are about ninety of these elementary
substances. In the little list of substances we have just given, for
instance, gold, lead, and iron are elements. Table salt is a compound
of two elements called sodium and chlorine. Air is a mixture of various
elements of which nitrogen and oxygen are the chief. Water is a
compound of two elements, hydrogen and oxygen. Gum and leather are more
complicated compounds.
Now it is interesting enough to know that all substances are either
elements or can be decomposed into two or more elements. But the most
interesting aspect of this fact, and what makes it of great scientific
importance, is that when elements combine to form a substance they
always do so in exactly the same proportions. When hydrogen combines
with oxygen to form water, for instance, exactly the same proportions
of hydrogen and oxygen are concerned. We will illustrate this very
important law by considering the decomposition of that well-known
substance sal ammoniac. It is a pure solid substance. If it be heated
it turns into a mixture of two gases. These two gases can be separated
from one another and are found to be ammonia gas and hydrochloric
acid gas. Now the ammonia gas can in its turn be decomposed into a
mixture of the two gases, nitrogen and hydrogen, and these two gases
can be separated from one another. The hydrochloric acid gas can also
be decomposed. It can be decomposed into chlorine and hydrogen. We
have now decomposed our sal ammoniac into three substances, nitrogen,
hydrogen and chlorine. Each of these three substances is an element;
no one of them can be decomposed into anything else. And we can find
in what proportions they combine to make sal ammoniac. If we began our
experiment with 100 grammes of sal ammoniac we should have at the end
26·16 grammes of nitrogen, 7·50 grammes of hydrogen, and 66·34 grammes
of chlorine, the combined weight of these substances making up exactly
100 grammes. And in whatever way we perform the decomposition of sal
ammoniac we always get these three substances and always in exactly the
same proportions. By starting with nitrogen, hydrogen, and chlorine in
the above proportions we can, of course, make sal ammoniac. And there
is no way of making sal ammoniac except with just those proportions. No
specimen of sal ammoniac ever has slightly more chlorine or nitrogen
or slightly less hydrogen, for example, than any other specimen.
The same remarks apply to every other compound. The general law may
be enunciated thus: _the same compound is always formed of the same
elements in exactly the same proportions_.
In the above example we obtained, in our preliminary dissociation
of sal ammoniac, two substances each of which contained hydrogen.
We obtained ammonia gas, which is made up of nitrogen and hydrogen,
and we obtained hydrochloric acid gas, which is made up of chlorine
and hydrogen. We might ask the question whether there is any simple
relation between the amount of nitrogen which combines with, say, one
gramme of hydrogen, and the amount of chlorine which combines with one
gramme of hydrogen. But before dealing with this question we will deal
with another which has some bearing on it. Can two elements combine in
different proportions to form different substances, and, if so, what is
the relation between the proportions? The answer is that two substances
can combine in different proportions to form different substances, but
that, when this occurs, the proportions are simple multiples of one
another. Thus, 3 grammes of carbon can unite with 8 grammes of oxygen
to produce a substance called carbon dioxide. But 3 grammes of carbon
can unite with 4 grammes of oxygen to produce a different substance
called carbon monoxide. It will be noticed that the amount of oxygen
in the first case is just twice that in the second. This example is
typical. Whenever there is more than one compound of two elements the
ratio by weight of the elements in the two compounds is always a
simple number. This fact is very suggestive, as we shall see.
We can now deal with our first question, and we can make it more
general. Consider, for instance, hydrogen, oxygen, and carbon. We can
take 2 grammes of hydrogen and combine them with 16 grammes of oxygen.
The result is water. Again, if we take 16 grammes of oxygen and combine
them with 12 grammes of carbon we shall obtain carbon monoxide. Here
the 16 grammes of oxygen is the common factor. The appetite of this
amount of oxygen for combination can be satisfied, apparently, either
with 2 grammes of hydrogen or 12 grammes of carbon. And the interesting
fact is that we can combine hydrogen and carbon in precisely this
proportion. Two grammes of hydrogen combine with 12 grammes of carbon
to form a substance called olefiant gas.
Now these are the facts that the atomic theory so beautifully explains.
Let us see how it is done. Dalton’s atomic theory is to the effect that
every element is built up of small equal particles. These particles
are indivisible in the sense that less than one of them cannot take
part in any chemical reaction. They are called _atoms_. The smallest
part of a compound substance is called a _molecule_. It is built up
out of atoms of the elements which unite to form that compound, and it
is the smallest part of the compound which can exist as that definite
substance. If a molecule were split up we should simply get the
constituent elements again; the compound substance itself would have
ceased to exist. Consider, for instance, a molecule of carbon monoxide.
We know that this molecule is formed from one atom of carbon and one
atom of oxygen. We write it CO. The carbon dioxide molecule, on the
other hand, is formed from one atom of carbon and two atoms of oxygen.
We write it CO_{2}. A carbon dioxide molecule contains exactly twice
as much oxygen as does a carbon monoxide molecule. It cannot possibly
contain 1–1/2 times as much or 1–3/4 times as much, since the amount of
oxygen present in a molecule must vary by at least one atom. Thus we
see how it is that the proportions are whole multiples.
The atomic theory gave so clear and simple an account of the laws of
combination that there could be little doubt of its truth. The ordinary
chemical methods, however, did not enable one to decide unambiguously
what were the exact relative weights of the atoms of the different
elements. This question is obviously of great importance, but the law
discovered by Avogadro, called Avogadro’s hypothesis, enabled the
matter to be cleared up. This hypothesis asserts that _equal volumes of
different gases, under the same conditions of temperature and pressure,
contain equal numbers of molecules_. We may mention here that many
elements normally exist in a molecular form, that is, their atoms unite
together in twos or threes to form molecules.
§ 3. _Relative Weights of Atoms_
We will now give the reasoning by which, from Avogadro’s hypothesis,
the relative weights of atoms may be deduced. Suppose we have a number
of precisely similar vessels, each having the same volume _V_, and
each filled with a gas at the same temperature and pressure. Then,
according to Avogadro’s hypothesis, they each contain the same number
of molecules. Suppose we take two of these vessels, one containing
hydrogen and the other oxygen, and compare the weights of the two
quantities of gas. Since they have the same number of molecules,
the relative weights of the two quantities of gas is the same as
the relative weights of their molecules. But is this sufficient to
determine the relative _atomic_ weights of hydrogen and oxygen?
Obviously not, for the molecule of hydrogen, for all we know, may
contain two or more atoms, and so may the molecule of oxygen. This
method will not give us the desired result.
But we have said that the atom is the smallest part of an element
that takes part in any chemical combination. What we really mean by
that is that the smallest part of an element which takes part in any
known chemical reaction is called an atom. Suppose, therefore, we
consider all the compounds into which hydrogen enters. Amongst these
compounds there will be one whose molecules contain a minimum amount
of hydrogen. The molecules of this compound contain, therefore, one
atom of hydrogen. The volume _V_ of this compound, in the gaseous
state, and at a certain pressure and temperature, contains a mass of
hydrogen which can be measured. Call this mass _H_. Now, of all the
oxygen compounds, select that compound which contains the minimum
weight of oxygen. The molecules of this compound contain one atom of
oxygen. The volume _V_ of this compound, in the gaseous state, and at
the same pressure and temperature as the hydrogen compound, has a known
weight of oxygen. Call this mass _O_. Both the oxygen and the hydrogen
compounds have the same number of molecules, by Avogadro’s hypothesis.
Corresponding to each molecule of the hydrogen compound is one atom of
hydrogen, and corresponding to each molecule of the oxygen compound is
one atom of oxygen. We have, therefore, the same number of atoms of
hydrogen in the one vessel that we have of oxygen in the other. The
ratio of the weights of the hydrogen and the oxygen—that is, the ratio
of _H_ and _O_—is therefore the ratio of their atomic weights. By a
similar process we find the relative atomic weights of other elements,
carbon, chlorine, etc. For the purpose of comparing these relative
weights, oxygen is taken as the standard, simply because oxygen occurs
so frequently in chemical combinations. It is nearly 16 times heavier
than hydrogen, the lightest atom. Its weight is therefore taken as
_exactly_ 16. Compared with this hydrogen is 1·008. On this standard
carbon’s atomic weight is 12, and chlorine 35·456.
It is evident, from Avogadro’s hypothesis, that 1·008 grammes of
hydrogen contain as many atoms as 16 grammes of oxygen or 12 grammes of
carbon or 35·456 grammes of chlorine, and so on. The number of grammes
of an element which is equal to its relative atomic weight is called a
_gramme-atom_ of the element. All gramme-atoms contain the same number
of atoms. This number is known. It is 660,000 times a million billion.
This is the number of atoms in 1 gramme of hydrogen, 12 grammes of
carbon, 16 grammes of oxygen, etc. The actual weight of an atom,
therefore, is to be obtained by dividing its gramme-atom by this number.
§ 4. _Some Experimental Evidence_
The figure we have just given for the weight of an atom is evidently
exceedingly minute. Such small quantities are, of course, altogether
below the limits of observation. Nevertheless, there is a series of
experiments which enables us to see that the ultimate particles of
matter must be extremely minute. Gold-leaf, for instance, can be
prepared of a thickness of one ten-thousandth of a millimetre. In
this state, gold-leaf is transparent and transmits a greenish light.
It cannot be beaten out more thinly merely because of the difficulty
of manipulating such thin sheets without tearing them. It is certain,
therefore, that the diameter of a gold atom is less than the thickness
of one of these sheets, that is, is less than 10^{-5} cm. The weight of
a cube of gold, having this length for the length of its side, would
be 10^{-14} gramme. The hydrogen atom is about 200 times lighter than
the gold atom. On this showing, therefore, the mass of a hydrogen
atom is certainly less than 1/2 × 10^{-16} gramme. The study of thin
films takes us very much further. The black spots so familiar to us
on soap bubbles are the thinnest part of the soapy film. The blacker
they are the thinner they are. The thickness of these extremely thin
films can be measured, and is found to be about 4·5 × 10^{-7} cm.
The films produced by letting oil drops spread on water are even
thinner. Films no thicker than 1·1 × 10^{-7} cm. have been obtained.
The maximum possible diameter for an oil molecule, therefore, would be
about 1 × 10^{-7} cm. A hydrogen atom would weigh nearly a thousand
times less than one of these oil molecules, and we can calculate, on
this basis, that the mass of a hydrogen atom would be of the order of
10^{-24} gramme. The actual mass of a hydrogen atom, as can be shown by
other calculations, is 1·65 × 10^{-24} gramme. By actual experiment,
therefore, we can obtain films so thin that they are not much more than
one molecule in thickness.
§ 5. _Molecular Movements_
If two liquids are taken and one is placed on top of the other, we know
that they will begin to mix. In some cases the mixing process may take
a long time and may seem to be incomplete, as when water and ether are
superposed, for example. But even in this case we would find, after a
time, that every part of the layer of ether contained some water, and
that in every part of the water there was some ether. With most pairs
of liquids the diffusion is more rapid and obvious. Even solids diffuse
very slightly. With pairs of metals which have been kept in contact
for years, it is found that the bottom layer of one and the top layer
of the other have become, to some extent, intermingled. In the case
of gases, diffusion is rapid and complete. Berthollet took a globe
containing carbon dioxide, a heavy gas, and put it in communication
by means of a stop-cock with another globe containing hydrogen, the
lightest of gases. The globe of hydrogen was above the globe of carbon
dioxide, and in each globe the gas was at the same pressure. When the
stopcock was opened it was found that, after a little time, each globe
contained as much carbon dioxide as hydrogen. With any pair of gases
the result is the same.
This range of phenomena obviously points to the existence of molecular
motions. We must imagine that each tiny particle of a liquid or a gas
is in incessant movement. Even in the case of solids, there is some
movement of the molecules, although here the movement is much more
restricted. In a gas, in particular, the molecules must be moving about
in all directions, perpetually colliding and changing their directions.
A rise in temperature increases the velocity of these movements. All
phenomena of diffusion take place at a greater rate the higher the
temperature. What affects our senses as heat is, in fact, the energy
due to these molecular movements. The hotter the body the greater the
energy of motion of its molecules. Thus there is no such thing as a
greatest possible temperature. The temperature of the outer layers of
the sun is some thousands of degrees; the temperature of the innermost
parts may be some millions of degrees. But there is an absolute zero
of temperature; no body can be colder than the absolute zero. As
the temperature of a body decreases its molecular movements become
feebler and feebler until, at a sufficiently low temperature, they
cease altogether. This lowest possible temperature is the same for all
bodies. It is −273°C.
The hypothesis that a gas consists of a large number of molecules
moving about in all directions with all velocities is called the
Kinetic Theory of Gases, and its mathematical development enabled us
to account for the known laws of gases and to predict other phenomena
which have since been observed. At first sight the problem appears to
be a very complicated one. We have to assume that the molecules are
moving at random; some are moving slowly, some fast, some very fast,
and so on. They are moving in all directions; they are perpetually
colliding. Their motions are completely chaotic. But this very
fact, which seems to make the problem insoluble, was shown by James
Clerk Maxwell to lead to its solution. If we imagine our gas to be
enclosed in a box, for instance, then we may suppose that some of the
molecules, at a given instant, are moving towards one of the sides of
the box with a certain velocity—say 100 yards per second. But besides
having this motion, these molecules will also, in general, be moving
towards a side at right angles to the first one and also, it may be,
towards the floor or ceiling of the box. What do we know about these
other motions from the fact that these molecules are moving towards one
side at 100 yards per second? According to Maxwell, we know nothing
whatever about these other motions. They might be anything. And from
this mere fact he was able to deduce how different velocities are
distributed amongst the molecules of the gas by applying the theory of
probabilities. The pressure exerted by a gas is due to the incessant
bombardment of its containing vessel by its molecules. At a given
temperature there is a simple connection between the pressure and the
volume of the same mass of gas. If the volume is halved the pressure is
doubled; similarly, if the volume is doubled the pressure is halved.
The general relation is that, at constant temperature, the volume
multiplied by the pressure is constant. In virtue of their motion, the
molecules possess energy, and Maxwell showed that, for a given mass
of gas, the product of the pressure and volume of that mass of gas is
equal to two-thirds of the energy of translation of its molecules. At
the same temperature, therefore, it does not matter whether the same
mass of gas occupies a large volume or a small one; the energy due to
its molecular motions is the same. This energy is considerable. If the
molecular energy of 2 grammes of hydrogen could be utilised it would
be sufficient to raise a weight of 350 kilogrammes through 1 metre.
The speed of these flying molecules is very considerable. At the
temperature of melting ice the average velocity of oxygen molecules is
about 425 metres per second, which is nearly that of a rifle bullet.
At the same temperature, the hydrogen molecule is moving four times
as fast, namely, 1700 metres per second. These velocities are the
average velocities. Some molecules are moving more slowly, and some
faster. The molecules are constantly colliding. The average distance
between successive collisions is called the mean free path, and can
be calculated. For air at normal temperature and pressure, the mean
free path is about one ten-thousandth part of a millimetre. Collisions
occur, therefore, about 5,000 million times a second.
§ 6. _The Brownian Movement_
We now come to a remarkable discovery which gives us actual visible
evidence of the reality of these molecular movements. An English
botanist named Brown, using the improved microscope objectives
which had just been introduced, noticed, in 1827, that very small
particles suspended in water were in a state of constant movement.
This phenomenon was at first dismissed as being due to vibration or
to convection currents in the water. More careful experiments showed
that the motion certainly was not due to such causes. It does not occur
only in water. It occurs in all fluids, although the more viscous the
fluid the less active is the motion. The size of the small particles
is an important factor—the smaller the particles the more lively the
movement—but the substance or density of the particles seems to be
without effect. The movement never ceases. It has been observed in
liquid which has been shut up in quartz for thousands of years.
These movements have been very thoroughly observed, under a variety
of conditions, by Perrin, and their theory has been worked out by
Einstein. The correspondence between theory and observation is
remarkably satisfactory, and there can now be no doubt that the
Brownian movement is a direct manifestation of the chaotic molecular
movements of the fluid. We must imagine each small particle as being
constantly bombarded by the molecules of the fluid surrounding it.
If the particle be fairly large, these molecular impacts, occurring
irregularly and on every side of the particle, cancel out. No resultant
motion is given to the particle. But if the particle be small the
chances are less that the irregular impacts will cancel out. It may
happen that, for a time sufficient to produce visible motion in a very
small particle, the majority of the impacts are in one direction. A
moment afterwards, of course, the direction has changed. So we get
this incessant and extremely irregular motion called the Brownian
movement. The way in which the agitation depends on the molecular
energy of the fluid, on its viscosity, and on the dimensions of the
particles has been worked out by Einstein, and his results have
received experimental confirmation.
CHAPTER III: _Constituents of the Atom_
Chapter III
_Constituents of the Atom_
§ 1. _The Electron_
The notion that matter consists of discrete particles is, as we have
seen, a very satisfactory hypothesis. As opposed to the only other
possible theory, that matter is continuous, the atomic theory is more
successful in explaining phenomena, and it also appears to be a more
natural theory, one more easily grasped. The “continuum” theory has had
its supporters, however, amongst whom we may mention Goethe, besides
the more serious scientific names of Mach and Ostwald. But whatever
arguments there may once have been in favour of the continuous theory
of matter, recent work has caused the theory to be irretrievably
abandoned. But when we turn from matter to the “imponderables” such as
light, heat, electricity, the case is rather different. Both heat and
electricity were for a long time regarded as fluids. These fluids were
regarded as imponderable and continuous. There was even a two-fluid
theory of electricity according to which the two kinds of electricity,
positive and negative, were manifestations of two different fluids.
According to the one-fluid theory, the two kinds of electricity were
manifestations of the presence of a defect or excess of the fluid. But
these theories, although occasionally written about at length, were
rather perfunctory. They were little more than convenient mathematical
fictions. By assuming them, the mathematicians were enabled to get on
with their real interests, which consisted in working out the laws
according to which electrified bodies acted on one another. The whole
of this early work was purely formal. Experiment had shown that the
fundamental law of electrostatics was of the same form as the Newtonian
Law of Gravitation. Electrified bodies were regarded as geometrical
shapes carrying electric “charges” and attracting or repelling one
another according to the Newtonian law. “Action at a distance” was
assumed; that is to say, the change of force between electrified
bodies which accompanied change of position was assumed to take place
instantaneously, so that the positions and charges at a given instant
gave the forces at that same instant. This was the same assumption
that underlay the Newtonian Law of Gravitation, and it was open to the
same objection, namely, that it made it very difficult to conceive how
the action between distant bodies was propagated through the space
separating them. If the notion of propagation were given up the mutual
action between bodies not in contact became purely miraculous; if the
notion of propagation were retained it had to be conceived as taking
place with infinite velocity.
A very great advance on these conceptions was made by James Clerk
Maxwell. He directed attention to the “field,” to the space separating
electrified bodies, and he established mathematical equations whereby
the propagation of electric and magnetic actions in space could be
followed from point to point and from instant to instant. And he showed
that electromagnetic effects were propagated with the velocity of
light, _i. e._, 300,000 kilometres per second. Light itself was shown
to be an electromagnetic phenomenon, and hence the theory is usually
called the Electromagnetic Theory of Light. Heinrich Hertz, a brilliant
follower of Maxwell, succeeded in producing electromagnetic waves
some metres in length, and in showing that they could be reflected
and refracted and made to behave generally in ways characteristic of
light waves. Wireless telegraphy was developed directly from Hertz’s
work, and electromagnetic waves were produced several kilometres in
length. Thus the very important transition was made from the action of
a distance-theory to the field-theory of electric and magnetic action.
In the meantime, the study of the electric charges themselves had been
comparatively neglected. Certain phenomena attending the conduction of
electricity in solutions had, it is true, given rise to speculations
that electricity was probably atomic in constitution, but it was not
until the so-called cathode rays were studied that the existence
of atoms of electricity, disconnected from ordinary matter, was
experimentally confirmed. The apparatus necessary to produce cathode
rays consists of a glass tube in which an almost complete vacuum
exists. Through the walls of this tube two metallic wires are passed,
which are connected to a source generating electricity. One of these
wires is terminated, on the inside of the tube, by a metallic disc. If
now the potential difference between the two wires is sufficiently high
(some hundreds of volts) rays emanate from the metallic disc (called
the cathode) and proceed in straight lines, producing a fluorescence
at the other end of the tube where they strike the glass walls. That
the rays proceed in perfectly straight lines may be shown by placing an
object in the path of the rays—say a cross or a circular disc—when its
clear-cut shadow is thrown on the far end of the tube.
Now the fact that these rays are deflected when the tube is placed
in an electric or magnetic field shows that they consist of small
electrified particles in movement. Further, the nature of the
deflection shows that the electric charges carried by these small
particles are charges of negative electricity. The question arises:
What is the nature of the small electrified particles? Are they,
for instance, atoms of matter carrying electric charges? Are they,
perhaps, larger than atoms? Can it be that they are smaller than atoms,
that in the cathode rays we have matter existing in a sub-atomic
state? Certain measurements were made which allowed this question to
be answered without ambiguity. Each little electrified particle or
corpuscle carried a charge _e_ and had a mass _m_. The measurements did
not determine either _e_ or _m_ directly, but they did determine the
ratio _e/m_ of these two quantities. The ratio turned out to have the
extraordinary value of 1·77 × 10^{7} (electromagnetic) units. Let us see
just why this value was so extraordinary.
If _X_-rays or the rays emitted by radium are allowed to penetrate a
gas, they have the power of enabling that gas to conduct electricity.
The rays, in their passage through the gas, produce positively and
negatively charged carriers of electricity. These carriers are called
Ions. Now the most important characteristic of an ion is its electric
charge, and an ingenious experimental method enables this charge to
be determined. If air be saturated with water vapour and the air be
then suddenly expanded, the resultant cooling causes a cloud of small
drops of water to be formed. These drops coalesce round the tiny dust
particles present in the air. If the air has been purified of dust
particles it is possible for a considerable expansion to take place
without the formation of a cloud of drops. It was found, however, that
if ions are present they play the part of dust particles. Small drops
condense round the ions and a cloud is formed. By taking suitable
precautions, a single drop can be observed under the microscope. These
drops fall under their own weight. Now the rate of fall of such a
drop will depend on its size, its density, and on certain properties
of the gas through which it is falling. The mathematical problem of
determining the velocity of the drop from these other factors was
solved by Sir George Stokes. Now when the drops are formed round the
little electrified bodies called ions each drop carries an electric
charge. If, therefore, we cause an electric force to act on the drop,
say by letting the drop fall between two parallel electrified plates,
we can cause the electric force to act either with or against the
gravity of the drop and so either hasten or retard its descent. Knowing
the rate of fall under gravity alone, and also the rate of fall under
a known electric force, the actual charge carried by the drop can be
calculated. In this way it was found that the smallest charge, the
charge carried by a single ion, is 4·77 × 10^{-10} (electrostatic)
units. Now the ion, besides having a charge has also, of course, a
certain mass. The lightest ion known, the hydrogen-ion, which consists
of a single hydrogen atom carrying the above charge, has for the ratio
_e/m_, the ratio of charge to mass, the value 9649·4 (electromagnetic)
units. Let us contrast this with the ratio 1·77 × 10^{7} obtained for the
electrified corpuscles of the vacuum tube. This latter value is more
than 1800 times greater than the value for the hydrogen-ion. How is
this to be explained?
We might suppose that each electrified corpuscle is an atom carrying
a great many of the elementary electric charges—_i. e._, the smallest
charge carried by a single ion. But if we suppose the corpuscles to be
single atoms on which many charges are heaped, we should hardly expect
the ration _e/m_ to be always the same for every corpuscle. It would
seem that there ought sometimes to be more and sometimes fewer charges.
But a grave objection is that the ratio _e/m_ for the corpuscles
is quite independent of the nature of the gas of which a residuum
is always left in the vacuum tube, and is quite independent of the
material constituting the cathode. If the corpuscles are electrified
atoms, where do these atoms come from? Atoms of different substances
have different weights. How, then, does it happen that the ratio _e/m_
always remains the same? The only possible hypothesis which explains
all the facts is that the corpuscles consist of elementary charges of
electricity linked to a mass about 1800 times smaller than the mass of
a hydrogen atom. The corpuscles are of sub-atomic dimensions. These
tiny particles are called Electrons.
Of the existence of these bodies there can no longer be any doubt.
A great number and variety of phenomena are now known which point
to their existence; electric currents, radioactive processes, the
generation of _X_-rays, various optical effects, all bear witness
to the existence of these sub-atomic electrified bodies. Precise
measurements enable us to give the mass of an electron. It is 0·903 ×
10^{-27} gramme. As a comparison, we give also the mass of a hydrogen
atom, which is 1·650 × 10^{-24} gramme, a value about 1830 times
greater than that of the electron. The figure giving the mass of an
electron may be expressed by saying that one thousand million million
million million electrons would have a mass rather less than one gramme.
But the mass of an electron, although so small, is not zero. What
are we to suppose are the origin and nature of this mass? Here we
are led to a very startling and novel conception. We have always
supposed that only matter had mass; electricity has been classed as
an “imponderable,” that is, as something possessing no mass. But
this notion cannot be maintained. An electric current in a wire, for
instance, is produced by the application of an electromotive force, but
the current does not attain its full strength _instantly_ when the
force is applied. Similarly, when the force generating the current is
suppressed the current does not instantly vanish. It shows a tendency
to persist. It seems to be endowed with inertia, and inertia is a
property of mass. Further, Sir J. J. Thomson showed that an electrified
material sphere requires a greater force to set it in motion than if
it were unelectrified. The electric charge acted as if it imparted
some extra mass to the sphere. Part of the mass of the sphere could
be attributed to its ordinary matter and part to its electric charge.
If we regard our electrons, therefore, as small electrified spheres,
how much of their mass is to be referred to their electric charge?
We reach the startling conclusion that the _whole_ of the mass of an
electron is to be attributed to its electric charge. This conclusion,
we must mention, is not absolutely proved. It is a very convenient
and plausible assumption to make, however, and leads to a very simple
conception of matter. We shall see that all atoms may be conceived as
built up out of electrons, and since electrons consist of nothing but
electricity, we see that we reach an electric theory of matter, where
matter is held to consist of nothing but electric charges, and to have
no mass except the mass that results from these charges.
The initial difficulty of this conception resides wholly in its
unfamiliarity. When we become accustomed to the idea of attributing
mass to an electric charge, we shall find that it has thereby acquired
just the “materiality” necessary for it to figure as what we mean
by matter. On the hypothesis that the mass of an electron is due
wholly to its electric charge we find, assuming the electron to be a
sphere, that its radius is approximately 2 × 10^{-13} cm., or two ten
million-millionths of a centimetre. This is about 50,000 times smaller
than the radius of an atom. As compared with an atom, an electron would
be like a fly in a cathedral, to use Sir Oliver Lodge’s vivid image.
Although we have said that matter is built up out of electrons, we
cannot suppose it to consist of nothing but such negatively electrified
corpuscles as are produced in a vacuum tube. Ordinary matter is
electrically neutral; it does not exist in a state of permanent
negative electrification. These negative charges must therefore be
somehow associated with exactly compensatory positive charges. Now
the elementary positive charge of electricity, which is of the same
magnitude as the elementary negative charge, is never found associated
with a smaller mass than that of the hydrogen atom. The hydrogen-ion
carries the same positive charge that the electron carries negative
charge, but that positive charge is never found in a “dissociated”
state. We shall find, indeed, that the elementary positive charge plays
quite a different _rôle_ in the constitution of matter from that played
by the negatively charged electron.
§ 2. _Radium_
The theory we are introducing, that atoms of matter are built up out
of electric charges, is magnificently illustrated by the phenomena of
radioactivity. It was in 1896 that the French scientist Becquerel found
that uranium salts spontaneously emitted a radiation which could, to
some extent, pass through matter, whether transparent or opaque, could
influence a photographic plate, and could make air and other gases
conductors of electricity. Further investigation showed that other
substances also had the power of emitting these radiations, and some
of them, such as Radium, possessed this property in an extraordinary
degree. About forty radioactive substances are known at the present day.
The question arises, What is the nature of these radiations? To answer
this question the method of analysis was adopted that we have already
mentioned. The radiations, if they consist of electrically charged
particles, will be deflected both by a magnetic and by an electric
field. Each of these deflections gives us some information about the
ratio _e/m_ of the charge to the mass of the particles, and also
about the velocity _V_ with which the particles are moving. From the
information supplied by the two sets of deflections we can determine
these two quantities, _i. e._, we can find _e/m_ and also _V_. When
this method of analysis was applied it was found that the radiations
from radium consisted of three kinds of rays having entirely different
properties. These three types are called α-, β-, and γ-rays. The
γ-rays continued without deflection; it became apparent that they
did not consist of electrically charged particles at all. The β-rays
proved to be negatively charged, and the amounts of the electric and
magnetic deflections proved that they were of exactly the same type
as the streams of electrons in a vacuum tube. The α-rays behaved very
differently. They turned out to be positively instead of negatively
charged, and also to possess much greater masses than the β-rays. It
was found that the ratio _e/m_ for an α-particle was the same for all
α-particles, from whatever radioactive substance they were obtained.
This value was found to be 4823 (electromagnetic) units. Now this
value is one-half the value of the ratio _e/m_ of a hydrogen-ion. How
is this to be explained? There are three possibilities. We might say
that the α-particle carries a unit positive charge, the same as the
hydrogen-ion, but that this charge is united with _two_ hydrogen atoms.
Or we might say that it has a unit positive charge, but attached to
the atom of a new element which has twice the mass of a hydrogen atom.
The other possibility supposes that we are dealing with a helium
instead of with a hydrogen atom. Now the atomic weight of helium is
4, _i. e._, an atom of helium has four times the mass of an atom of
hydrogen. If, therefore, we assume that an α-particle is an atom of
helium, we must suppose it to be carrying two unit positive charges.
To distinguish between these possibilities, it obviously becomes
necessary to measure the actual charge carried by an α-particle. This
was done by direct experiment. The number of α-particles emitted from
a source can be counted directly, and the total charge they carry can
also be measured. The charge carried by a single particle can thus be
determined. Its value proved to be twice the value of the unit charge.
The hypothesis, therefore, that an α-particle consists of a helium atom
carrying two units of positive charge is justified by experiment. Thus
we see that radioactive elements can emit positively charged helium
atoms. This conclusion was directly confirmed by Rutherford and Royds,
who collected α-particles in an evacuated space, and, on causing an
electric discharge to pass, obtained the spectrum of helium.
The α-particles are easily absorbed in their passage through matter.
They can be stopped by an ordinary sheet of writing-paper. The velocity
of the α-particles varies with the nature of the radioactive substance
which emits them, but, speaking approximately, we may say that their
velocity is about 2 × 10^{9} centimetres per second. This is much less
than the velocity of light, which is about 3 × 10^{10} centimetres per
second.
The β-particles, on the other hand, sometimes have a velocity which is
within one per cent. of that of light itself. It is evident that the
radioactive process, whatever it may be, must be tremendously energetic
to produce these high velocities. But although, on the average, the
velocity of a β-particle is ten times that of an α-particle, the
latter, owing to its greater mass, has greater momentum and energy. The
β-particle, in its passage through matter, is readily deflected, and is
sometimes deflected through a very considerable angle. It may, in fact,
be turned so much out of its path as to emerge again on the same side
that it entered. For this reason, it is difficult to say just what
penetrative power the β-radiations have, but we may say, roughly, that
they are about 100 times as penetrating as α-rays.
The γ-rays, as we have said, do not consist of electrified particles at
all. They have the character of extremely minute light-waves, although
they do not, of course, cause visibility. They always accompany
the emission of β-particles from radioactive substances and their
penetrative powers are considerable, being about 100 times greater than
those of the β-rays. We shall learn more of their properties in the
section discussing _X_-rays.
Now what are we to suppose is happening during these radioactive
processes, attended, as they are, by so great an expenditure of
energy? The theory now universally accepted is that the atoms of a
substance manifesting radioactivity are actually disintegrating.
The atoms of such substances are unstable and are breaking up. The
electrified particles, the α- and the β-rays, are shot out by the
atom in its process of disruption. This process of disruption cannot
be hastened or retarded by any artificial means. It takes place, for
a given substance, at the same rate whether the temperature be that
of liquid air or of red-hot iron. The atom, on breaking up, becomes
transformed into a different atom, having a different atomic weight.
The second atom may be, in its turn, unstable, and disintegrate into
yet another atom. In this way, before a disrupting atom settles down
into a stable condition, it may pass through quite a long series of
states—transforming itself from one substance into another. Thus
uranium, with an atomic weight of 238, passes through a long series
of changes to reach stability finally as lead, with an atomic weight
of 206. This fact has led to a method of determining the ages of some
uranium minerals. The amount of lead produced by a known weight of
uranium in a given time can be determined, and the examination of the
amount of lead present in a uranium mineral enables a maximum age for
the mineral to be calculated. The assumption is that the lead present
in the mineral has resulted from the transformations of the uranium.
In this way a mineral of the Carboniferous period has been found to
have an age of 340 million years, and a pre-Cambrian mineral to have
an age of 1640 million years. We have seen, also, that the α-particles
expelled during some radioactive processes are really helium atoms.
Now helium is only found in large quantities in old minerals rich
in uranium or thorium (another radioactive substance), and if the
helium be supposed to have resulted from the disintegration of these
substances the age of the mineral can be calculated. But this value
will be a minimum value of the age of the mineral, since we must
suppose that some of the gas has been lost. In this way figures have
been obtained for different geological strata ranging from 8 million to
700 million years.
§ 3. X-_rays_
It was in 1895 that Röntgen discovered that invisible radiations of
some kind passed through the cathode tube and that these radiations had
great penetrative power.
He discovered that many substances, opaque to ordinary light, are
transparent to these _X_rays, as they were called. The rays arose
at the point where the stream of electrons within the tube struck
the glass walls, and radiated from these points of impact in all
directions. Ordinary deflection experiments showed that the _X_-rays
did not consist of electrified particles, but were a form of wave
motion. Now there are two forms of wave motion, _longitudinal_ and
_transversal_. If a rope, held by the hand at one end and permanently
fastened at the other, be shaken, a wave motion is propagated along
it. The peculiarity of this motion is that each point of the rope, as
the disturbance reaches it, moves in a direction at right angles to
the direction of propagation of the wave. Such a wave motion is said
to be transversal. The wave motion which constitutes ordinary light is
known to be of this character. But there is another form of wave motion
where each point of the medium set in motion moves to and fro in the
direction of propagation of the wave. Sound consists of waves of this
type. Such waves are called longitudinal. The question arose whether
the waves constituting _X_-rays were longitudinal or transverse. It
was not till ten years later that this point was definitely settled,
and it was shown that _X_-rays, like ordinary light, consist of
transverse waves, but waves which are, compared with light-waves, of
exceedingly small wave-length. The waves constituting _X_-rays are
about 10,000 times smaller than those constituting ordinary light. It
is this extraordinarily small wave-length that gives them their great
penetrative power. Not all _X_-rays have the same wave-length; their
wave-length depends on the manner in which they are generated. The
shorter the wave-length the greater the penetrative power or “hardness”
of the rays.
We have said that _X_-rays are produced by the sudden stoppage of the
electrons on striking the wall of a cathode tube. The sudden alteration
in velocity creates the wave disturbance called _X_-rays, and the
greater the velocity of the electrons the greater is the “hardness” or
penetrative power of the resultant waves. In modern cathode tubes, it
is usual, instead of allowing the stream of electrons to strike the
glass tube, to direct the stream on to a piece of metal having a high
melting point, such as platinum. This piece of metal, which receives
the impact of the electrons, is called the anti-cathode. Now the very
important discovery was made that the _X_-rays which result from the
bombardment of the anti-cathode are of two kinds. The first kind is due
merely to the stoppage of the electrons, as we have seen. But besides
these, the anti-cathode, under the influence of the bombardment, sends
out _X_-rays of its own. This second group of _X_-rays is of particular
wave-lengths, the same for the same substance, but different for
different substances. The _X_-rays so emitted are, in fact, entirely
characteristic of the substance that emits them. For a given element
these _X_-rays remain the same whether the element is isolated or
whether it is in chemical combination with others. It is evident,
therefore, that these _X_-rays manifest some property which belongs to
the _atoms_ of the element. If we compare the _X_-rays characteristic
of elements of different atomic weights we find that the heavier the
atom the shorter the wave-lengths of the characteristic _X_-rays. The
“hardness” of the _X_-rays proper to an element increases as the
atomic weight of the element increases. We shall find that this group
of _X_-rays, those proper to the substance itself, throws much light on
the structure of the atom.
The γ-rays, emitted by radioactive substances, resemble _X_-rays
in being waves of very small wave-length and consequently great
penetrative power. They are much smaller even than _X_-rays, for γ-rays
can be obtained about twenty times smaller even than the hardest
_X_-rays. But that they are essentially similar to _X_-rays there can
be no doubt, and it must be supposed that they have a similar origin.
We have seen that _X_-rays are produced by sudden alterations in the
velocity of a moving electron. We have also seen that the β-rays of
radioactive substances are electrons moving with very high velocities,
and we have further noted that γ-rays always attend the expulsion of
β-rays. It is very reasonable to suppose, therefore, that the γ-rays
are produced by the β-rays in their escape from the atom. But we
cannot go into this matter more closely until we know more about the
constitution of the atom.
CHAPTER IV: _The Structure of the Atom_
Chapter IV
_The Structure of the Atom_
§ 1. _The Order of the Elements_
We have already said that the various chemical elements are not
entirely unrelated to one another. The different chemical elements fall
naturally into groups, the members of each group greatly resembling
one another in their chemical properties. This fact particularly
excited the attention of an Englishman named Newlands, who, in 1864,
tried to show that the chemical elements fell into sets of seven,
analogous to “octaves” in music. The subsequent discovery of other
elements, however, made this scheme unsatisfactory, and the first
really convincing attempt at arranging the elements in this way was
made by the Russian chemist Mendeléev about 1870. In this “periodic
system,” as it is called, the elements are arranged in the order of
their atomic weights, beginning with hydrogen and ending with uranium.
If we now number the elements in the order of their atomic weights
we find a curious and interesting relation between the members of the
elements which have similar chemical properties. Elements numbered 3,
11, and 19 have similar properties. Elements 4, 12, and 20 have similar
properties. The properties of 5, 13, and 21 are similar; so are those
of 6, 14, and 22. And so on. We see that, for the elements belonging to
the same group, their numbers succeed one another by the same amount,
viz., 8. Thus 11 − 3 = 19 − 11 = 8, and 12 − 4 = 20 − 12 = 8, and so
on. It is as if approximately the same set of chemical properties
belonged to each eighth member of the table.
But the matter is not really as simple as this. The rule works well
enough provided we confine our attention to the earlier part of the
table, _i. e._, to the elements having comparatively low atomic
weights. As we go farther on in the table we find the recurrence of
chemical properties begins after the _eighteenth_ instead of the eighth
member, and, still later on, we have a group of no less than thirty-two
elements having different chemical properties. These facts are clearly
represented in the following table, where the lines join elements
having similar properties.
It will be noticed that the table of the elements terminates with a
row containing six members, the last of which is uranium. Uranium,
as we know, is not a stable substance; it is disintegrating, and it
is probable that no elements heavier than uranium are met with, not
because they are theoretically impossible, but because they would be
too unstable to survive.
We have seen that, neglecting the last six elements, all the other
elements may be arranged in rows in the following way: One row of two
elements, two rows of eight elements, two rows of eighteen elements,
and one row of thirty-two elements.
[Illustration: ARRANGEMENT OF THE ELEMENTS IN GROUPS IN ORDER OF THEIR
ATOMIC NUMBERS
Table showing the groups in the Periodic System and which elements are
related to one another in the different groups]
Names of Elements and their Atomic Weights arranged in order of their
Atomic Numbers.
No. Name Weight No. Name Weight
1. Hydrogen 1·008 47. Silver 107·88
2. Helium 4 48. Cadmium 112·4
3. Lithium 6·94 49. Indium 114·8
4. Beryllium 9·1 50. Tin 118·7
5. Boron 10·9 51. Antimony 120·1
6. Carbon 12 52. Tellurium 127·5
7. Nitrogen 14·01 53. Iodine 126·92
8. Oxygen 16 54. Xenon 130·2
9. Fluorine 19 55. Cæsium 132·8
10. Neon 20·2 56. Barium 137·37
11. Sodium 23 57. Lanthanum 139
12. Magnesium 24·3 58. Cerium 140·2
13. Aluminium 27·1 59. Praseodymium 140·6
14. Silicon 28·3 60. Neodymium 144·3
15. Phosphorus 31 61. Unknown —
16. Sulphur 32·06 62. Samarium 150·4
17. Chlorine 35·456 63. Europium 152
18. Argon 39·9 64. Gadolinium 157·3
19. Potassium 39·1 65. Terbium 159·2
20. Calcium 40·07 66. Dysprosium 162·5
21. Scandium 44·5 67. Holmium 163·5
22. Titanium 48·1 68. Erbium 167·7
23. Vanadium 51 69. Thulium 168·5
24. Chromium 52 70. Neoytterbium 172
25. Manganese 55 71. Lutecium 174
26. Iron 55·8 72. Hafnium —
27. Cobalt 58·97 73. Tantalum 181
28. Nickel 58·68 74. Tungsten 184
29. Copper 63·6 75. Unknown —
30. Zinc 65·4 76. Osmium 191
31. Gallium 70·1 77. Iridium 193·1
32. Germanium 72·5 78. Platinum 195
33. Arsenic 74·96 79. Gold 197·2
34. Selenium 79·2 80. Mercury 200·5
35. Bromine 79·9 81. Thallium 204
36. Krypton 82·9 82. Lead 207·2
37. Rubidium 85·45 83. Bismuth 208
38. Strontium 87·63 84. Polonium 210
39. Yttrium 88·7 85. Unknown —
40. Zirconium 90·6 86. Niton 222
41. Niobium 93·5 87. Unknown —
42. Molybdenum 90 88. Radium 226·4
43. Unknown — 89. Actinium (226–227)
44. Ruthenium 101·7 90. Thorium 232·1
45. Rhodium 102·9 91. Protoactinium —
46. Palladium 106·7 92. Uranium 238·5
Two points must be mentioned about the periodic table as we have
represented it. In the first place, we have left spaces for five
elements which have not yet been discovered, but whose properties and
places in the table can be predicted. Such predictions have been made
before, and the elements, when discovered, have completely verified
the predictions. In the second place, we have not, at every place in
the table, adhered to the order of the atomic weights. There are four
places where a heavier element has been put before a lighter one. In
such cases we allow the whole complex of the chemical properties of
the element, considered as a whole, to outweigh the considerations
based only on its atomic weight. In the table as now arranged each
element, including the five undiscovered elements, receives a number
corresponding to its position in the table. These numbers range from 1
to 92, and they are called the _atomic numbers_ of the elements. The
atomic number of an element is, in the light of the new theories, a
more fundamental and important characteristic than the _atomic weight_
of the element. There is obviously a close connection between the
atomic number and the atomic weight of an element, for the order of the
atomic weights is almost exactly the same as the order of the atomic
numbers and, further, the atomic weight of an element is, for the early
part of the table, approximately twice its atomic number, excepting, of
course, hydrogen, the first member of the table. This latter property,
that the atomic weight is twice the atomic number, is truer for the
first part of the table than for the latter part. As we proceed along
the table the atomic weights seem to depend less and less directly on
the atomic number. It is obvious that we are not dealing with a case of
simple proportionality, but that the atomic weight is, in reality, a
quite complicated function of the atomic number.
The fact that the periodic classification of the elements is possible,
that is to say, the fact that elements having different atomic weights
can be arranged in groups because of the similarity of their physical
and chemical properties lends great support to the theory that an atom
is not a single, simple entity. There must be some similarity between
the atoms of similar elements, and it is difficult to see what this
similarity can be unless it be a similarity of structure.
§ 2. _The Atom as a Planetary System_
It is time now that we began to consider what sort of structure the
atom may be supposed to possess. We have seen that the discovery of
electrons, and the phenomena of radioactivity, lead us to suppose
that electrons somehow form part of the constitution of the atom. We
have seen further that, since atoms are electrically neutral, we must
suppose the electrons to be associated with an equal positive charge.
How are we to suppose the electrons and the positive charge to be
distributed? We shall see that certain experimental results lead us to
adopt a planetary configuration for the atom. The positive charge is
imagined as placed at the centre of the system, and circulating round
it are a number of electrons sufficient to balance its charge exactly.
The simplest conceivable case is of a unit positive charge, and one
electron circulating round it. The distance of the electron from the
positive charge would be, of course, the radius of the atom. It is
supposed that the hydrogen atom is built up in just this way, namely,
that it consists of a nucleus containing one positive unit of charge
and, circulating round this nucleus, one electron. Such a conception
is extremely simple, but before it can be considered as satisfactory
we must make it more definite. We have seen that an electron has a
mass which is only 1/1800 part of that of a hydrogen atom. If there
is only one electron in a hydrogen atom, therefore, we must imagine
that practically the whole mass of the atom is concentrated in its
positive nucleus. Besides the fact, therefore, that the ultimate
positive charge, the nucleus, has an equal and opposite electrical
charge to that of the ultimate negative charge, the electron, we must
imagine that it is about 1800 times more massive than the electron.
The nucleus, deprived of its electron, would still behave, so far as
mass is concerned, like a complete hydrogen atom. But it would behave
like a hydrogen atom carrying one unit of positive charge. Such atoms
are known. Heavier atoms, containing several electrons surrounding a
nucleus having several positive units of charge, could conceivably lose
one, two, three, four, or more electrons and consequently manifest
as an atom carrying one, two, three, four, or more positive charges.
But it would be impossible, if our simple picture is right, for the
hydrogen atom ever to manifest more than one positive unit of charge.
And, in fact, no hydrogen atom has ever been discovered which does
manifest more than one positive unit of charge, although heavier atoms
have been found which manifest several positive charges.
The element that follows on hydrogen in the order of atomic numbers is
helium, and the simplest hypothesis to make concerning the structure
of the helium atom is that it consists of a nucleus containing two
positive charges and, circulating round it, two electrons. How these
two electrons are supposed to be arranged is a problem of some
difficulty. The most obvious idea would be to suppose that they were at
opposite ends of a diameter and moving round the nucleus in the same
circle. But there are reasons for thinking that this picture cannot be
true. We shall take up this question later when we come to consider the
general group of problems relating to the distribution of electrons
within atoms. But, however they may be arranged, we suppose the
helium atom to consist of two electrons circulating round a nucleus
containing two positive charges. Now, if this picture is correct, we
cannot simply suppose the helium nucleus to be composed of two hydrogen
nuclei. It is true that this would give two positive charges for the
nucleus, but the weight of the nucleus would be wrong. The atomic
weight of helium is not 2, but 4, and we have seen that practically the
whole mass of an atom is concentrated in its nucleus. Since the nucleus
of a helium atom has four times the mass of a hydrogen atom, it follows
that the helium nucleus must contain no less than four hydrogen nuclei.
Yet its charge is only two positive units. How is this to be accounted
for? We can only account for it by giving the nucleus itself a rather
complicated structure. We must imagine that the helium _nucleus_,
besides containing four hydrogen nuclei, contains also two electrons.
The charge of these two electrons neutralises the charge of two of the
hydrogen nuclei and leaves, for the resultant positive charge of the
helium nucleus, two units. Thus we see that, if we are to consider all
atoms as built up out of hydrogen nuclei and electrons, it cannot be
done by simply adding hydrogen nuclei together in order to produce the
nucleus of another atom.
The principle is, we see, simple. The number of hydrogen nuclei which
go to make up the nucleus of an atom must be equal to the atomic weight
of that atom, since it is from the hydrogen nuclei that the atom
acquires its weight. The resultant positive charge on the nucleus,
however, is equal to the _atomic number_ of the atom. An atom of gold,
for instance, has a mass of 197. Its atomic number is 79. Its nucleus
consists, therefore, of 197 hydrogen nuclei and 118 electrons, since
197 − 118 = 79, and the resultant positive charge on the nucleus is
79. To balance this resultant positive charge of 79 there are 79
electrons circulating round the nucleus. It is this resultant positive
charge, and the electrons circulating round it, which determine the
physical and chemical properties of the atom. The actual mass of the
atom affects these properties only to a very small degree. It is for
that reason that it is not the atomic weight, but the atomic number,
which is the fundamental characteristic of an atom. It is obvious,
for instance, that we might obtain the same resultant positive charge
with quite a different atomic weight. In the gold atom we get a charge
of 79 by combining 197 hydrogen nuclei with 118 electrons. But if we
had taken 198 hydrogen nuclei and 119 electrons we should have had an
atom of different atomic weight, viz., 198 instead of 197, but of equal
charge, namely, 79, and therefore of the same properties. We shall see
that such variations in atoms exist, _i. e._, we can have atoms of the
_same substance_ but of different weights.
Our picture of the helium atom is perfectly compatible with the
fact that the α-particles shot out by radium are found to consist
of helium atoms each of which carries two positive units of charge.
Each α-particle is, in fact, a helium atom which has lost both its
circulating electrons and which manifests, in consequence, two positive
charges. In the same way that a hydrogen atom could not manifest more
than one unit of positive charge, so a helium atom cannot possibly
manifest more than two units of positive charge. But it is perfectly
possible for a helium atom to lose only one of its two electrons and
therefore to manifest only one unit of positive charge. Such atoms are
known to exist, whereas a helium atom carrying more than two positive
charges has never been discovered.
Of the next element, lithium, we need only say briefly that its nucleus
carries three positive charges and that, circulating round the nucleus,
are three electrons. The lithium atom which has lost one electron, and
consequently manifests one positive charge, is known, but the lithium
atom which is minus two electrons has not yet been experimentally
obtained.
Each step along the periodic table corresponds to the increase of the
resultant charge on the nucleus by one positive unit and, consequently,
to the addition of one electron to the circulating planetary system.
By the time we get to uranium we have an atom which has 92 electrons
in its planetary system, circulating round a nucleus containing a
resultant positive charge of 92 units. Such a system is enormously
complex. The complete mathematical treatment of such systems would
lead to the elaboration of what is, at present, the practically
non-existent science of mathematical chemistry. But the mathematical
difficulties are enormous. They depend not only on the large number of
“planets” which have to be treated, but on the peculiar difficulties
offered by the very extraordinary nature of the laws which govern their
motion. The further treatment of this point, also, we must leave till
later.
§ 3. _Experimental Evidence_
When the α-particles from radium are passed through matter they suffer
a certain amount of dispersion. In passing through a thin sheet of
metal, for instance, the α-particles are deviated from the straight
line they were pursuing when they encountered the metal. The amount of
the deviation varies from one α-particle to another, but, on the whole,
the deviations are very similar to those of shots round a target. The
cause of these deviations must be sought in the encounters between the
α-particles and the atoms of the metal. The α-particles are, as we
have seen, the positively charged nuclei of helium atoms. In passing
through the metal sheet they will sometimes pass near or even through a
metallic atom and experience a deflection due to the attraction of the
electrons of that atom. It may be that a number of such encounters will
happen to deflect the α-particle in the same direction, so that the
resultant deflection may be considerable. But the chances of this can
be worked out, and we reach the interesting conclusion that some of the
observed enormous deflections which α-particles occasionally experience
cannot be explained by any such cumulative effects. Deflections of
150°, _i. e._, an almost complete reversal of direction, have been
observed. It is true that such large deflections are not numerous (on
passing through platinum, for instance, about 1 in 8000 α-particles
are so affected), but the theory of successive small deviations cannot
explain them. Also, the path of an α-particle through air can, in
certain circumstances, actually be photographed, and the photographed
path sometimes exhibits extremely abrupt changes of direction. Suddenly
to deflect the massive α-particle, travelling at about 20,000 miles
a second, requires an intense force. It is necessary, therefore, to
consider where these intense forces could come from.
As a result of measurements of the deflections of α-particles, moving
with various velocities through different substances, Rutherford came
to the conclusion that the abnormal deflections were produced when an
α-particle happened to approach very closely to the nucleus of an atom.
To account for the observed results it was necessary to suppose that
the charge on the nucleus was concentrated within a very small region.
An α-particle which approached sufficiently close to this highly
concentrated positive charge would experience an intense repulsive
force, and would be deflected in a hyperbolic path. The deflections
enabled the actual positive charges carried by the nuclei of the atoms
of the different metals to be calculated, and also the maximum value
for the size of these nuclei. The charge was found to be greater the
greater the atomic weight of the metallic atom and to be, within the
limits of experimental error, equal to the atomic number of the atom.
Thus, the experimental values for platinum, silver, and copper were
found to be 77·4, 46·3, and 29·3 respectively. The atomic numbers
are 78, 47, and 29, and these figures agree with the experimental
figures to within the limits of experimental error. Thus we have an
experimental demonstration of the important law that the positive
charge on the nucleus of an atom is equal to the atomic number of that
atom. The experiments also showed that the maximum size that can be
attributed to the nucleus of an atom is exceedingly small. Like the
electron, the nucleus of an atom is very much smaller than an atom;
it is of subatomic dimensions. There is reason to suppose, indeed,
that the hydrogen nucleus is small compared even with an electron. It
is probable that the radius of a hydrogen nucleus is not greater than
10^{-16} cm., which is about 1/2000 part of the radius of an electron.
One of the most interesting and striking confirmations of our general
theory is provided by radioactive phenomena. We have said that there
are about 40 radioactive substances known, and they are all substances
having high atomic weights. The nuclei of such heavy atoms must be
very complicated structures, built up, as the gold atom is built
up, of a large number of hydrogen nuclei and several electrons.
Now a radioactive substance, in the course of its disintegration,
may give rise to several substances. Thus radium, in the course of
disintegrating, gives rise to the following substances:—It produces
Radium Emanation, Radium-_A_, Radium-_B_, Radium-_C_, Radium-_C_′,
Radium-_C_″, Radium-_D_, Radium-_E_, Radium-_F_, Radium-_G_. Radium-_F_
is polonium and Radium-_G_ is lead. Two kinds of particles are shot out
during this series of disintegrations, α-particles and β-particles.
We have seen that α-particles are helium nuclei and β-particles are
electrons. The question arises, Where do these particles come from? The
answer is that they come from the nuclei of the heavy, disintegrating
atoms. It may astonish us that they are helium nuclei and not hydrogen
nuclei that are shot out by the disrupting atoms. But we shall see
later that the helium nucleus, consisting of 4 hydrogen nuclei and 2
electrons, is a very stable affair, so stable that it enters as a sort
of indivisible unit into the structure of more complicated nuclei. Now
let us, remembering our general theory, trace exactly what happens in
the above series of radium changes. A radium atom turns into an atom
of radium emanation by losing an α-particle. The α-particle carries
two units of positive charge. It is shot out from the nucleus of the
radium atom, and therefore the new nucleus is minus two positive
charges. That is to say, the nucleus of an atom of radium emanation
carries two charges less than the nucleus of a radium atom. But the
charge on the nucleus is, as we have seen, equal to the atomic number
of the atom. It follows that the radium emanation atom must be placed
two steps lower than the radium atom in the periodic table. But the
α-particle contains four hydrogen nuclei. Therefore the atomic weight
of the radium emanation atom must be four units less than that of the
radium atom. The result of an atom losing an α-particle, therefore, is
to give rise to a new atom whose atomic weight is less by four units,
and which belongs to a place two steps back in the periodic table. What
is the effect of losing a β-particle? The nucleus of every atom except
a hydrogen atom contains, besides a number of hydrogen nuclei, a
smaller number of electrons. These electrons neutralise an equal number
of the hydrogen nuclei contained in the nucleus of the atom, leaving
over a number of hydrogen nuclei equal to the charge on the nucleus,
which is itself equal to the atomic number of the atom. A β-particle
shot out from the nucleus, therefore, leaves one extra hydrogen nucleus
unneutralised. In consequence, the charge on the atom’s nucleus
increases by one unit, and therefore the atomic number increases by
one. The new atom, therefore, moves one place up in the periodic table.
And what happens to its atomic weight? Its atomic weight is unaffected,
for we have seen that electrons play almost no part in contributing
to the mass of an atom. The loss of an electron makes practically
no difference to the weight of an atom. Besides, the new atom soon
captures a free electron (of which there are always a large number
about) to compensate for its extra positive charge. This electron does
not fall into the nucleus, but joins the group of electrons which are
rotating round the nucleus.
We are now in a position to understand the series of radium changes
given above. Radium, with an atomic weight of 226, loses an a-particle
and becomes radium emanation, with an atomic weight of 222. Radium
emanation, losing an α-particle, becomes radium-_A_ with an atomic
weight of 218. The loss of α-particles continues, and radium-_A_ gives
rise to radium-_B_, with atomic weight 214. At radium-_B_ the process
alters. Radium-_B_ loses a β-particle and turns into radium-_C_. The
atomic weight is, of course, unaltered, so radium-_C_ also has the
atomic weight 214. Having got as far as radium-_C_, a very interesting
thing happens. Some radium-_C_ atoms, by shooting out an α-particle,
pass straight to radium-_C_″, with an atomic weight of 210, and then,
through radium-_C_″ losing a β-particle, to radium-_D_, also with an
atomic weight of 210. Other radium-_C_ atoms, however, shoot out a
β-particle instead of an α-particle, and so become radium-_C_′, with an
unchanged atomic weight of 214. Radium-_C_′ shoots out an α-particle
and so it also becomes radium-_D_, atomic weight 210. Thus the two
paths lead to the same result, viz., radium-_D_. Radium-_D_ is not
stable, however; it loses a β-particle and becomes radium-_E_. That
also loses a β-particle and becomes radium-_F_, _i. e._, polonium.
Both these substances, radium-_E_ and polonium, have, of course, the
same atomic weight, 210, as radium-_D_. Having reached polonium, the
series has one more step to go. Polonium, by losing an α-particle,
becomes lead, with an atomic weight of 206. With lead, the process of
disruption seems to have stopped. There is no evidence that lead is
disintegrating; if it is, it must be at an exceedingly slow rate which
has hitherto avoided all means of detection. It must be noted here that
the lead reached in this way has not the same atomic weight as ordinary
lead. Ordinary lead has the atomic weight 207·2. By taking a different
series of radioactive changes, starting from thorium, we also reach
lead as the final substance. But the lead so obtained has an atomic
weight of 208. These curious facts, and a number of others like them,
we must now proceed to consider.
§ 4. _Isotopes_