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Title: Atoms and electrons
Author: J. W. N. Sullivan
Release date: January 11, 2026 [eBook #77675]
Language: English
Original publication: New York: George H. Doran Co, 1924
Credits: Thiers Halliwell, Tim Lindell and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)
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In this plain-text e-book, italic text is denoted by _underscores_.
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ATOMS AND ELECTRONS
_J. W. N. Sullivan_
_DORAN’S MODERN READERS’ BOOKSHELF_
ST. FRANCIS OF ASSISI
_Gilbert K. Chesterton_
THE STORY OF THE RENAISSANCE
_Sidney Dark_
VICTORIAN POETRY
_John Drinkwater_
THE POETRY OF ARCHITECTURE
_Frank Rutter_
ATOMS AND ELECTRONS
_J. W. N. Sullivan_
EVERYDAY BIOLOGY
_J. Arthur Thomson_
_Other Volumes in Preparation_
ATOMS
AND ELECTRONS
BY
J. W. N. SULLIVAN
[Illustration]
NEW YORK
GEORGE H. DORAN COMPANY
COPYRIGHT, 1924,
BY GEORGE H. DORAN COMPANY
ATOMS AND ELECTRONS
—B—
PRINTED IN THE UNITED STATES OF AMERICA
GENERAL INTRODUCTION
_Of all human ambitions an open mind eagerly expectant of new
discoveries and ready to remold convictions in the light of added
knowledge and dispelled ignorances and misapprehensions, is the
noblest, the rarest and the most difficult to achieve._
JAMES HARVEY ROBINSON, in “_The Humanizing of Knowledge_.”
It is the purpose of Doran’s Modern Readers’ Bookshelf to bring
together in brief, stimulating form a group of books that will be fresh
appraisals of many things that interest modern men and women. Much of
History, Literature, Biography and Science is of intense fascination
for readers today and is lost to them by reason of being surrounded by
a forbidding and meticulous scholarship.
These books are designed to be simple, short, authoritative, and such
as would arouse the interest of intelligent readers. As nearly as
possible they will be intended, in Professor Robinson’s words quoted
above, “to remold convictions in the light of added knowledge.”
This “adding of knowledge” and a widespread eagerness for it are two
of the chief characteristics of our time. Never before, probably, has
there been so great a desire to know, or so many exciting discoveries
of truth of one sort or another. Knowledge and the quest for it has now
about it the glamour of an adventure. To the quickening of this spirit
in our day Doran’s Modern Readers’ Bookshelf hopes to contribute.
In addition to the volumes announced here others are in preparation
for early publication. The Editors will welcome suggestions for the
Bookshelf and will be glad to consider any manuscripts suitable for
inclusion.
The Editors.
CONTENTS
PAGE
Chapter I
UNITS AND NOTATION 11
Chapter II
ATOMS AND MOLECULES 21
Chapter III
CONSTITUENTS OF THE ATOM 51
Chapter IV
THE STRUCTURE OF THE ATOM 77
Chapter V
QUANTUM THEORY 111
Chapter VI
THE GROUPING OF ATOMS 137
Chapter VII
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
Atoms and Molecules
§ 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_
The chemical and physical properties of an element depend on its atomic
number, _i. e._, on the positive charge carried by the nucleus of an
atom of that element. And this positive charge is, as we have seen, a
_resultant charge_. It is a result of the combination of a number of
unit positive charges with a smaller number of unit negative charges.
We can obviously reach the same resultant figure in as many ways as
we please. If the resultant charge on the nucleus is to be 5, for
instance, then we could take the combinations +6 and −1, or +7 and −2,
or +8 and −3, and so on. Each of these arrangements would give atoms
having identical chemical and physical properties. But their atomic
weights would be different. The atomic weights depend, not on the
resultant positive charge, but on the actual number of positive charges
present in the nucleus, including those that are compensated for by
negative charges as well as those that are not. In the above case, for
instance, our atoms would have atomic weights 6, 7, 8, and so on. And
this is the only difference they would have. By no other chemical or
physical properties could they be distinguished one from another.
It is therefore a very interesting fact, and one fitting in beautifully
with our theory, that many elements have been shown to consist of a
mixture of atoms having different atomic weights, but identical in
every other respect. The element chlorine, for example, has the atomic
weight 35·46. This number is about as far removed as it could be from
being a whole number, and is therefore specially fatal to the theory
that all atomic weights are simple multiples of the same unit. But
it has been shown that chlorine is really a mixture of two groups of
atoms, the atomic weight of the atoms of one group being 35 and the
other 37. These groups are mixed together in about the proportion of 3
to 1, and the ordinary measured atomic weight of 35·46 is really the
average weight of the mixture. Neon, again, whose atomic weight is
ordinarily given as 20·2, is found to consist of two groups of atoms
with atomic weights 20 and 22. Much more complicated groupings have
been discovered. Thus krypton, whose atomic weight is put as 82·92,
is made up of groups of atoms having the weights 78, 80, 82, 83, 84,
86. Such elements are called _Isotopes_, the name indicating that the
groups of atoms belonging to these elements occupy the _same place_ in
the periodic table. It will be noticed that the atomic weights of these
groups of atoms are all whole numbers. This is on the basis of oxygen
taken as 16. On this basis hydrogen is not exactly unity, but is 1·008.
It appears probable, then, that all atoms have atomic weights which are
nearly, but not quite, whole multiples of hydrogen.
The existence of isotopes definitely destroys the great importance
that chemists had always assigned to atomic weights. We have atoms
of different atomic weights but of the same properties. Further, as
we saw in studying the disintegration of radium into lead, we have
elements of the same atomic weight but with wholly different chemical
and physical properties. The atomic weight of an element, therefore, by
no means suffices to determine its chemical and physical properties.
We see once more that the really important quantity to be known about
an element is its _atomic number_, _i. e._, its position in the
periodic table. It is worth noting that the existence of isotopes was
not suspected until comparatively recent times, although very delicate
determinations of atomic weights have been practised for decades.
The most refined measurements customary in such determinations never
varied from sample to sample of the same element. Exactly the same
mixture of atoms constitutes chlorine, for instance, wherever the
chlorine is obtained, and always has done so ever since men began to
study chlorine. The groups of atoms which make up chlorine or any other
isotope must have been thoroughly and universally mixed long ages
ago—in all probability before the formation of the earth’s crust, when
such universal and complete diffusion would have been possible.
§ 5. _Relativity and the Atom_
It is necessary, now, to say a little about the Restricted Principle
of Relativity, since certain points about the modern theory of atomic
structure cannot be understood without it. But it is not necessary to
explain the principle itself. It is only necessary to describe the
relation between energy and mass that the theory shows to exist. In
pre-Relativity mechanics, it was always assumed that the mass of a
body was completely independent of its velocity. There was no reason
to suppose otherwise. Whether a body was moving fast or slow, or
whether it was at rest, its mass, when measured, was always found to
be the same. But the theory of relativity asserts that the mass of a
body does vary with its velocity. As the body moves faster its mass
increases. The mass increases in such a way that, at the speed of
light, it becomes infinite. This can only mean that the velocity of
light is a natural limit, that no material body could possibly exceed
this speed. If it be true that the mass of a body increases with its
velocity, it might be thought that experiment would long ago have led
us to suspect that fact. But the law according to which the increase
occurs is such that the increase is not measurable except at very
great speeds. Now we are not familiar with bodies moving at very great
speeds. We know of velocities such as 100 miles per hour and even,
in astronomy, of velocities which reach a few miles per second. But
velocities which are a considerable fraction of the velocity of light,
viz., 186,000 miles per second, are practically unknown. It is the α-
and the β-particles which furnish us with examples of bodies moving at
speeds comparable with that of light. And experiments on these bodies
show that their mass does increase with their velocity, and precisely
in the way predicted by Einstein’s theory. So that the ratio _e/m_, the
ratio of charge to mass of an electron, varies with the velocity of the
electron. As the velocity increases _m_ increases and therefore _e/m_
grows smaller. The value of _e/m_ usually given, viz., 1·77 × 10^{7}
(electromagnetic) units, is the value for low velocities, when m may be
taken as the mass of the electron at rest. We will denote this value
of _m_ as _m__{o}; _m__{o} is the mass of the stationary electron. At
half the velocity of light, the mass of the electron is 1·15 _m__{o},
_i. e._, it is about one-seventh greater. If the electron is moving at
nine-tenths the velocity of light its mass is 2·3 _m__{o}, or nearly
two and a half times greater. At ninety-nine-hundredths of the velocity
of light the mass of the electron is seven times its value at rest, and
at the velocity of light itself, as we have said, its mass is infinite.
This result of relativity theory must obviously be borne in mind in
any attempts to ascertain in detail what goes on inside an atom. If
the mass of the rotating electrons is a quantity which enters into our
calculations, then obviously we must remember that the mass varies
with the velocity of rotation we ascribe to the electrons. Another
important aspect of this theory is that it shows we must ascribe _mass_
to _energy_. This, again, is a very novel conception. We are used to
thinking of energy as something to which the property of possessing
mass cannot be ascribed. The two things seem to have nothing to do with
one another. But it can be shown that energy certainly does possess
inertia, and the property of possessing inertia is what we really mean
by mass. The mass of a body is, indeed, only another way of measuring
the total amount of energy it contains. Every piece of matter possesses
a vast store of internal energy. If the piece of matter begins to
move its energy is increased in virtue of its motion. Its mass also
is increased. But the increase in mass due to increase in energy is
usually extremely small. In any chemical combination which is attended
by the development of heat, for instance, there is a certain loss of
mass due to the energy radiated away during the process of combination.
The resultant mass of the compound is less than the sum of the original
masses of its constituents. But the loss which occurs in this way
during any chemical process is exceedingly small, and the old law of
the invariability of mass is, in all such cases, quite good enough.
But there appears to be a beautiful and highly interesting exception.
We have seen that there is reason to suppose that the helium nucleus,
which is shot out of radioactive bodies as an α-particle, is a very
stable structure. It is composed, as we have said, of four hydrogen
nuclei and two electrons. The great stability of this structure
suggests that its formation was attended by a great expenditure
of energy, so that an enormous amount of energy would have to be
communicated to it to break it up. Now the atomic weight of helium is
4, and the atomic weight of hydrogen is not 1, but 1·008. Four times
the mass of the hydrogen atom would give an atomic weight of 4·032. The
suggestion is that the difference between this value and the actual
measured value of 4, represents the _mass_ of the _energy_ lost in the
process of combining the four hydrogen nuclei into the helium nucleus.
This gives a measure, also, of the amount of energy that would be
required to split up the helium nucleus into its original components.
The amount of energy represented by this figure is really enormous.
It is sixty-three million times greater than the energy expended in
ordinary chemical processes, and this figure is a measure of how much
more stable the helium nucleus is than an ordinary chemical compound.
A chemical compound can often be dissociated merely by raising its
temperature a few degrees, but even the enormous energy possessed by
the fastest α-particles is only about a third of that required to
dissociate the helium nucleus.
CHAPTER V: _Quantum Theory_
Chapter V
_Quantum Theory_
§ 1. _The Stability of the Atom_
We have seen that the theory we have been describing, called the
nuclear theory of the atom, gives a very satisfactory account of a
large number of phenomena. The observed scattering of α-particles
on passing through thin sheets of metal, the existence of isotopes,
the changes which occur in radioactive phenomena, all receive very
convincing explanations. There can be no doubt that the nuclear theory
of the atom is essentially true, that the atomic models we have
imagined correspond closely to actual atoms. But there is a fatal
objection to this theory of the atom, as we have presented it hitherto.
Such an atom could not continue to exist!
According to the classical theory of electrodynamics every change of
motion on the part of an electrically charged body is attended with
a radiation of energy. In wireless telegraphy, for instance, it is
the rapid oscillations of the electrons in the sending apparatus which
produce the electromagnetic waves. Each time an electron suffers a
change in the direction or speed of its motion, or in both, it sends
out an electromagnetic wave. Such a process cannot be kept up without a
continual supply of energy. In the atomic model, as we have presented
it, the outer electrons, which we imagine to be continually circulating
round the nucleus, would be continually sending out energy. For a
circular motion is a perpetually changing motion, and every change of
motion on the part of a charged body is accompanied by the emission
of energy. For an electron not to radiate energy, according to the
classical theory, it must either be at rest, or be moving uniformly in
a straight line. It is obvious that the outer electrons of our atom
cannot be imagined as at rest. They would be attracted by the nucleus
and simply fall into it, just as the planets would fall into the sun if
they were robbed of their orbital motion. In order to counterbalance
the attraction of the nucleus the outer electrons must have a circular
or elliptical or some such motion. And any such motion would be
attended by a radiation of energy. As a result of this radiation of
energy it can be shown that the orbit of the rotating electron would
grow smaller and its velocity of rotation greater. This process would
continue until finally the electron fell into the nucleus. That is to
say, the atom, as we have depicted it, is, on the classical theory of
electrodynamics, essentially unstable. The whole material world, as we
know it, ought to have vanished long ago. Further, the spectrum of any
element contains perfectly sharp lines which are situated in perfectly
definite parts of the spectrum. The radiations from the atoms of a
given element are perfectly definite; they do not assume all values.
But if the outer electrons, from which these radiations proceed, are
continually changing their orbital distances and velocities, then there
ought to be a continuous succession of lines in the spectrum of that
element, instead of the perfectly distinct and permanent arrangement
which exists in fact.
So we see that, when we come to investigate the mathematical theory
of our atomic model it turns out to be highly unsatisfactory. Are we,
therefore, to abandon our model completely? Before we answer this
question we will look at one or two other phenomena where similar
extraordinary difficulties have been found. We will consider, in the
first place, the phenomena of heat radiation, since it is here that
the insufficiency of the old theory of electromagnetic radiation
was first demonstrated. Let us consider the heat rays radiated by
what is called a “black body.” A black body is defined as one which
absorbs the whole of the radiant energy that it receives. There is no
substance which exactly satisfies this condition, but it is possible
to produce the equivalent of it by artificial means. It was shown by
the German physicist Kirchhoff that a space enclosed by an opaque
envelope, and maintained at a uniform temperature, is filled with a
radiation identical with that which would be emitted by a black body
at the same temperature. If, therefore, a small hole be made in the
opaque envelope, the rays which escape through it will be the same as
those that would be produced by a black body. Several physicists have
studied these rays, and they have reached extraordinarily interesting
results. The way in which the total amount of energy radiated is
distributed amongst the different rays has been the chief object of
their researches. The rays which come from the enclosure are of very
different wave-lengths; they vary between wide limits. Corresponding to
each wave-length is a certain fraction of the total energy radiated,
and this fraction depends upon the length of the actual wave concerned
in a rather complicated way. It is found, as the result of actual
measurements, that the longest waves have very little energy. As the
wave-lengths decrease the energy increases until a certain wave-length
is reached where the energy has a maximum value. As we go on past this
point to shorter and shorter wave-lengths the energy decreases, until
for very short wave-lengths it is practically zero. Now this result is
in the most flagrant contradiction with the theoretical calculations.
According to the mathematical theory, the energy contained in the
very short wave-lengths should be very great. As the wave-lengths get
shorter and shorter, tending towards zero, the energy contained in
them should, according to the calculations, tend towards infinity.
Observation shows that it tends towards zero. The contradiction is as
striking as it could be.
We can see how extraordinary this observed result is if we consider
an analogous case. Suppose that we have a number of corks floating
on the surface of a bowl of water. Now suppose that, by some means,
we agitate these corks, causing them to oscillate up and down in the
water, and then leave them to themselves. We know that the oscillations
will, after a time, die down. The whole mass, water and corks, will
once again become quiescent. The difference is that the water will be
slightly warmer. The energy which was contained in the oscillating
corks is ultimately transferred to the molecules of the water and
appears as heat energy. Now this result is quite in accord with the
calculations. But if the result were to be analogous to the radiation
result mentioned above, the corks would have to go on oscillating
for ever with undiminished vigour. We should all agree that such a
phenomenon was highly mysterious. The results obtained in the radiation
experiments are no less mysterious.
Let us turn to yet another phenomenon which is entirely contradictory
of our expectations. It is found that light of high frequency, _i.
e._, of short wave-length, when allowed to fall on a metal, liberates
electrons from the metal. The old scientific question of “How much?”
immediately, of course, comes to the fore. We want to know the
number of the electrons liberated and their velocities. And we want
to know how these two quantities depend on the light which is used.
We find, as the result of careful experiment, that the _number_ of
electrons liberated depends on the _intensity_ of the light, but that
the _velocity_ of the electrons depends on the _frequency_ of the
light. This result is very surprising. We should have expected that
the more intense the beam of light the higher the velocity of the
liberated electrons. But only the number of electrons is influenced by
the intensity. A very weak beam of high frequency light will cause
electrons to be shot out of the metal with high velocity. We get a
firmer grasp of the paradoxical nature of this result if we first
create _X_-rays by bombarding an anti-cathode with electrons, and then
use the _X_-rays to liberate electrons from a metal. _X_-rays, as we
have said, may be regarded as extremely high frequency light-waves.
Now let us suppose that we produce some electrons in a cathode tube,
and cause them to bombard the anti-cathode, so producing _X_-rays. The
electrons will have a certain velocity, depending upon the voltage
applied to the tube, and they will generate _X_-rays having a certain
frequency. The higher the velocity of the electrons the higher the
frequency of the resulting _X_-rays. These _X_-rays are now allowed
to fall on a sheet of metal. Immediately electrons are liberated from
the metal, and the astonishing discovery is made that the electrons
so produced have the same velocity as the electrons which generated
the _X_-rays. We may illustrate this result by an analogy used by Sir
William Bragg. Imagine that we drop a plank, from the height of a
hundred feet, into the ocean. The impact produces waves in the ocean
which spread out in circles around the point of impact. As the waves
spread out they naturally get feebler and feebler, since the same total
amount of energy is distributed over a longer and longer circumference.
After travelling, say, two miles, let us suppose that the outermost
wave reaches a ship. We are to imagine that, immediately the wave
reaches the ship, it causes a plank to be shot up out of the ship to
a height of one hundred feet. This case seems precisely analogous to
the liberation of electrons by _X_-rays. The _X_-rays have spread out
in ever increasing spheres from the point of impact, and yet, wherever
they touch a metal, they liberate electrons having precisely the energy
of the electrons which generated the _X_-rays.
The key to these extraordinary results is to be found in Planck’s
Quantum Theory. It was at the end of the year 1900 that Max Planck
published his theory that energy is not emitted in a continuous
fashion, but only in little finite packets, as it were. An oscillating
atom, for instance, is to be conceived as sending out little doses of
energy, one after the other. It does not emit energy continually. And
Planck asserted that the size of these little packets depended on the
frequency of the oscillation, being greater the greater the frequency.
Such an hypothesis is very strange, and is in entire contradiction to
the classical dynamical theory on which the whole science of physics
had been built. Yet, strange as the theory was, the results it was
invented to explain certainly existed, and it could be shown that the
old dynamics not only had not explained them, but could not possibly
explain them. It was clear that any satisfactory explanation would have
to be something quite revolutionary in character. And Planck’s theory
did, as a matter of fact, explain the observed radiation phenomena
extremely well. Planck calculated, on his theory, how the energy of
radiation should be distributed amongst the different wave-lengths,
and his calculations precisely agreed with the experimental results.
It is possible that, even so, this revolutionary theory would not have
obtained general acceptance. But Einstein applied the theory to the
phenomena attending the liberation of electrons from metals under
the influence of light, and his calculations, also, were shown to be
in precise agreement with the evidence. The quantum theory, then,
although strange and, in many respects, little understood, has become
one of the great arms of modern physical research. It is still attended
with very grave difficulties. The phenomena of electron emission from
metals, for instance, certainly suggests that light energy exists in
small bundles, dotted about round the surface of the sphere which was
regarded as forming the old “wave-front.” Each bundle, we may suppose,
contains sufficient energy to liberate an electron with the velocity
of the electron which gave rise to the bundle. On the other hand,
certain well-known phenomena in light, particularly the phenomenon of
“interference,” seem utterly irreconcilable with this assumption; they
are perfectly well explained on the old wave theory of light, but they
seem quite inexplicable on the new quantum theory of light. It depends
on which phenomenon we want to explain which theory we employ. Neither
of them seem in the least adequate to explain all the known phenomena,
and they also seem quite irreconcilable with one another. The physicist
must keep both and yet they cannot live together. A compromise has been
tried. Sommerfeld and Debye, for instance, have endeavoured to work
out a theory whereby the energy brought by the light waves has been
regarded as continuous, but as being able, in some way, to accumulate
until the amount contained in a quantum “bundle” is reached. Having
accumulated to this amount, the energy is then supposed to work
suddenly and to shoot out the electron with the requisite velocity.
But the period required for this accumulation can be calculated, and
it is found that, to explain the effects produced by _X_-rays, an
accumulation period amounting to some years is required. So that the
emission of electrons under the influence of _X_-rays should not take
place until some years had elapsed. It is found, however, that the
emission takes place immediately the _X_-rays are applied, and ceases
instantly when they are discontinued. The contradiction is complete.
But the quantum theory, however puzzling it may be in certain aspects,
has shown itself competent to deal with very baffling phenomena.
It was natural, therefore, faced by the great puzzle presented by
the stability of the atom, to surmise that here, also, the quantum
theory would prove competent to overcome the difficulties. In its
original form, the theory could not be applied to the atom. It was
first necessary to extend it. This was first done, and the theory
successfully applied, by a brilliant young Danish physicist, Niels Bohr.
§ 2. _Bohr’s Atom_
Before we go on to describe Bohr’s conception of the atom we must
make a few remarks about spectra, since the explanation of spectrum
lines is one of the most important duties that an atomic model has to
fulfil. The whole science of spectrum analysis began with Fraunhofer’s
discovery that light from the sun, if spread out in a coloured band
by a prism, contained, besides its different colours, a large number
of fine dark lines crossing the band at right angles to its length.
Kirchhoff found that the light from incandescent gases, when treated
in the same way, also gave lines, although in this case the lines were
bright lines. But he further found that a gas will absorb the same
lines that it emits, so that if light be passed through a gas, dark
lines will occur at the same positions as the bright lines occur when
the gas is incandescent. Each chemical element was found to have its
own appropriate series of lines, and these lines serve, with remarkable
delicacy and exactitude, as a means of recognising the presence of
these elements. The lines in the sun’s spectrum, for instance, can
be disentangled into the groups belonging to each separate chemical
element in the sun. A similar analysis, performed on the light from
various stars, enables us to say what chemical elements are present in
those stars.
Every incandescent substance sends out light of several different
wave-lengths. These different rays are, in the ordinary way, jumbled
together, but, on being passed through a prism, they are separated
out in an orderly manner. The spectrum ranges from the red to the
violet. The waves giving red light are the longest waves and those
giving violet the shortest. Waves longer than red waves, the so-called
infra-red waves, do not affect the retina of our eye as light at
all, and the same remark applies to the waves shorter than violet
waves, the so-called ultra-violet waves. But such waves, although
they do not affect our eyes, can be made to affect certain chemical
preparations; with ultra-violet waves, for instance, photographs may
be taken of invisible objects, a fact perfectly well known to certain
“spirit” photographers. Now each line on a spectrum corresponds to a
definite wave-length. Light which is all of one wave-length is called
monochromatic light; each line on a spectrum corresponds to a certain
wave-length of monochromatic light. Corresponding to each line in the
spectrum of a given element the wave-length can be measured, and the
interesting question arises as to whether there is any relation between
the lengths of the different waves emitted by that element. We shall
see that there are such relations, and that Bohr’s theory of the atom
takes us some way towards explaining them.
In the first place, we have to assume, in applying quantum theory to
the atom, that an electron describes a circle or an ellipse round
the nucleus without radiating any energy. This assumption is in flat
disagreement with the classical theory of electrodynamics, but it is
in agreement with the quantum theory. Another assumption we must make,
and which is not in agreement with the old theory, is that the electron
can only move in certain orbits. If the orbit be a circular one, for
instance, then an electron can only circulate round the nucleus at
certain definite distances from it. It could not describe a circle
whose radius was intermediate between two of these distances. Whatever
one of the possible circles the electron is on, it will continue to
traverse that circle indefinitely unless some external force acts on
it. If an external force does act on it, then the electron passes
directly to another of the possible circles. During this transition
from one possible circle to another the electron radiates energy, and
this energy is monochromatic, that is, it is energy of a perfectly
definite wave-length. And the amount of energy so emitted is a quantum
of energy. The quantum of energy belonging to a certain frequency
depends upon that frequency. Its amount is, in fact, equal to the
frequency multiplied by a certain extremely small figure called
Planck’s constant. Thus the quantum, or the atom of energy, is not
an invariable thing. Like the atoms of matter, energy atoms are of
different sizes. The higher the frequency the greater the atom of
energy. As we have said, a monochromatic radiation is emitted by the
electron in passing from one possible orbit to another. This radiation
has, of course, a definite wave-length and therefore a definite
frequency corresponding to it. This frequency, multiplied by the
quantity called Planck’s constant, is equal to the total energy emitted
by the electron in passing from one orbit to the other.
We have said that certain relations have been found to exist between
the lines in the spectrum of a given element. It was in 1885 that
Balmer discovered that the lines in the spectrum of hydrogen could
be represented by a certain very simple formula. The frequencies
corresponding to a certain prominent group of lines in the hydrogen
spectrum may be represented by multiplying a certain constant figure
by the quantity (1/4 − 1/_n_^{2}) where _n_ takes on the values 3, 4,
5, 6, 7. These are the five strongest hydrogen lines, and for them
the quantity in the brackets becomes (1/4 − 1/9), (1/4 − 1/16), (1/4
− 1/25), (1/4 − 1/36), (1/4 − 1/49). Each of these values is to be
multiplied by a certain figure, the same in each case, and the results
will be the frequencies corresponding to each of these five lines
respectively. Another series of lines in the hydrogen spectrum is
obtained by using, instead of the general quantity in brackets given
above, the quantity 1/9 − 1/_n_^{2}, where _n_ takes on the values 4, 5,
6, etc. Still another series can be obtained from the general formula
1/1 − 1/_n_^{2}, where _n_ has the values 2, 3, 4, etc. It is easy to see
that the most general formula, including all these cases, is 1/_m_^{2} −
1/_n_^{2}. In the first formula we gave, for instance, _m_ = 2. In the
second _m_ = 3, and in the third _m_ = 1. Formulæ which are a trifle
more complicated were discovered later, and were found to represent
still other series of lines. And these formulæ were applied to other
elements besides hydrogen.
On Bohr’s theory, when an electron passes from one orbit to another,
it emits a certain quantity of energy, and the energy so radiated has
a certain frequency. If, therefore, we subtract the energy possessed
by the electron in its second orbit from the energy it possessed in
its first orbit, we have the total quantity of energy emitted by it
in passing from one to the other. The frequency, therefore, could be
calculated from the subtraction of these two quantities. Now it is
suggestive that Balmer’s formula for the frequency, given above, is
expressed by the subtraction of two quantities. Bohr showed that this
was no accident, and that the two quantities in Balmer’s formula do
indeed correspond to the energies before and after the transition of
the electron from one orbit to the other. In fact, Bohr was able, on
his theory, to deduce Balmer’s formula. It no longer appeared as a mere
empirical rule, but as a theoretical consequence of the structure of
the atom. This result was a most striking success for Bohr’s theory to
achieve. He also deduced, from his theory, the value of the constant
figure which is used to multiply the different quantities in brackets
given above; his calculated figure and the empirically ascertained
figure were in precise agreement. The values of the different possible
radii on which the electron in a hydrogen atom can move were also
deduced by Bohr. The electron is most stable when on its first orbit,
the orbit nearest the nucleus. This is the normal condition for a
hydrogen atom. The actual diameter of a hydrogen atom in this condition
can be calculated on Bohr’s theory, and the value so obtained is found
to be in agreement with the value obtained by quite other methods.
The fact that the spectrum of hydrogen possesses a number of lines,
therefore, shows us that, in the immense number of atoms present in any
specimen of hydrogen, there are always many whose electrons are passing
from one orbit to another. In one atom an electron will be passing from
the second to the first orbit, or from the third to the second, or
from the fourth to the third, and so on. Such transitions must always
be going on, for it is only in virtue of them that the hydrogen atoms
radiate any energy at all. The state to which all these changes tend
is the most stable state, when the electron is on its first orbit. We
may say, then, as Bohr puts it, that the spectrum of hydrogen shows
us the formation of the hydrogen atom, since the transition to the
successively decreasing orbits may be regarded as stages in the process
by which the hydrogen atom reaches its normal condition.
§ 3. _The Fine Structure of Hydrogen Lines_
We may summarise the theory of the hydrogen atom we have given hitherto
by saying that the hydrogen atom consists of a positive nucleus
carrying one unit of charge, and that a single electron is describing
an elliptical orbit about it. We can imagine a number of ellipses,
of different sizes, enclosing the nucleus. Each of these ellipses
will have a common focus, and it is at this focus that the nucleus is
situated. The single electron can move on any one of these ellipses,
but only on these; it cannot describe an intermediate orbit. Under
the influence of an external force the electron may jump from one
of these ellipses to another. During this jump it radiates energy in
the form of monochromatic waves. As long as it remains on any one of
these ellipses it is not radiating energy. These elliptical motions
are called _stationary states_. The electron only radiates energy,
then, in passing from one stationary state to another. This simple
theory suffices to explain the positions of the lines in the hydrogen
spectrum. We reach a formula which is exactly like Balmer’s formula
showing the distribution of these lines.
When we come to look more closely into the matter, however, we find
that there is a factor we have neglected in our calculations. We have
said that the electron describes an ellipse about the nucleus. We
suppose that it describes this ellipse in obedience to the ordinary
laws which regulate the motion of a single planet about the sun. It is
a peculiarity of such motion that the speed is not uniform. A planet,
in its elliptical orbit about the sun, is sometimes moving faster
and sometimes slower, depending upon which part of the ellipse it is
describing. At those parts of the ellipse which are nearest the sun
the planet is moving fastest. At the parts most remote from the sun it
is moving most slowly. As precisely the same laws apply to our electron
moving round the nucleus, we have to take into account the fact that
the speed of the electron in its orbit is continually changing. This
is where the theory of relativity comes in. We have seen that it is a
consequence of that theory that the mass of an electron varies with
its velocity, becoming greater the greater the velocity. Our electron,
therefore, is not only moving with a varying speed; it is also moving
with a varying mass. What influence will this variation of mass have on
the motion?
This problem was solved by Sommerfeld. The result is that the electron
continues to move in an almost elliptical orbit, but this orbit itself
is slowly and uniformly rotating. The actual motion of the electron
in space is a combination of these two motions. The effect of this on
the spectrum of hydrogen will be that corresponding to each hydrogen
line there will be two or three lines extremely close together. Each
hydrogen line will really consist of more than one line. These lines
will be so close together that it would be almost impossible to see
them separately. Nevertheless, measurements have been made, and these
measurements are in agreement with Sommerfeld’s theory. The fine
structure, as it is called, of the hydrogen lines, is due to the
variations in mass of the electron in describing its orbit about the
hydrogen nucleus. The complete explanation of the hydrogen spectrum
requires both quantum theory and relativity theory; conversely, the
striking agreement between calculation and observation in the hydrogen
spectrum greatly supports both these theories.
So far we have considered the theory, in detail, only in its
application to the hydrogen atom. The hydrogen atom is the simplest
atom, and we should expect the theory to be most adequate in dealing
with this case. But although the sheer complexity of the heavier
atoms has hitherto prevented so complete a description of them being
formulated, the general theory of their structure, as we shall proceed
to show, has much that is of interest and value to tell us.
CHAPTER VI: _The Grouping of Atoms_
Chapter VI
_The Grouping of Atoms_
§ 1. _The Outer Electrons_
Any theory of the atom which is to secure our assent must, in broad
lines if not in detail, account for the remarkable periodicity in
the properties of the chemical elements. We have already shown that
this periodicity, the recurrence of similar physical and chemical
properties, led Mendeléev to construct the Periodic Table. In each of
the columns of the diagram in Chapter IV the elements run through a
cycle of chemical properties which is approximately repeated in the
next column. This repetition of properties is not perfectly regular.
The columns are of unequal length; some contain 8, some 18, and some
32 elements. But the periodicity, although not perfectly simple, is
quite unmistakable, and is one of the most important and outstanding
properties of the chemical elements. Instead of arranging the atoms by
their general chemical properties we may arrange them according to some
specific property. We may, for instance, arrange them in accordance
with what is called their “atomic volumes.” If we do this we again get
a periodic relation. Still other properties, such as “compressibility,”
“expansion coefficient,” etc., show the same intriguing peculiarity.
All these properties seem to be connected with the actual amount of
space taken up by the atom. They are not properties of the nucleus;
they are dependent upon the outer electrons. And also, if we study
the visible spectra of the various elements, we find the same curious
recurrence. All those elements which are called Alkalis, for example,
have spectra which seem to be constructed on the same ground plan.
The different alkalis differ enormously from one another in the
complication of their structure; their atomic numbers are 3, 11, 19,
37, 55, so that we pass from a system containing three circulating
electrons to one containing fifty-five. And yet their spectra are
fundamentally the same. Here, also, we are concerned with the outermost
electrons. The nuclei of these atoms are not concerned in their
visible spectra. The nuclei of the various atoms, arranged according
to their atomic numbers, simply show a straightforward advance from
complexity to complexity. There is no kind of repetition or recurrence
in the properties which depend on the nucleus. But the way in which
the outer electrons are arranged does show a recurrence, and all those
physical and chemical properties which show a recurrence may be assumed
to depend on the outer electrons. Thus we may say that _the chemical
properties of an atom depend not on its nucleus, but on its outer
electrons_.
The visible spectrum, as we have said, depends upon the arrangement
of the outer electrons. But _X_-rays also possess a spectrum. The
_X_-rays emitted from any source are not all of the same wave-length
and these waves, by a method of which we shall learn more later, can
be arranged in order like those of visible light. Now the _X_-ray
spectra of the elements do not manifest a recurrence. They advance, in
a straightforward way, with the atomic number. They depend upon the
inner part of the atom and not upon the outer electrons. And it is
because they originate in the neighbourhood of the nucleus, where the
atomic forces are most intense, that the _X_-rays possess their great
penetrative power. Periodicity is not an inner, but only an outer,
property of the atom.
The great dominating factor which governs the properties of an atom
is the charge on its nucleus. We see this very clearly in the case of
isotopes. Two isotopic varieties of an element cannot be distinguished
from one another by their chemical properties. The outer electrons are
arranged in the same way in the two varieties of atoms, and it is this
arrangement which determines the chemical properties. Their visible
spectra are also the same, and so are the spectra in the ultra-violet
region. This fact furnishes an even more exact proof that their outer
electrons are arranged in the same way than does the identity of their
chemical properties. Two isotopic elements also have the same _X_-ray
spectrum; therefore the inner structure of the atoms, also, is the
same in the two cases. The whole structure of the atom is evidently
dependent on the charge carried by the nucleus; where this charge is
the same the atomic structure is the same.
The general question of how the electrons in a heavy atom are to
be supposed to be arranged is one of great difficulty, and no
perfectly precise answer can yet be given. There are certain general
considerations, however, which enable us to give a partial answer
to the question. In the periodic table each column ends with what
is called an “inert gas.” These elements are so called because they
possess great stability; they are not in the least eager to enter into
combination with other elements. Let us consider the element argon,
for instance. It is an inert gas, and occurs at the end of the second
group of eight in the periodic table. Its atomic number is 18. It
therefore contains 18 electrons rotating round the nucleus. Owing to
the marked stability of argon we must suppose that these 18 electrons
are arranged in some peculiarly stable configuration. The natural ideal
of every atom would be to reach so stable a condition. It is a state
to which every atom aspires. The atom of chlorine, which just precedes
argon in the table, and therefore possesses only 17 electrons, shows a
marked disposition to capture one additional electron. It is striving
towards the perfect state of possessing 18 electrons—not because it
requires the extra electron to become electrically neutral, of course,
but because the extra electron gives it greater mechanical stability.
On the other hand, the element potassium, which immediately follows
argon in the table, shows a marked tendency to get rid of one of its
19 electrons—again in order to attain the perfect state of possessing
18 electrons. If we go back to sulphur, which has 16 electrons, or
forward to calcium, which has 20 electrons, the same tendency manifests
itself. Sulphur has a tendency to capture two electrons and calcium has
a tendency to lose two electrons. We can understand, therefore, why the
Germans call the inert gases, like argon, the “noble” gases. It is not
only that they are sublimely inactive, but their condition is that to
which all the others aspire.
The great stability of the inert gases, and the fact that they occur
at the end of each period in the periodic table, so that, immediately
after each inert gas, the whole cycle of chemical properties begins
again, show us that they are, as it were, the natural terminations
of the building schemes which led up to them. After each inert gas a
fresh building scheme has to be adopted for the next group of atoms. We
have seen that each step along the periodic table means the addition
of a fresh electron. We can imagine the outer electrons of an atom
to be arranged in a ring, or on the surface of a sphere, or in what
configuration we like. When a fresh electron has to be added to produce
the atom one step on in the periodic table, we may imagine that, in
general, this new electron joins the rest. It takes its place in the
ring or on the sphere or whatever it may be. But there will come a
moment when the addition of a fresh electron will spoil the stability
of the whole structure. There will be no place for it in the ring,
and it will have to start a new ring, by itself, outside the existing
one. When yet another electron joins up, it will help the first one in
establishing the new ring. Presently the new ring will itself have all
the members it can stably hold, and further electrons will have to
build up yet another ring. The process will not be quite so simple as
this, for as outer rings continue to be built they will so influence
the inner rings that these will be able to take more members than
they could originally accommodate. But, in the broadest outlines, the
process is as we have described. Now the inert gases form such points
of departure. By the time an inert gas is reached the system which led
up to it has done all it could; it has fulfilled itself in producing an
inert gas. If atom building is to continue, it must be on a different
system, although the system of the new atom will, of course, resemble
the system of the atom to which it is connected by a line in the
periodic table. In just the same way, all the different inert gases
have systems which resemble one another.
The inert gas which precedes argon is neon, an element possessing ten
electrons. There is reason to suppose that it contains 2 inner and 8
outer electrons. The inert gas preceding neon is helium, the first of
the inert gases, and helium has 2 electrons. With the obvious exception
of helium it is supposed that the chemical similarity of all the inert
gases is due to their possessing 8 outer electrons, however many groups
of inner electrons they may have. The following table, showing the
number and arrangement of the electrons in successive groups, going
outwards from the nucleus, has been proposed by *Bohr*.
Helium 2
Neon 2, 8
Argon 2, 8, 8
Krypton 2, 8, 18, 8
Xenon 2, 8, 18, 18, 8
Radium Emanation 2, 8, 18, 32, 18, 8
How are we to consider these different groups of electrons to be
arranged? No precise answer can yet be given to this question, but the
whole trend of the most modern speculations is to emphasise the fact
that it is not sufficient to regard the different groups as lying in
plane rings. It is necessary to investigate the _spatial_ configuration
of the electronic orbits. It is very probable that different electrons
move in orbits which are inclined at various angles to one another.
Even in the solar system, the planets do not all rotate in precisely
the same plane. In the electronic orbits, we must imagine these
differences to be much greater. It has even been suggested that the
number 8, which occurs with such frequency in electronic groups, may
indicate that these groups of eight are arranged like a cube, one
electron being at each corner. The idea has something to recommend it,
although it appears that such an arrangement cannot be explained by the
known forces within the atom. But it serves as an indication of the
direction in which a solution is being sought. We shall now deal with
this question in more detail.
§ 2. _Hydrogen and Helium_
Hydrogen and helium are the two members of the first group in the
periodic table, and we shall now proceed to examine their atomic
structure. We have already described the structure of the hydrogen atom
in some detail. We know that it consists of a single electron rotating
about a nucleus. The electron can circulate on a number of different
orbits, but its most stable state is obtained when it circulates on
the first orbit, the one nearest the nucleus.
When we come to the helium atom the question is much more complicated.
A helium atom which had but one electron would be essentially similar
to a hydrogen atom, with the difference that the nucleus would carry
two positive charges instead of one. The real problem of the helium
atom is to determine the way in which the second electron enters into
its constitution. A spectrum of helium consists of two complete series
of lines, and for this reason helium was supposed to consist of two
different gases, called “orthohelium” and “parhelium.” But it is now
known that these two series of lines arise from the fact that the
second electron can enter into the constitution of the helium atom
in two different ways. The two electrons may be describing orbits of
the same kind, but inclined at an angle to one another, or they may
be describing orbits of different kinds, one outside the other. The
first case gives the most stable state for the atom, and in reaching it
the atom emits the spectrum which used to be referred to “parhelium.”
The second case is less stable and the process of reaching it gives
the “orthohelium” spectrum. This state was produced experimentally
by bombarding helium atoms with electrons. Such a bombardment could
produce what was called a “metastable” condition of the helium atom,
and it was found that the atom could not return to its normal condition
merely by radiating energy. The bombardment had caused the second
electron to move in an orbit outside that of the first electron—an
orbit of a different kind. And, having once done this, the second
electron could not make a jump back to its original orbit. Before it
could return to normal the “metastable” atom had to interact with atoms
of other elements—it had to go through a sort of chemical reaction.
In its normal state, then, the helium atom may be said to consist of
two electrons moving round the nucleus in similar circles, these two
circles being inclined at an angle of 120° to one another. And owing
to the interaction between the two electrons the planes of these two
circles are slowly moving. So that already, and when we are dealing
with an atom containing only two electrons, we are in the presence
of very considerable complications. The detailed working out of the
constitution of more complicated atoms would obviously be a task of
immense difficulty. Bohr has been able, however, to say something about
the broad lines of their structure.
§ 3. _Lithium—Neon_
We now come to the second group of the periodic table, a group
possessing eight members. We begin with lithium. Its atomic number is
3, and therefore an atom of lithium consists of 3 electrons revolving
about a nucleus. We shall assume that two of these electrons move in
orbits similar to those characteristic of the normal helium atom, that
is, in orbits which are not in the same plane but which are otherwise
similar. This assumption is very natural, for the normal structure of a
helium atom is a very stable condition. It is distinctly more stable,
for instance, than the structure of the hydrogen atom. Helium is the
first of the inert gases. We assume, then, that two of the electrons
in a lithium atom move as do the two electrons of the helium atom. How
are we to suppose the third electron to move? The spectrum of lithium
shows us that the third electron moves in orbits which are altogether
outside the region containing the first two electrons. The spectrum
also shows that the third electron sometimes moves in orbits which,
although they lie outside the region of the first two electrons for
the greater part of their length, yet, at their nearest point to the
nucleus, approach it as closely as do the first two electrons. These
are the orbits characteristic of the lithium atom in its normal state.
The firmness with which the outer electron is held in these orbits is
only about one-third of that with which the electron in a hydrogen
atom is held, and only about one-fifth of that with which the helium
electrons are held. The chemical properties of these three elements,
therefore, depending, as they do, on the outer electrons, should be
very different, as, in fact, they are.
We may assume that, in any atom, the third electron moves in the same
kind of orbit as does the third electron of the lithium atom. This
orbit is, as we have said, very excentric. It may be regarded as
markedly elliptical. That part of it nearest the nucleus is within the
region in which the two inner electrons move. The rest of it extends
far beyond this region. We may imagine that the fourth, fifth, and
sixth electrons move in similar orbits. There is reason to suppose
that the four electrons, from the third to the sixth inclusive, which
move in these excentric orbits, are so distributed as to form an
exceptionally symmetrical configuration. Each of these outer electrons
penetrates to the region occupied by the inner electrons, but not at
the same moment. Bohr supposes that the outer electrons reach their
nearest point to the nucleus separately at equal intervals of time.
This structure carries us as far as carbon, which has six electrons.
Lithium has one outer electron, beryllium two, boron three and carbon
four. Each of these outer electrons moves in very excentric orbits
which enclose and partly penetrate the approximately circular orbits
within which the two inner electrons move. This method of building
reaches completion in the carbon atom. If yet another electron were
added to the four outer electrons of carbon the symmetry of the
arrangement would be destroyed. There is, as it were, no room for
five such orbits. Also, the fact that the elements in the second half
of this group in the periodic table have very different properties
from those in the first half suggests that a new system of building
comes into existence directly we proceed beyond carbon. Bohr supposes
that in nitrogen, an element possessing seven electrons, the seventh
electron moves in a large and approximately circular orbit. It lies
completely outside the two inner electrons, although the outermost
parts of the excentric orbits on which the other four outer electrons
lie extend beyond it. The eighth, ninth and tenth electrons also move
in large circular orbits of this kind. The great stability of the last
element reached in this way, the inactive gas neon, suggests that the
final arrangement possesses great symmetry. We must suppose that, with
this element, the four large circular orbits are not only symmetrical
amongst themselves, but also in relation to the four elliptical orbits.
§ 4. _Sodium—Argon_
We have, so far, considered two types of orbits, the approximately
circular, and the markedly elliptical. For the first two electrons we
assume circular motion. For the next four we assume elliptical motion,
and for the next four we again assume circular motion. In this way we
have got as far as neon, and we now begin another group of the periodic
table. Acting on the same general principles, we shall assume that the
eleventh electron inaugurates a new era of elliptical orbits. These
orbits are very elliptical. For the most part they are well outside the
orbits of the first ten electrons, but for part of their course they,
like the first group of elliptical orbits, penetrate even closer to
the nucleus than do the two innermost electrons. The existence of such
markedly elliptical orbits, passing, during part of their course, so
close to the nucleus, greatly helps the stability of the atom. In the
distribution of the twelfth, thirteenth, and fourteenth electrons we
meet conditions similar to those we encountered when considering the
fourth, fifth, and sixth electrons. There seems to be an exception in
the case of aluminium, the element whose atom contains 13 electrons.
In this case the thirteenth electron seems to move in a less markedly
elliptical orbit. But Bohr does not regard this behaviour as typical
for the thirteenth electron in all atoms; it is peculiar to aluminium,
where the thirteenth electron is also the last electron. By the time
we get to silicon, containing 14 electrons, we find the thirteenth
electron, like the eleventh, twelfth, and fourteenth, moving in the
markedly elliptical type of orbit inaugurated by the eleventh electron.
As in the preceding cases, we suppose this type of construction to be
completed when we have four electrons describing these new orbits.
The fifteenth electron introduces a new system, just as the seventh
electron did. But whereas the seventh electron introduced an almost
circular type of orbit, the fifteenth electron continues with the
excentric type of orbit, although the excentricity is not so marked
as in the case of the orbits we have just left. These new orbits
are excentric enough to penetrate closer to the nucleus than do the
circular orbits inaugurated by the seventh electron, but they do not
reach the region of the two innermost electrons. These orbits will
accommodate four members, so that this type of construction will carry
us up to the atom possessing 18 electrons, _i. e._, up to the element
argon. Thus we again reach an inert gas, and, allowing for the greater
complexity, we see that its symmetrical properties closely correspond
to those of the preceding inert gas, neon.
§ 5. _The Remaining Elements_
The development we have been describing hitherto is straightforward
in the sense that fresh groups of electrons have been regarded as
possessing fresh types of orbits which are, as it were, independent of
those previously existing. We have not considered the later electrons
as causing any development of the inner groups of electrons. That
there must be some interaction is obvious, but we have not found
it necessary to assume that the interaction is sufficient to cause
any fundamental modification of the orbits already established.
When we come to the fourth period of the periodic table, however,
matters are different. As we see from the diagram in Chapter IV, the
fourth period contains 18 elements. At the beginning of this period
the atom continues to develop in a way analogous to that we have
already studied. The first two elements of this period are, as shown
by the connecting lines, analogous to the first two elements of the
third period. But then occurs a group of eight elements which do not
correspond, in our diagram, to anything in the third period. And
after this group occur two elements which are again analogous to the
first two elements of the third period. Why is it that we have this
interregnum, as it were, lasting over eight elements? Bohr’s answer is
that we are here concerned with the development of one of the inner
groups of electrons. The normal system of atom building, as we have
sketched it, cannot now proceed. The later electrons captured will
now be concerned in the internal rearrangement, and only when this is
completed will the normal process be able to proceed.
This theory gives an interesting explanation of the facts that many
elements of the fourth period differ markedly from the elements of
the preceding periods in their magnetic properties and also in the
characteristic colours of their compounds. That highly magnetic
substance, iron, for instance, occurs in the fourth period. To
understand the explanation, offered by the theory, of the magnetic
properties of these elements, we must revert to the familiar fact that
an electric current is always attended by magnetic force. Electric
currents are constituted by the movements of electrons, and the
moving electrons within an atom will give rise to their appropriate
magnetic forces. Now we may imagine that, in any thoroughly symmetrical
arrangement of the electrons within an atom, these magnetic forces
form a closed system within the atom, so that no resultant external
effects are manifested. With any markedly unsymmetrical arrangement of
the electrons, however, we may expect appreciable external magnetic
effects to manifest themselves. Bohr supposes, therefore, that the
process of reorganisation within the atom which characterises a group
of elements in the fourth period, is attended by the lack of symmetry
which would result in magnetic forces being exhibited. Where the
symmetry is at last restored the magnetic effects cease. In Bohr’s
words: “On the whole a consideration of the magnetic properties of the
elements within the fourth period gives us a vivid impression of how a
wound in the otherwise symmetrical inner structure is first developed
and then healed as we pass from element to element.”
The characteristic colours to which we have alluded also find an
explanation on this theory. These colours are due, of course, to the
absorption of light, and they are thus evidence that energy changes
are going on comparable with those giving visible spectra. This is in
contrast to the elements of the earlier periods, where the electrons
are more firmly held and where the less rigid conditions, due to the
development of an internal group of orbits, do not occur.
--------+-------+-----------------------------------------------------------
| | NUMBER OF ELECTRONS IN DIFFERENT TYPES OF ORBITS.
ELEMENT.|ATOMIC |-+-+-+-+-+-+-+-+-+--+--+--+--+--+--+--+--+--+--+--+--+--+--
|NUMBER.|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23
--------+-------+-+-+-+-+-+-+-+-+-+--+--+--+--+--+--+--+--+--+--+--+--+--+--
Helium | 2 |2| | | | | | | | | | | | | | | | | | | | | |
Neon | 10 |2|4|4| | | | | | | | | | | | | | | | | | | |
Argon | 18 |2|4|4|4|4|-| | | | | | | | | | | | | | | | |
Krypton | 36 |2|4|4|6|6|6|4|4|-| -| | | | | | | | | | | | |
Xenon | 54 |2|4|4|6|6|6|6|6|6| -| 4| 4|--|--|--| | | | | | | |
Niton | 86 |2|4|4|6|6|6|8|8|8| 8| 6| 6| 6|--|--| 4| 4|--|--|--|--| |
? | 118 |2|4|4|6|6|6|8|8|8| 8| 8| 8| 8| 8|--| 6| 6| |--|--|--| 4| 4
--------+-------+-+-+-+-+-+-+-+-+-+--+--+--+--+--+--+--+--+--+--+--+--+--+--
Table showing distribution of Electrons in the Inert Gases, including a
hypothetical element of atomic number 118.
The building up of the rest of the elements, up to and including the
seventh period, may be supposed to take place on the broad lines we
have now laid down. The process is a double one. New groups of outer
orbits will be formed, and also there will be a development of groups
of inner orbits. The whole process is very complex, and no attempt has
yet been made to examine it in detail.
The seventh period ends abruptly with uranium, whose atomic number is
92. The last elements in this period are all radioactive, and, as we
have said before, it seems probable that an element of higher atomic
number than 92 would be too unstable to exist. Nevertheless, on the
principles we have followed hitherto we can construct theoretically,
and in its main lines, the structure of an atom having a higher atomic
number than 92. The last inert gas known to us, niton, has an atomic
number 86. The next inert gas, if it existed, would have an atomic
number 118. Bohr gives a table, which we reproduce, showing in some
detail the number of electrons and the characters of their orbits for
the six inert gases. He includes, as a seventh, the imaginary gas
having an atomic number 118 and shows its hypothetical construction.
CHAPTER VII: _The Inner Regions_
Chapter VII
_The Inner Regions_
§ 1. _X-Ray Spectra_
In speaking of _X_-rays we have referred to their wave-lengths and
to their spectra, but we have not yet given any indication as to
how these wave-lengths are measured. The most satisfactory method
of determining the wave-lengths of ordinary light is by means of a
“diffraction grating.” This apparatus consists, essentially, of a sheet
of glass on which a large number of very fine lines have been ruled
very close together. The lines should be parallel and equidistant.
Now the distance between two adjacent lines should be of the same
order of magnitude as the wave-lengths to be measured. The lengths
of visible light waves are comprised between 4 × 10^{-5} cm. and 7 ×
10^{-5} cm., _i. e._, they lie between 4 and 7 hundred-thousandths of a
centimetre. _X_-rays, as we have said, have wave-lengths about 10,000
times smaller than this. It is difficult enough to rule lines close
enough together for the distances to be comparable with the lengths of
light-waves; it is utterly impossible to rule them ten thousand times
closer still. The distance between adjacent lines would have to be of
the order of 10^{-8} cm., _i. e._, of the same order of magnitude as
the molecular distances in a solid body. Manifestly such an apparatus
is impossible to construct. But it so happens that nature has provided
such an apparatus.
Certain mineralogists and mathematicians were long ago concerned to
elucidate the regular shape and structure of crystals in terms of
regular arrangements of their molecules or atoms. These molecules or
atoms were supposed to be arranged in definite patterns, so that a
crystal consisted of layers, arranged one behind the other, containing
these regular assemblages. The distance between the molecules or atoms,
so arranged, would be of the order of 10^{-8} cm. A crystal of salt,
for instance, would have as the distance between its molecules 5·6 ×
10^{-8} cm. The brilliant idea occurred to a German scientist named
Laue that such an arrangement really constituted a sort of diffraction
grating and one, moreover, of just the right dimensions to serve for
the measurement of _X_-ray wave-lengths. The realisation of this idea
was highly successful, and the employment of crystals has not only
served to measure _X_-ray spectra, but has also taught us a great deal
about the structure of the crystals themselves. It is now possible,
employing this method, to obtain photographs of _X_-ray spectra.
As a result of these researches we now know that the wave-lengths of
_X_-rays vary within fairly wide limits, according to the conditions of
their emission. The longest waves are about 12 × 10^{-8} cm. in length,
while the shortest are about 3 × 10^{-8} cm. The shorter the wave the
greater its penetrative power or “hardness.” Now we have already said
that each of the chemical elements, on being bombarded by cathode
rays, emits a group of _X_-rays which is characteristic of it. The
hardness of these _X_-rays varies with the substance that emits them,
and in such a way that the greater the atomic number of the substance
the harder are the emitted rays. We are concerned here with a wholly
atomic phenomenon, for if a substance be chosen as the anti-cathode
which is a compound of two or more elements, it is found that the
resultant _X_-ray emission, when the anti-cathode is bombarded, is
really a combination of the _X_-ray groups which would be emitted
separately by the elements that have gone to make up the compound.
These important facts were discovered by Barkla, who also discovered
that there were two series of _X_-rays in the characteristic _X_-ray
emission from an element. He called these two series the _K_-group and
the _L_-group. He observed that the lighter elements (up to silver)
gave the _K_-group of _X_-rays, and that heavy metals (such as gold and
platinum) gave the _L_-group. Of these two groups, the _K_-group is
the more penetrating. The harder or more penetrating the _X_-rays, the
greater the impact of the cathode rays necessary to produce them, and
Barkla saw that the _K_-group, in the case of the heavy metals, would
be so hard that the experimental methods known to him would not suffice
to produce them. Similarly, the _L_-group for the lighter elements
would be too little penetrating, too soft, to be observable by the then
known means. Barkla had determined the hardness of the rays he obtained
by measuring their absorption by thin sheets of aluminium. And he had
established a relation, as we have said, between hardness and atomic
weight.
These results were made much more precise when the analysis of _X_-ray
spectra by crystals replaced the absorption method of measurement, and
when the wave-lengths so determined were related, not to the atomic
weight, but to the atomic number. Besides the _K_- and _L_-groups, a
third group, called the _M_-group, has been discovered. The _M_-group
of rays is still softer than the _L_-group. The _K_-group, so far as
our means of observation carry us, begins with sodium, whose atomic
number is 11. With this light element the _K_-group, the hardest of
the three groups, is distinctly weak. As the atomic number advances
the _K_-groups emitted by the corresponding elements grow harder and
harder, reaching their extreme degree of hardness with wolfram, whose
atomic number is 74. For one and the same element, emitting both the
_K_-group and the _L_-group, the _L_-group is much the softer. The
_L_-group has been observed with copper, whose atomic number is 29,
and here it is even weaker than the _K_-group of sodium. From copper
onwards the _L_-group gets harder and harder, and it has been observed
right up to the last of the elements, uranium. The still weaker
_M_-group has only been observed so far with the heaviest elements, and
even then special precautions have to be taken to observe it at all.
These three groups of rays together make up the _X_-ray spectrum.
§ 2. _The K-Group_
Moseley, probably the most gifted of the young English men of science
killed in the war, was the first to make a considerable advance on
Barkla’s work. His first photographs (1913) were devoted to the
_K_-group, and extended from calcium, with atomic number 20, to copper,
with atomic number 29. These elements were used, successively, to form
the anti-cathode of a cathode tube, and were therefore bombarded
directly by electrons. To obtain the _X_-ray spectra he used, of
course, the method of crystal analysis, but not in its most modern
form. He established the following results.
As the atomic number increases the corresponding lines in the spectrum
move regularly in the direction of smaller wave-lengths, that is, the
hardness of the lines increases with the atomic number. This result, in
a less definite form, was, as we have seen, already reached by Barkla.
Each element gives two _K_-lines. The stronger, more obvious, line
corresponds to the longer wave-length. This line in the _K_-spectrum of
an element is called the _K_α-line. The weaker line is the harder line,
_i. e._, it corresponds to the shorter wave-length. This line is called
the _K_β-line.
The _X_-ray spectrum of an element is purely a property of the atoms
of that element. Brass, for instance, which is an alloy of copper and
zinc, gives four _K_-lines, of which two are the _K_-lines of copper,
while the other pair are the _K_-lines of zinc. Thus the _K_-spectrum
of a complex substance is obtained by merely adding together the
_K_-spectra of its elementary constituents.
The fourth result is of particular interest. It will be remembered
that, for a few places in the periodic table, we inverted the order
of the elements as given by their atomic weights. There are two or
three places where a heavier element is put before a lighter one. The
whole complex of the chemical and physical properties of such pairs of
elements is allowed to determine their position in the periodic table,
even when this is not in agreement with the atomic weight. Nickel and
cobalt form such a pair. Cobalt is heavier than nickel, with an atomic
weight of 58·97 as against an atomic weight of 58·68. Nevertheless,
cobalt is written before nickel. This order, justified by general
considerations, was completely confirmed by the _X_-ray spectra of
these elements. The _K_-group for nickel has harder lines than the
_K_-group for cobalt, and the increase in hardness corresponds to an
advance of one step in the periodic table. Here we have a clear proof
that the _X_-ray spectra follow the order of the atomic numbers, not
the order of the atomic weights. To settle this point was the original
object of Moseley’s research.
The fifth result which emerges from these researches is also of great
interest. We have spoken of gaps in the periodic table and we have
left spaces for elements which have not yet been discovered, but
to which we have ascribed appropriate atomic numbers. In Moseley’s
original research there was a gap between calcium and titanium. This
gap was immediately revealed by the _X_-ray spectra. The advance in
hardness from one element to another is quite uniform, and in passing
from calcium to titanium a sudden jump was found, corresponding to
the omission of one element. This missing element is known. It is the
rare substance named Scandium, with atomic number 21. Its absence from
Moseley’s series was at once revealed by the _X_-ray spectra. The
regularity of the growth in hardness of the _X_-ray spectra enables
us, without ambiguity, to say precisely how many elements (up to
uranium) are yet undiscovered, and exactly whereabouts they occur in
the periodic table. Thus, corresponding to atomic number 43, there is
a missing element. It has received the name Ekamanganese. Other gaps
in the system occur at atomic numbers 61, 75, 85, and 87. The study
of the _X_-ray spectra of the elements, therefore, enables us to say
definitely that five elements are missing.
Moseley’s results have been followed up, and his experiments repeated
with better apparatus. The main discoveries that have been made by
these later researches on the _K_-group are that there is a third line
belonging to the group, and that the _K_α-line really consists of two
lines very close together—what is called a doublet. The third line
of the _K_-group is even weaker and harder than the _K_β-line. It is
called the _K_γ-line. The same law holds for this third line as for
the other two. Like them, it increases in hardness for elements of
increasing atomic number.
The beautiful simplicity and precision of the results make this
research on the _K_-group one of the most interesting in all the modern
work on the atom.
Of the _L_- and _M_-groups we need only say at present that they
contain a large number of lines of which many are doublets. The general
law of their variation in hardness with the atomic number is the same
as for the _K_-group.
§ 3. _The Electrons near the Nucleus_
We shall now proceed to show how these experimental facts are explained
by the theory of atomic structure that we have outlined. In doing so we
shall present the problem in a rather simplified form, but one which
serves, in its main lines, as the basis for the detailed examination
which Bohr, and one or two others, are attempting. We recall again
the fact that the atom is regarded as a kind of planetary system, of
which the nucleus is the central body and the electrons the revolving
planets. We have already discussed the way in which we may suppose
these electrons to be arranged. They exist in groups; each member of
any one group moves in the type of orbit characteristic of that group.
We shall find that it simplifies our ideas and does not essentially
disturb the main lines of the theory if we imagine these groups of
electrons to be situated on circles all centring about the nucleus.
The circles get larger and larger, of course, as we proceed outwards
from the nucleus. The circle closest to the nucleus we shall call the
_K_-circle and the others, as we go outwards from the nucleus, the
_L_-, _M_-, _N_-, etc., circles.
Let us now consider how we may suppose a radiation belonging to the
_K_-group to be caused. We may suppose the first step to consist in the
removal of an electron from the _K_-ring to the periphery of the atom,
or else outside the atom altogether. If this removal be effected by a
cathode-stream bombardment, we may imagine that it is the result of
the direct impact of one of the bombarding electrons on the electron
of the _K_-ring. A certain minimum amount of energy is necessary for
this impact to be powerful enough to remove the electron. The electrons
of the _K_-ring, the innermost ring, are powerfully attracted by the
nucleus, and the bombarding electron must be moving sufficiently fast
for its impact to overcome this attraction. There is therefore a
certain minimum velocity below which the cathode-stream bombardment
cannot detach an electron from the _K_-ring. The higher the atomic
number the greater the charge on the nucleus, and the more firmly,
therefore, the electrons in the _K_-ring are held. For elements of high
atomic numbers, therefore, only the most intense bombardment would
suffice to detach an electron from the _K_-ring.
When the electron is detached, the _K_-ring is left incomplete, and
an electron from another ring will rush to take the vacant place.
Now we must remember that each ring corresponds to a different level
of energy, in accordance with Bohr’s quantum theory of the atom. In
passing from one ring to another an electron passes from one energy
level to another. A certain amount of energy is liberated by the
process, and this energy manifests itself as a radiation. It will
be what we have called a “monochromatic” radiation, that is, it
will be of one definite wave-length. It will furnish a line in the
_K_-spectrum. Now it may happen that the electron which rushes to
take the vacant place comes from the ring next to the _K_-ring, or
from the ring next but one, or from the ring next but two, and so
on. It is not at all likely to come from a very far-off ring, so we
may say that it will come from the _L_-ring, or the _M_-ring, or the
_N_-ring. But the farther off the ring from which it comes the greater
is the energy liberated, and the higher the frequency of the resultant
radiation or, what comes to the same thing, the greater the hardness
of the resultant radiation. So that an electron which falls from the
_N_-ring to the _K_-ring will give a harder radiation, _i. e._, one of
smaller wave-length, than an electron which falls from an _M_-ring to
a _K_-ring, and harder still, of course, than an electron which falls
from an _L_-ring to a _K_-ring. At the same time, it is more _likely_
that the missing _K_-ring electron will be replaced from the ring next
to it, the _L_-ring, than from the other more distant rings. And, as
between the _M_-and the _N_-rings, an electron is more likely to come
from the _M_-ring than from the _N_-ring. So that we should expect the
least hard line in the _K_-spectrum, the one due to the passage of an
electron from the _L_-ring to the _K_-ring, to be also the strongest
line, since the proportion of atoms where this particular change
is occurring is the largest proportion. And, by the same reasoning,
we should expect the hardest line, the one due to the passage of an
electron from the _N_-ring to the _K_-ring, to be also the weakest
line. The other line, the one due to the passage from the _M_-ring to
the _K_-ring, would be intermediate, of course, both in strength and
hardness. Thus our theory explains the observed fact that the hardest
line is the weakest and that the softest line is the strongest, while
the other line is, of course, intermediate in both respects.
A similar explanation holds good for the _L_- and _M_-groups of the
_X_-ray spectrum. The bombardment will sometimes detach an electron
from the _L_-ring. It is to be noticed that the energy necessary to
do this is less than in the case of the _K_-ring, and that for two
reasons. In the first place, the electrons in the _L_-ring are farther
removed from the nucleus than the electrons in the _K_-ring, and in the
second place they are subject to a certain repulsive effect from the
electrons of the _K_-ring. All electrons repel one another. An electron
belonging to any ring is repelled by the other members of that ring,
as well as by the members of other rings. As we get farther away from
the nucleus this effect becomes more marked, and it acts, to a first
approximation, as if the charge on the nucleus had been reduced, and
therefore exerted a less firm binding effect on the electron. It
requires less energy, therefore, in the case of any given element,
to detach an electron from the _L_-ring than from the _K_-ring. The
electron having been detached the vacant place may be occupied by an
electron from any of the farther outlying rings. And, here again, an
electron is more likely to come from the next farther ring than from a
more distant ring. At the same time, the passage of the electron from
the nearer ring will radiate less energy than the passage from a more
distant ring. So that in this case also the weaker line should be the
harder. This agrees with the experimental results.
The same general remarks apply to the detachment and replacement of an
electron from the _M_-ring, with the difference that the detachment is
still easier than in the case of the _L_-ring. The _M_-ring is farther
from the nucleus and also the repulsive effect of the inner electrons
is more noticeable.
§ 4. _Doublets_
The simplicity of the _K_-spectrum is due to the fact that we are here
concerned only with the innermost electrons of the atom and, in this
region, the charge on the nucleus exerts a very firm control. The
stability of the electrons close to the nucleus is very considerable.
As we get farther away from the nucleus, however, the conditions
become more complicated and the resulting spectra, indicating what
changes are going on, also become more complicated. When we reach the
outer electrons, those concerned in producing the visible spectrum,
the changes going on are of the greatest complexity. This growth
in complexity is apparent directly we pass from the _K_-spectrum
to the _L_-spectrum. The _L_-spectrum contains more lines than the
_K_-spectrum, and their explanation is less simple. An interesting
feature of the _L_-spectrum is the large number of doublets it
contains. It is found that close pairs of lines may be distinguished in
the _L_-spectrum and that the distance between these pairs is constant.
It is this fact, that the doublets are of the same size, as it were,
that calls for explanation. The explanation offered by the theory is
that the _L_-ring is not really a single ring, but consists of two or
more rings, each ring corresponding to a slightly different energy
level. Let us suppose that the _L_-ring really consists of two rings.
Then an electron from the _M_-ring may fall on to one or the other of
these two rings. We shall denote these two _L_-rings by _L__{1} and
_L__{2}.
If an electron falls from the _M_-ring on to the _L__{1}-ring, it will
radiate an amount of energy slightly different from that radiated
by an electron falling from the _M_-ring on to the _L__{2}-ring.
The wave-lengths corresponding to these radiations will therefore
be slightly different and the corresponding lines in the spectrum,
indicating these wave-lengths, will therefore consist of a pair of
lines close together—a doublet. Now let us consider what happens when
the electrons fall from the _N_-ring. The electron which falls from
the _N_-ring, whether it falls on the _L__{1}- or the _L__{2}-ring,
will radiate more energy than the electron from the _M_-ring. But the
_difference_ in the energy radiated, depending on whether it falls
on to the _L__{1}- or the _L__{2}-ring, is obviously the same as the
corresponding difference in the case of an electron falling from the
_M_-ring. It is the difference in the two paths which is concerned,
and this difference is simply the distance between the _L__{1}- and
the _L__{2}-rings. In the case of electrons falling from the _N_-ring,
therefore, although the actual amounts of energy radiated are greater,
and therefore the corresponding wavelengths are shorter, yet the
resulting pair of lines are at the same distance apart as in the case
of the _M_-ring. Similar reasoning applies to any pair of electrons
which start from the same outer ring and fall, one on the _L__{1}-ring,
and the other on the _L__{2}-ring. In each case, a doublet is produced,
and all these doublets have their component lines separated by the same
interval.
This theory gives a satisfactory explanation of the observed equality
of the _L_-doublets, but we can go on to deduce a result from it
which can be used as a test. We have seen that the _K_ α-line in
the _K_-spectrum is produced by the passage of an electron from the
_L_-ring to the _K_-ring. But there are two _L_-rings. The passage of
an electron from each of these to the _K_-ring should produce a line in
the _K_-spectrum. These two lines should be very close together; they
should form a doublet. Now we have seen that the _K_ α-line actually is
a doublet. But we can go further. The _difference_ in path, according
to whether the electron falls on the _K_-ring from the _L__{1}- or
the _L__{2}-ring, is the same as the difference in the paths of two
electrons, coming from the same outer ring, but falling one on the
_L__{1}-ring and the other on the _L__{2}-ring. So that the interval
between the components of the _K_-doublet should be the same as the
interval between the components of the _L_-doublets. This result is
confirmed by actual measurement. The “interval” or “distance” between
the components of a doublet is really a difference, of course, in the
hardness of the corresponding waves.
We have said sufficient to make the main lines of the theory clear. We
need only add that the further explanation of the _L_-spectrum and also
of the _M_-spectrum requires us to assume that the _M_-ring also is not
a single ring, but consists of two or more.
INDEX
A
α-RAYS, 65
Aluminium, 154
Anti-cathode, 73
Argon, 141
Atom, 33
Atomic numbers, 82
Avogadro, 34
B
ß-rays, 65
Balmer, 127
Barkla, 168
Black body, 114
Bohr, 123
Bragg, 118
Brownian movement, 45
C
Cathode rays, 55
Compounds, formation of, 29
Crystal analysis, 166
D
Dalton, 23
Debye, 122
Diffusion, 40
E
Einstein, 46, 105, 120
Electron, mass of, 60
—— radius of, 62
Element, 28
F
Fraunhofer, 123
G
γ-rays, 65, 74
Gases, Kinetic Theory of, 42
Geological strata, age of, 70
Gold atom, 88
Gramme-atom, 37
H
Helium atom, 86, 147
—— nucleus, 87, 108
Hertz, 54
Hydrogen atom, 85
I
Inert gases, 142
Ions, 56
—— charge on, 58
Isotopes, 102
K
Kirchhoff, 114, 123
L
Laue, 166
Light, velocity of, 54
Lithium atom, 90, 149
M
Magnetic properties of the elements, 157
Maxwell, 42, 53
Mendeléev, 77
Molecule, 33
Monochromatic light, 125
Moseley, 170
N
Neon, 144
Newlands, 77
Nitrogen, 152
P
Periodic system, 77
Perrin, 46
Planck, 119, 127
Prout, 25
R
Radium, 63
—— disintegration of, 95
Relativity and the atom, 104, 133
Rutherford, 93
S
Sommerfeld, 122, 134
Stokes, 57
T
Temperature, absolute zero of, 42
U
Uranium, 79
W
Waves, longitudinal and transverse, 124, 165
X
_X_-rays, 70, 167, 168
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