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r 1 

Physics I 






EiQHT Warren Strbbt 

copTmiOHTy 1991, nr 




This volume is intended for readers who wish 
to obtain a familiarity with the basis of modem 
physical science. Without mathematical formula- 
tion it deals with moduli theories as to matter and 
energy^ emphasizing the granular structure and 
electrical nature of matter^ and the apparently 
corpuscular character of energy. 

The reader need have no previous knowledge of 
electricity, mechanics, or chemistry. For the appre- 
ciation of the evidence of certain critical experi- 
ments upon which mod^n scientists base their be- 
lief in electrons and in quanta of energy some 
knowledge of electricity, however, is required. To 
supply this in a quick and easy manner, the usual 
historical order of presentation is abandoned and 
the correctness of modem theories is assumed at 
the start. There are postulated the electron and its 
counterpart, the proton. In terms of these there 
are then described those few phenomena of elec- 
tricity which are essential to the later consideration 
of the evidence. In this way, it is hoped most 
rapidly to introduce the reader to modem theories 
as to the invisible workings of the physical univ^-se. 

J. M. 

Wyoming, N. J. 
June, 1921. 





Preface iii 

Intboduction . . . " vii 

I Atomic Stbuctums 1 

II Satisfied and Unsatisfied Systems . . 11 

III The Periodic Table of Atomic Systems . 20 

IV Mass and Inebtia of Atomic Systems . . 37 
V Radioactive Disintegrations .... 48 

VI Conduction of Electricity through Gases 57 


Electrical Phenomena 69 

VIII The Proof for the Existence of an 

Electron 84 

IX Isolating a Proton 99 

X X-RAYS AND Atomic Numbers . . . . 115 

Between Chapters — ^A Dialogue . . . 135 


XI Photo-electric Effects and the Quan- 
tum OF Energy . 139 

XII Light Radiation and Atom-Models . . 155 

XIII More Evidence for the Quantum Hy- 

pothesis 168 

XIV Energy and Its Availability .... 184 

Appendix — The Magnitudes of Electrons 

AND Quanta 195 

Glossary 207 


In the constellation of Orion is the bri^t reddish 
star Betelgeuse. For centuries it served with oth^ 
stars as a guide to marin^r^ and as an object for 
consideration by philosophers and myth makers. 
Although we still retain the name given to it by 
the Arabs and still see it as the right shoulder of 
the mi^ty hunter, science has removed all but the 
nomenclature of the earlier animistic interpretation 
and substituted cold quantitative facts. Since our 
school days we have known that Betelgeuse is a 
sun, essentially like that which illuminates our 
earth. Very recently we have been told by Pro- 
fessor Michelson of Chicago as to its astounding 
magnitude — ^three hundred times the diametar of 
our own sun. The methods by which he arrived at 
this relationship involve interesting theories and 
required precise experimentation. Like the news- 
papers, however, of the day following his announce- 
ment let us be content for the moment with the I 
fact itself. 

In the midst of the universe in which Betelgeuse 
is but a speck exists a smaller sun on a planet of 
which there crawl what Bertrand Russell aptly 
called tiny lumps of impure carbons and water. 
What a shock to the "ego-centricity'' of these car- 
bon compounds to realize their quantitative in- 
significance in comparison with Betelgeuse. 



About this larger sun there are probably en- 
circling planets. Are there organic compounds on 
any of these and how do they arise from inorganic 
compounds as the ageing planet slowly cools? Are 
there conditions of temperature and atmospheric 
content which are accompanied by such chemical 
changes? If organic substances can be formed wiU 
life appear on tiie planet? What intimations of Ihe 
evolution of life can be found in modem science? 

Our questions grow by association, ov^lapping 
one another, repeating and varying their content;- 
and our apparently unbound speculation leads only 
to fiulher questions. Some answers and much ma- 
terial for thought are vouched by modem science 
althou^ the specific question as to the mechanism 
and process in the evolution of life remains un- 

What in fact do we mean by life? The cater- 
pillar in its cocoon awaits the proper temperature 
for its metamorphosis: the radioactive atom spon- 
taneously emits an electron and becomes a new 
substance. Both caterpillar and radioactive atom 
are but stages in a sequence of events, the one to 
be followed by more caterpillars all of which will 
differ slightly from the original and the other by 
more atoms which will differ radically from the 
original. The comparison is not too s^iously in- 
tended although it is safe to say that the offspring 
of the radium atom will be moving in fast circles 
ages after the descendants of the moth have per- 
ished from the face of tiie earth. 

When we have reached a satisfactory definition 


of life shall death be its negative? Are life and 
death merely convenient terms which we loosely 
apply to phases in 'a wide process of continuous 
change? and What are the entities which are con- 
served during the change? To the last question 
science today may apparently give answer for in 
energy and in electricity it has two entities which 
are conserved in amount. The former manifests 
itself by changes in the location of the latter, for 
electricity is the only known constituent of the 
ponderable matter of which our universe is com- 

Whether we are interested in speculative ques- 
tions like those just mentioned, in less speculative 
but yet unsolved questions like the mechanism for 
tixe transmission of stimuli by nerves, or in the 
purely practical matter of the eflBcient organization 
and operation of the multiplicity of machines which 
condition our daily lives, we must seek explanations 
in terms of energy and electricity. 

The reduction of the number of unknowns with 
which science deals is a recent advance which has 
foEowed discoveries like those of radium and 
X-rays. Widely diflferent branches of science are 
now known to be dealing with the same funda- 
mentals of electricity and energy. For the first time 
in centuries there exists the material which a genius 
could synthesize into a universal science, in which 
physics arid chemistry, biology and geology, will 
lose their identities in a common set of principles. 

So rapid, however, has been the advance of sci- 
ence toward this simplification of terms and prin- 


ciples that few except those immediately concerned 
are aware of the possibilities. With the change of 
base and point of view which has followed the dis- 
covery of the electron, and the consequent interre- 
lation of branches of science long held apart, there 
have arisen innumerable questions which occupy 
the time of those best able to expound the new 
science. Our schools follow but tardily in their 
elementary classes the conclusions of researchers in 
science and our text-book writers must comply with 
existing distinctions between branches of science. 

The fundamental concepts of the new science are 
easy to grasp and may be stated in relatively simple 
terms, although the quantitative relationships are 
to be expressed only in mathematical ssmabols. The 
complete ssoithesis may be upon us some day as 
unexpectedly as were Einstein's hjrpotheses and 
presumably to find us as unprepared. For its 
critical consideration but few will be competent. 
For a more popular appraisal many of us may be 
prepared if we have learned to think of all scientific 
problems in terms of elect^*icity and energy. 

Unfortunately the popularizer of these concepts 
must run some risk of false statement for he is 
limited first by his own knowledge and interpreta- 
tion of the accepted body of scientific truth, an(| 
second by the necessity of purely verbal expression. 
Word pictures are all that he may give and the 
selection and emphasis of their material may carry 
implications which time shall disprove. 

One difficulty which confronts those who would 
impart the concepts, evidence, and conclusions of 


modem science to readers untrained or impatient of 
mathematical formulation, arises from a weakness 
which is characteristic of modern research itself. 
Science today is quantitative rather than qualita- 
tive. It expresses the relationship of the intensities 
of two phenomena, as for example the intensities of 
the electric current and of the illumination of an 
incandescent lamp, and compensates for its in- 
ability to answer the question "how" by its wealth 
of data as to "how much." Research monograph 
and text-book alike emphasize the observable quan- 
titative relationship and rarely venture far into the 
speculative hinterland where "how" must precede 
"how much." As we teach science today in our 
schools the effort of learning the quantitative rela- 
tionships too frequently leaves neither the instruc- 
tor nor the student leisure for fruitful inquiry or 
speculation as to the mechanism itself. 

Rare indeed is the Faraday whose pictures of in- 
visible processes satisfy and vivify quantitative 
relationships during a century of fruitful research. 
That particular genius was discovered by Sir 
Humphrey Davy, himself a broad and versatile 
mind. One wonders whether our phonographic 
classroom methods and the machine processes of 
our laboratory instruction can create an environ- 
ment for that inspiration of another Faraday which 
the present development seems to require. 

Faraday^s pictures were in the nature of working 
hypotheses as to an all-embracing and continuous 
mediima^— an elastic ethereal medium. Assuming 
that an ether existed, the attraction or repulsion of 


electrified bodies was explainable, in terms of the 
strains which the bodies introduced into the me- 
dium, without recoiu'se to a theory for action at a 

During the later half pf the 19th century, the 
assumed medium became of first importance and 
scientifically electricity was in danger of becoming 
a phenomenon of the very medium which had been 
assumed to explain its own phenomena. The 
emphasis on the medium, however, had happy re- 
sults for it led Maxwell to the conclusion that light 
was an electro-magnetic phenomenon. 

With the discovery of the electron — ^the appar- 
ently indivisible particle of electricity — the ether 
rapidly lost its importance and finally with the 
work of Einstein it has ceased to be a necessary 
postulate in physical science. 

The terminology of the older physics of the ether 
is unavoidable, however, if one approaches the new 
physics of electrons in the historical ord^ of its 
evolution. Such a method of presentation has the 
advantage that tiie experimental evidence may be 
set forth in 'conjunction with each statement of fact. 
On the other hand, the method demands on the 
part of the reader a knowledge of the phenomena 
and laws of electricity, mechanics, and chemistry 
which is seldom possessed by the hypothetical per- 
son "the general reader." This deficiency may, of 
course, be supplied by devoting to that purpose the 
earlier chapters of an exposition, but several of 
these would raise memories of high sdiool text- 
books. The facts which must be acquired would 


of necessity be presented in a conventional manner. 
It would, therefore, be necessary to return to them, 
after treating the fundamentals of the new science, 
and attempt a corrective interpretation in the new 
terms. The process would not only be wasteful of 
time but difficult of attainment for first impres- 
sions, even of science, lie deep in the mind. 

It is perhaps better to start out boldly, stating 
the physical basis of the new science and building 
as far 83 practical on its firm foundation. For cer- 
tain portions of the superstructure only sketches 
are available, and for others not even such indica- 
tions. Occasionally there may be sketches of sev- 
eral draftsmen neither of whom seems destined to 
be accepted as the final designer. Enough material, 
however, may be inspected by the reader so that 
he may appreciate the problem of the new science 
and the point of view. Only when the structure is 
partially completed should the reader be expected 
to recognize its relation to the science of his own 
school days, for the new science starts with the 
invisible and intangible entity of electricity. 




The story is told of the debutante who met the 
raiowned astronomer^ the lion of the evening^ with 
an appreciative remark as to the wonders of as- 
tronomy^ ''And do you know I think the most 
wonderful thing is how we know the names of the 

Now imagine^ if you can, two types of particles, 
each invisible, intangible and infinitesimal in the 
ordinary senses of these words, and indeterminate 
in form and substance. For one tjrpe, wonderfully 
enough, we know the name "electron/' but for 
the other type there is no agreement. We are 
free to choose from a number advanced by various 
scientists and shall arbitrarily adopt the term 

Electron and proton are complementary. To- 
gether they may merge in a union so close that their 
combined size is less than that of the electron alone. 
Such a statement may sound absurd but experi- 
ments seem to indicate that ihe union of two or 
more protons with one or more electrons is a smaller 
particle than is a single isolated electron. The form 




and size of the electron and proton must then be 
different in combination from that of the free elec- 
tron and free proton respectively. 

We apprehend at the start two tyi)es of particles 
both invisible but both independently observable 
by certain effects which they produce. To these we 
ascribe complementary properties. In so doing we 
meet at once a serious difficulty of existing language 
for there is a paucity of terms by which we may 
describe the particles without connotations of an 
animistic bias. . The protons and electrons are com- 
plementary, mutually supplying each other's needs. 
Electrons, however, are mutually antagonistic and 
depart from each other's presence unless restrained. 
The same is true of protons. It is only by virtue of 
the complementary properties of proton and elec- 
tron that two or more electrons, for example, are 
constrained to the same infinitesimal space. 

A close union of a group of protons and electrons 
is conceivable from a social parallel for it may re- 
semble geometrically the careful seating of guests 
at a large dinner. Between those of opposing in- 
terests might be placed others whose interests are 
mutual with those of their immediate neighbors. 
The dinner guests have various degrees of sjon- 
pathy and antipathy for each other. Between elec- 
trons, however, there is but one degree of antago- 
nism since all experiments point to the exact 
similarity of all electrons without r^ard to their 
individual histories. The same apparefitly is true 
of protons although the isolation of the latter has 
been a more recent advance and there is not as 


large a volume of evidence in this case. We are 
probably entirely safe in assuming that protons are 
indistinguishable and are interchangeable to an ex- 
tent that would excite the admiration of the piece- 
part manufacturer of the present days of quantity 

Any grouping of antagonistic elements, for ex- 
ample, electrons, can persist only by virtue of tiie 
presence of the complementary type, in this caae 
protons, and by virtue of such geometrical arrange- 
ment that the opposing tendencies of the elements 
of the same type are neutralized by the complemen- 
tary tendencies of elements of a different type and 
in part by tendencies which axe discussed on page 
76. According to some theories^ however, two elec- 
trons or two protons are pictured as mutually at- 
tracted when they are very dose together, although 
at larger separations they are repellent. Similarly 
an electron and a proton would start to repel each 
other after they had approached to within a certain 
small distance of each other. In any case the 
permanence of a group of protons and electrons will 
depend upon the geometrical arrangement. The 
picture which we may form is like that of some state 
of society where man shuns man, and woman avoids 
woman, but unrestricted promiscuity prevails. Pro- 
miscuity, however, carries no stigma for individu- 
ality is entirely lacking. 

In many ways their society approaches an angelic 
state, for its members are not confined to a terres- 
trial plane but hover and flit about in space, subject 
to the opposmg tendencies which were just men* 


tioned. Nor are tiieir antagonisms destructive like 
those of humans, despite the fact that electrons 
may rush about with a speed almost that of li^t. 
Actual collisions between like elements are always 
avoided by swerving to one side or in the extt^me 
instances of head-on approach by retracing their 
paths. A deathless existence these particles lead 
and altiiough there is marriage and giving in mar- 
riage the unions are fruitless. The number of elec- 
trons or of protons in our universe is believed to be 
eternally fixed so that their immortal society may 
alter only in its configurations. 

Such new configurations as these elements may 
assume are formed under the action and in con- 
formity with the laws stated figuratively above. In 
more classical terms these may be expressed by 
saying that like elements repel and imlike attract. 
To place this idea completely beyond the animistic 
bias two words of recent coinage and incompletely 
sanctioned usage may be employed. Electrons 
pellate, protons pellate, but an electron and a 
proton tractate. 

The law reminds one of that for the action of 
electrical charges, since like charges repel and im- 
like attract. It may be admitted at once that elec- 
trons are elements of so-called negative electricity 
and protons elements of positive electricity. It is 
preferable, however, to consider further this ques- 
tion of configuration of these elements before at- 
tempting to relate our present treatment with the 
familiar facts of electricity. We shall nevertheless 


find it most convenient to speak of electrons and 
protons as the '^electrical elements." 

The electrical elements are found associated in 
configurations which increase rapidly in complexity 
as we pass from the simple union of one proton and 
one. electron to systems which involve hundreds or 
thousands of elements. When more than one pro- 
ton is involved two types of systems are possible. 
In the simpler type all the protons are associated 
in a compact group which comprizes also sufficient 
electrons to secure a certain degree of stability for 
the coalition. Such other electrons as may be asso- 
ciated with the system under consideration are 
external to the compact group or nucleus as we shall 
call it. This simpler type of system we shall call 
atomic^ and to the question of its stability we shall 
return later. 

The second type of system is that which involves 
two or more nuclei and associated external elec- 
trons. Again we postpone the question of degree 
of stability and class such systems as molecular. 

For completeness we should mention at this point 
also systems which may be formed by combinations 
of the two main types. A number of similar sys- 
tems, for example, molecular systems, may become, 
closely associated by a temporary relinquishment 
of individual freedom and form a federation, to 
borrow a term which closely fits. As long as the 
external conditions remain as they were this federa- 
tion may persist but its component members may 
on occasion and without prejudice assume again 


their individual existences. Polymeric systems of 
this kind are of frequent occurrence. 

As the opposite of poljrmerization there is dis- 
sociation, the process of separating a polymeric or 
even a molecular system into the smaller systems 
which compose it. With the latter process particu- 
larly we shaU have more to do later. 

For the moment, however, we shall consider only 
the simplest type of system, namely the atomic, 
which is formed by a nucleus and a number of elec- 
trons external to it. In the nucleus there are al- 
ways more protons than electrons. It is this excess 
of protons that serves by virtue of their inherent 
complementary characteristics to retain in the 
region immediately external to the nucleus a num- 
ber of electrons. 

Consideration will be further limited by exclud- 
ing for the present all systems in which the total 
number of electrons, including those external to 
the nucleus as well as those comprized by it, is 
unequal to the number of protons in the nucleus. 
Systems in which there is numerical equality be- 
tween protons and electrons we shall call normal 
atoms or, more conventionally, imcharged atoms. 
We shall further find it convenient to classify such 
atomic systems by the number of electrons external 
to the nucleus, or what amounts to the same thing 
by the excess of protons in the nucleus. This num- 
ber will be designated the "atomic number.'^ 

The largest known atomic number is 92 and this 
corresponds to the chemical element uranium, a 
metallic element found in pitchblende. It was in 


residi^ of this mineral, from which the uranium 
had been extracted,- that Professor and Mme. Curie 
discovered the element radium. Radium has an 
atomic number of 88. Another chemical element, 
which has a large atomic number, is thorium, a rare 
metal used in making incandescent gas mantles. Its 
atomic number is 90. 

Atomic systems with such high atomic numbers 
are very rare in the collector's sense of the word. 
Let us imagine a period long past in the history of 
our universe when such systems predominated even 
to the exclusion of systems of smaller atomic num- 
bers. Their nuclei were crowded spaces filled with 
antagonistic electrical elements — ^insecure coalitions 
ready if necessary to sacrifice some of &eu- mem- 
bers. Whether imder external influence or solely 
from internal causes these coalitions started to 
expel their members. The electrons left as indi- 
viduals, ejected with enormous velocity, or in com- 
pany with protons with smaller velocities as be- 
fitted a larger party. Such a party was apparently 
composed of four protons and two electrons, and 
to it we give the name "alpha particle." 

Under some conditions the reduced coalition 
would be left so unstable by such action that a 
further expulsion would be necessary in the next 
few seconds. Sometimes days would elapse and 
under other conditions years or even ages might 
pass before such violent readjustments again took 

Today we may observe the same process in the 
case of atomic groups of high atomic numbers — 


the so-called raxiioactive elements. The changes 
in nuclear composition appear in the case of these 
elements to be independent of external conditions 
and to occur solely because of the need of readjust- 
ment on the part of the elements of the nuclear 

By a sequence of expulsions of electrons and of 
alpha particles the highly complex nuclei of the 
prehistoric atomic systems were reduced in number 
of electrical elements and increased in stability imtil 
finally the apparently stable atomic structiu'es of 
our ordinary chemical elements were attained. In 
other words, we may consider the chemical elements 
like tin, lead, sulphiu* and oxygen to be "end- 
products" of a long series of radioactive changes. 
The character of these changes and the alterations 
in the properties of the atomic ^stems which result 
will be discussed in considerable detail in later 

Although the disruption of the complex nuclear 
structure of a radioactive atom is spontaneous in 
the sense of occurring without the stimulus of ex- 
ternal agents, similar disturbances do not occur 
simultaneously in all the individual atoms of a large 
group. Some of the atoms of a bit of uranium, 
for example, or of radium, are always breaking 
down. The product of the disintegration may be 
removed by trained experimenters and hence the 
rate at which it is formed may be measured. Know- 
ing the rate at which disintegration is occurring, it 
is a matter of simple mathematics to calculate Hie 
average life, that is the time required until half 


the original atomic systems will have disintegrated. 
This is using the term ''average life" as actuaries 
do, for of course some of the atoms may last for 
ages without dissociating. 

In the case of radium the average life is estimated 
as about 1600 years; that is, it should require that 
time for half the atoms of any bit of radium to 
become changed into atomic systems of smaller 
numbers of elements. Curiously enough the next 
atomic system, a gaseous element known as "niton," 
has a short average life of only five or six days. The 
atomic number of niton is 86, for it is the result of 
the ejection of an alpha particle from the nucleus 
of the radium system, which has an excess of 88 

The alpha particle is itself an atomic system, al- 
though it is not a normal or uncharged atom since 
it involves more protons than electrons. If two 
external electrons are associated with it, it becomes 
a normal atom, namely that of heliima, a light in- 
active gaseous element which has recently attracted 
public, attention as a desirable substitute in filling 
balloons for the lighter but active element hydrogen 
which bums with oxygen. 

It was perhaps by such spontaneous changes in 
the composition of the nuclei of atomic systems, 
as are illustrated today by radium, that the known 
chemical elements were produced. The definition, 
however, of the term "chemical element" is no 
longer as simple as it was in the days before this 
disintegration theory was advanced and accepted 
by scientists. Until we have discussed with further 


detail th.e possible changes which may occur in 
atomic systems, we may use the term in its usual 
sense, and say that the ei^ty, or so, known chem- 
ical elements are the products of radioactive dis- 
integration for which ihe further disintegration is 
so slow as to be n^ligible or inappreciable. For 
aU practical purposes, however, we may assume 
that our chemical elements are end-products of pre- 
historic disuit^ration. 



It is difficult to describe the interactions of the 
electrical elements without recourse to words which 
have an emotional significance. Words like stable 
and unstable, or active and inert, might be used 
but they have scientific connotations which are bet- 
ter avoided at present. In continuing the discussion 
of atomic systems we shall use words which are 
frankly animistic and classify these systems as sat- 
isfied, unsatisfied, or dissatisfied. The radioactive 
systems which were described in the previous diap- 
ter are evidently violently dissatisfied systems. 

A failure of satisfaction may be the result of a 
deficiency in the quantity or in the quality of the 
desired good. Quantitatively an electrical system 
is satisfied if there is an equality in the number of 
protons and electrons which comprise it. Satisfac- 
tion as to quality, on the other hand, depends upon 
the configuration of the component elements of the 

Dissatisfaction when it occurs is deep seated — 
a neurotic condition of the nucleus which may re- 
sult without any external stimulus in violent out- 
bursts and a veritable orgy of smashing china and 
throwing things about. This excitable state is 



characteristic of those atomic systems which have 
retained their youth and been imchanged by the 
years. When they shall have become as lead, a 
long peaceful life will confront them, in which they 
may be at times unsatisfied but practically never 
dissatisfied. During the formative years of their 
discontent the nature of tiieir dissatisfaction adapts 
itself to their condition, being now concerned with 
quantity and again with quality or configuration. 
At times they throw off alpha particles and thus 
find themselves with an excess of electrons which 
are a source of dissatisfaction in their innermost 
and nuclear hearts. The electron which is then ex- 
pelled from the nucleus is sometimes spoken of as 
a beta particle. By expulsions of alpha and beta 
particles the radioactive systems lose much of their 
energy and all appearances of radicalism. 

For a time, however, we shall deal with the con- 
servative atoms which never become more than 
mildly unsatisfied. Systems which are unsatisfied 
in the numerical equivalence of protons and elec- 
trons show the effect of electrical charges. The 
consideration of these effects also must be post- 
poned and our attention fixed upon systems which 
are satisfied in this quantitative relationship but 
are unsatisfied in the configuration of their com- 
ponent elements. Such absence of satisfaction as 
then exists is solely a matter of the arrangement of 
the electrons external to the nucleus siniee, if the 
source of the trouble were in the latter, dissatisfac- 
tion would be manifest unmistakably. 

The electrons which are external to the nucleus 


of an atom are separated from it and from ea(di 
other by relatively large distances. Perhaps as good 
a picture of an atomic system as may be easily 
formed is obtained by a comparison with our solar 
system. The distances between sun and planets 
and between the various planets are very large as 
compared to the diameters of any of the planetary 
bodies. If we now imagine the sun to be very small 
as compared to the earth and then imagine all the 
distances and sizes to be proportionally reduced 
until the i^stem is invisible even with the most 
powerful miqroscope we have a possible picture of 
an atomic i^stem. The sim is first made smaller 
because the nucleus is small compared to the elec- 
tron. Some dimensions of such a system are quite 
accurately known for they are determinable by 
methods which will be described later. 

The diameter of the atom depends upon its con- 
struction, being smaller for some chemical elements 
than for others. If we wished, for example, to keep 
out of the way of a hammer thrower, starting his 
turns, we would assume that liis diameter was that 
of the circle through which the hammer head 
swung. In much the same way the diameter of 
any atom is that of the circle of which the center is 
the nucleus and the radius the distance to the outer- 
most electron. 

The hydrogen atom is composed of only one 
proton and one electron. The two elements are 
probably whirling about each other in space much 
like a rapidly whirling dumbbell except that there 
is no direct connection between the ends of the 


dumbbell. Its diameter is about two himdredths of 
a millionth of a centimeter^ but this is about one 
hundred thousand times as large as that of the 
electron so that the diameter of an electron is about 
two tenths of a millionth of a millionth of a centi- 

The other atoms are not so simple. The helium 
atom, of which we have spoken before, consists of 
a nucleus and two external electrons. The atom of 
sodium has eleven, and that of chlorine seventeen 
electrons, external to the nucleus. We do not know 
as much about the arrangement of the electrons in 
the atomic structures as we ^ould like or as we 
probably shall in the near future. For the purpose 
of discussing the effects of the configuration of the 
external electrons we may, however, draw one or 
two parallels of a kindergarten nature which will 
serve in default of more authoritative pictures. 

The ^stem of nucleus and external electrons may 
be likened to a few children playing a circle game 
about a teacher. Suppose that the game goes best 
with eight in the ring but is possible with any num- 
ber between six and ten. If ten are playing, that 
is if the teacher's responsibility is for ten, as might 
be the case for electrons if the nucleus has ten excess 
protons, then there is some crowding. An oppor- 
tunity for two children to join an adjacent but less 
crowded circle wiU be welcomed by the children, and 
by the teacher also, if she can satisfy her quantita- 
tive obligations by supervising their play in a 
neighboring circle. 

An atom with a circle crowded by electrons is in 


an unsatisBed condition which is favorable to losing 
electrons. If it does so it will have more protons' 
than electrons. This tendency towards an excess of 
protons is ordinarily described by calling the atom 
electropositive. It can supply electrons to any other 
atom which can accommodate them m its circle. If 
it does so, however, the two atoms must remain 
together for each nucleus has responsibiUty for a 
definite number of the total of electrons. For such 
a combination into a molecule the second kind of 
atom must have a complementary need, having 
fewiM' electrons than can be satisfactorily accommo- 
dated in its ring. Its tendency to acquire added 
electrons is indicated by calling it electronegative. 

If an atom has a ring of electrons just sufficient 
to play their circle game without crowding th^e will 
be no need for loaning or borrowing from an adja- 
cent atom, and hence no occasion for combination 
into a molecule. The elements with atoms of this 
character are ''inert" substances such as the gases 
helium, argon, neon and krypton. Niton is also an 
example of such an arrangement. Niton, however, 
is inert only as far as concerns its possibility of com- 
bination with other atoms, for, due to its radio- 
active properties,. it can very markedly influence the 
chemical behaviour of oliier substances. 

So far as concerns the combination mto molecular 


systraas of two different kinds of atomic systems, we 
should expect electropositive atoms to unite with 
electronegative ones. Common salt, NaCl, is the 
combination of the electropositive sodium atom, 
which would spare one electron, with the electroneg- 


ative chlorine atom, which would accommodate an 
extra electron. In forming the molecule the electrons 
probably redistribute themselves about the two 

Under certain conditions the combinatbn so 
formed may be broken up into two new ^stems, 
which are slightly different from the ori^al sodium 
and chlorine atoms. If salt is dissolved in wat^ 
some of its molecules separate into these two parts. 
One has the nucleus of a sodium atom and the other 
that of a chlorine atom. The number of electrons 
about each of these nuclei is not that of the normal 
atom. In the process of separating, the electron 
which was borrowed by the ring about the chlorine 
nucleus is not returned. 

The chlorine nucleus and its ring with an excess 
electron is not a chlorine atom, nor is the sodium 
nucleus with its ring, which has lost an electron, an 
atom of sodiimi. When ordinary table salt breaks 
up in solution, it does not give the elementary sub- 
stances of sodium and chlorine, neither of which is a 
possible food. These new atomic systems move 
about in the solution exactly as do unsplit molecules. 
To them is given a new name, that of "ions" since 
th^ are go-ers. Sometimes they come together in 
their wanderings and for a time form again a salt 
molecule but later they may break apart. 

The phenomena of solution and in fact all matters 
having to do with the motions through' space of 
atomic or molecular systems must be postponed. 
The dissociation of the molecular S3rstem of gKxlium 
chloride into atomic systems has been cited as a step 


toward^the fuller study of the combination of atomic 
systems into molecular systems. When the sodium 
ion^ that is the positive ioU; comes into the inmie- 
diate neighborhood of the chlorine, that is the nega- 
tive ion, recombination will again occur although a 
dissociation may immediately follow as the result 
of those external influences which we are at present 
assuming without explaining. 

Ions are atomic systems Unsatisfied in quantity 
rather than in configuration of electrical elements. 
Combination of atomic ^stems into molecular sys- 
tems is, therefore, seen to occur as the result of 
either type of unsatisfaction. For historical reasons 
both of the kinds of combination, which we have 
pictured above, are called chemical combinations 
without regard to our more recent knowledge that 
they are entirely electrical phenomena. 

The ability of an electropositive atom, for ex- 
ample sodium, or of a n^ative ion, for example the 
chlorine ion, to enter into a molecular combination 
depends (as we have seen) upon the possession of 
one (or more) electrons in excess of those requisite 
to satisfaction in configuration or in quantity, re- 
spectively. We may therefore express the ability of 
aa atomic system to combine, which is conven- 
tionally termed its valence, in terms of the nimiber 
of electrons which measure its unsatisfaction. Thus 
we may say that the atomic systems mentioned im- 
mediately above have a positive valence of one. The 
atoms or ions which become the partners in such 
combinations have a complementary need of elec- 


irons. They may be described as having a n^ative 
valence of one. 

For a satisfied system, that is for an inert atom, 
the valence is, of com-se, zero. 

The satisfaction of that need on the part of an 
atomic system which is expressed quantitatively by 
its valence may be obtained in a numba* of ways. A 
monovalent atomic system like sodium requires only 
another monovalent ^stem, like chlorine, which has 
a complementary need to form a satisfied molecular 
structure. A divalent atom, on the otiier hand, may 
be satisfied by a union with another divalent atom 
or with two monovalent atoms. In the latter case 
the two necessary atoms may be of the same kind 
or different. In the molecular sjrstem of water the 
divalent oxygen atom is combmed with two similar 
monovalent hydrogen atoms. The sjnnbol H2O, in 
which the subscript indicates the number of atoms 
of the type to which it is affixed, is a convenient 
representation of this combination. In similar man- 
ner the molecular system formed by the divalent 
oxygen atom with two unlike atoms of sodium and 
hydrogen is symbolized as NaOH. 

Many atomic structures attain satisfaction by 
combining into molecular form with others of their 
own type. Thus hydrogen normally exists in a 
diatomic naolecular state represented as Hg. The 
same is true of oxygen which forms a molecular )^s- 
tem of Og. In such cases we find a combination of 
two atomic systems with similar rather than comple- 
mentary needs. The rearrangement of the electrons 
about the two nuclei, apparently, reisults in a more 

I \ 


stable oonfiguration than exists in the individual 
atomic structures although sometimes not as stable 
as it might be. A spark will expbde a mixture of 
hydrogen and oxygen and result in two molecules of 
water beingiormed from one molecule of oxygen and 
two molecules of hydrogen. The operation is con- 
veniently symbolized as O2 + 2H2 -> 2H2O. 

The atoinic system of oxygen is the great joiner 
and has fraternal relations with all except the most 
deadly dull and inert atoms.^ It belongs to thou- 
sands of complex molecular societies. Associated 
with hydrogen it enters as water of crystallization 
into secret organizations of molecules of which it is 
not a bona fide member but from which it may be 
expelled only by heated action. Even then all the 
water molecules do not leave with equal readiness 
for some resist expulsion with considerable tenacity. 

It was largely by a study of combinations of oxygen 
with nitrogen that Dalton arrived at his well known 
laws as to molecular composition. The substance of 
these laws has been tacitly assumed in our earlier 
discussion. The unit in chemical combinations is 
ihe atomic system; and molecular systems are 
formed only from whole numbers of atomic systems. 

'And fluorine. 



An atomic system is formed by a nucleus and a 
number of electrons external to it. In the configura- 
tion of these external electrons is to be found the 
secret of the ability of one atomic ^stem to combine 
with one or more other systems to form a molecular 
system. The valence, which measures this ability 
to combine, may be jx>sitive or negative depending 
upon whether the system imder consideration is un- 
satisfied as the result of too many or of too few 
electrons for a stable configuration of the external 

In the nucleus there is always an excess of protons 
and the number by which this excess is specified is 
known as the atomic number. The largest known 
atomic number is 92. On the basis of atomic num- 
bers, therefore, a classification may be established of 
92 types of atomic ^stems. These types may then 
be cross-classified on the basis of valence. 

As we proceed from one type of atomic system 
to that with the next atomic numbei: there is a 
change of one in the number of excess protons in 
the nucleus and a corresponding change otone in the 
number of external electrons. For example, let us 
enter our system of classification by atomic numbers 



at the eleventh type, which is that of the sodium 
atom. We must picture this atomic system with 
eleven excess protons in the nucleus and eleven ex- 
ternal electrons, the actual configuration of which 
is still problematical. Despite the fact that there 
is a quantitative balance between the protons and 
the electrons, of complementary properties, there is 
a lack of satisfaction in the portion of the system 
comprised by the external electrons. 

In the system of next smaller number there are 
ten external electrons; and with the reduction in 
niunber the unsatisfaction has disappeared, for the 
tenth typical system is that of neon, an inert atom. 
The equivalence of number of protons and electrons 
still remains for both kinds of electrical elements 
have undergone the same reduction in number. The 
external electrons, however, no longer crowd each 

What would one naturally expect as the atomic 
number is further reduced? Eleven electrons crowd, 
ten do not, but nine are too few for satisfaction of 
the requirement of stability. The atomic system 
of the nmth type, known as fluorine, despite its 
quantitative satisfaction, is unsatisfied in configura- 
tion by one electron. Like the sodium system it 
also has a valence of imity but negative instead of 

The satisfied atomic system is thus seen to occur 
as a transition between systems of negative and posi- 
tive valence. Such transitions occur at the atomic 
systems of helium, neon, argon, krypton, xenon, and 
niton for which the atomic numbers are respectively, 


2, 10, 18, 36, 54 and 86. For convenience tiie names 
of the various types of systems corresponding to the 
atomic numbers below 22 are given in the accom- 
panying table. 

Tabie I 

The Names and Numbers of the Atomic Systems 

1 Hydrogen H 12 Magnesium Mg 

2 Helium* He . 13 Aluminum Al 

3 Lithium Li ^ ., - 14 Silicon' Si 

4 Beryllium Be '15 Phosphorus P 

5 Boron B 16 Sulphur S 

6 Carbon C - 17 Chlorine CI 

7 Nitrogen N 18 Argon* A 

8 Oxygen O 19 Potassium K 

9 Fluorine Fl 20 Calcium Ca 

10 Neon* Ne 21 Scandium Sc 

11 Sodium Na 22 Titanium Ti 

* Transition efystem 

The atomic system for which the atomic number 
is one less than that of a transition sjrstem has a 
n^ative valence of one, and the system of the next 
greater numb^ hsa a positive valence of one as in 
the case just mentioned of tiie sequence fluorine, 
neon, and sodium. Progressing toward higher num- 
bers the positive valence increases, and toward lower 
atomic numbers the negative valence. In progress- 
ing from one satisfied system to the next as, for 
example, from neon to argon, there must therefore 
be another kind of transition from negative valence 
to positive. Between these satisfied stystems there 
are ihree types with positive valence of one, two 
and three, respectively, namely, sodium, magnesium, 
and aluminium, and three types, namely, chlorine, 
sulphur and phosphorus, witii the corresponding 
values of negative valence. 


The middle sysbsm of the sequence^ whidi we are 
considering, is like a hostess who is planning a din- 
ner. Shall she invite four more guests or four less? 
The decision wiU depend upon circumstances, that is 
upon who the guests are to be, but the number she 
will add or scratdi from her list is preferably foxu*, 
since that will make a satisfactory grouping. Some- 
times she makes one choice and again the opposite 
choice and the same is true of the atomic systsm 
of silicon. Its valence is four but it is amphoteric 
for it partakes of the character of both electroposi- 
tive and electron^ative elements. 

The simile of the hostess, however, is madequate, 
because the electrons are disposed about the nucleus 
in a space of three dimensions. The pictures of their 
disposition, which have been proposed from time to 
time, are all incomplete and none has been gen- 
erally accepted by scientists. The successful picture 
must account for the known facts of chemistry and 
also for those facts of physics which relate to the 
radiation of light from atomic structm^. The maju- 
mum niunber of electrons which may be concerned in 
atomic phenomena is, of course, definitely known 
since the atomic numbers are well substantiated 
facts. The grouping of these electrons, however, is 
still in the stage of hjrpothesis and the picture which 
will now be given is merely tiiat which today most 
satisfactorily accounts for the largest number of the 
known phenomena. 

We imagine ^ that the electrons are disposed about 
the nucleus as if they lay in the shells of one of those 

^According to Lewis and Langmuir. 


Chinese toys which consists of a concentric series of 
wooden egg-shaped shells. Let the inna:inost egg 
represent the nucleus. In the next or first shell th«^ 
may be one or two electrons, one in the case of hydro- 
gen and two in that of helium. The latter condition 
would obviously admit of a stable structure in which 
electrons on diametrically opposite sides of ihe 
nucleus were held in the ^stem, because they trac- 
tate with this nucleus, despite the fact that they 
peUate with each other. Because of this electrical 
stability, the atomic system of helium is inert 

Except for the hydrogen system all atomic struc- 
tures have these two electrons. The uns3nimietrical 
configuration of the hydrogen system accoimts for its 
extreme activity as a chemical element, and also for 
its formation of diatomic molecules of hydrogen gas. 

When an atomic system contains more than two 
external electrons, all electrons in excess of two are 
disposed on shells external to that which was just 
described. The next outer shell is believed to be 
twice as far from the nucleus, and hence to have four 
times the superficial area. In it a total of eight 
electrons may be located. 

The atomic system which has one electron in this 
second shell is that of lithium. This atom readily 
parts with its third electron and assumes the more 
stable configuration of the helium atom. That is 
what takes place when the molecular system of 
lithium chloride, LiCl, dissociates into a lithium ion 
and a chlorine ion. Geometrically a lithium ion is 
similar to the stable helium atom, but it does not 
act at all similarly because the nucleus of lithium 


haa three excess protons instead of the two of helium. 

With two electrons in the second shell the atomic 
system is that of beryllium which has a positive 
valence of two since it takes the loss of two electrons 
to convert it into the stable configuration of the 
helium system. Boron is a system with three elec- 
trons in this shell. When the number is four, there 
is reached the important system of carbon which 
enters into all organic compounds. Its four external 
electrons in pellating with each other probably take 
places such as to form the comers of a solid figure 
of four equal sides. Nitrogen has five, oxygen six, 
fluorine seven, and neon eight electrons in this 
second layer. In the last case the electrons will dis- 
tribute themselves four on each hemisphere, so that 
they form the comers of a cube at the center of 
which is the inner shell with its two electrons and 
within this the nucleus. The inertness of the neon 
atom is well accounted for by this symmetrical and 
stable arrangement of external electrons. 

The system of fluorine with its seven electrons in 
the second shell may be considered either as having 
seven too many for such stability as is possessed by 
the helium system, or one too few for the stability 
of the neon system. In other words, it has either a 
positive valence of seven or a negative valence of 
one. Oxygen has six and two respectively. The re- 
arrangement which is required to make these sys- 
tems stable, that is satisfied in configuration, is less 
if electrons are added than if they are subtracted, so 
that such systems tend in combination to attain 
their satisfaction by borrowing from the other com- 


ponents of the molecular systems in whidi they are 

In the dissociation of sudi molecular systems the 
atom tends to retain its satisfaction by a failure to 
return the borrowed electron which amounts to aa 
actual theft. Dissociation, therefore, results in the 
formation of n^ative ions, that is those with a quan- 
titative excess of electrons. 

In a large numba* of cases of molecular systems 
the electrons are shared so that borrowing and theft 
do not occur. It seems probable, however, that in- 
dividual electrons may not be shared but only pairs 
of electrons.^ It is further believed that in the shar- 
ing of pairs of electrons the adjacent atomic groups 
so combine as to form as nearly as possible stable 
arrangements roughly similar to that of the neon 
atom, that is groups of dectrons at the ei^t comers 
of a cube, at the center of which is a kernel com- 
posed of two electrons and a nucleus. ' This hypo- 
thetical process is peculiarly adapted to explain, for 
example, the large number of compounds which are 
formed by oxygen with nitrogen. 

As, the number of external electrons is increased 
beyond ten a new outer shell is required. Let us 
picture this third shell as practically coincident with 
the second. The first electron to be disposed in it 
occupies a position with much the same precarious- 

^ Chlorine, which forms a diatomic molecule, Clt, \s a good 
illystration of the sharing of electrons between the atoms of 
molecular systems. Ekich chlorine atom lacks one electron of 
the number required for satisfaction in configuration. Hence, 
each atom shares one of its electrons with the other atom of its 
.molecule. The requirements of configuration are thus satined, 
and in effect a pair of electrons is shared. 



Bess as did ihe first electron of the second shell, and 
hence, sodium, the eleventh system, has much the 
same properties as lithium, the third. 

For similar reasons there is a periodic recurrence 
of the properties of beryUium when we reach the 
twelfth system, that is magnesium, and correspond- 
ing recurrences until we reach argon, where the shell 
has its complement of eight electrons. Again we 
have a stable structiwe. 

A new sheU, a fourth, is required for electrons in 
excess of eighteen. This may not be superimposed, 
as was the third shell upon the second, for these 
inner shells now hold too many electrons to permit 
so near a position for additional electrons. The 
fourth shell is presumably three times as far from 
the nucleus as is the first and hence its area is nine 
times as great and its capacity for electrons eighteen 
instead of two. 

The first three of the atomic systems which are 
formed by the addition of electrons in this new shell 
also partake of the properties of the corresponding 
three in the two series previously considered. The 
area of the fourth shell is larger, however, and it is 
not filled until eighteen electrons are in it. The 
atomic system which exists when this fourth diell 
has four electrons has no such amphoteric properties 
as have silicon and carbon. It has no choice in its 
method of obtaining stability since to progress to 
stability would require the addition of fourteen elec- 
trons, while to regress would require only the loss 
of four. Similarly the next atomic system, with five 
electrons in this shell, can have only a positive 


valence. To assume the nearest stable structure, 
that of argon, would require tiie subtraction of aJl 
five electrons. 

Here we are met by a choice of kinds of satisfac- 
tions. A satisfaction of configuration requires the 
loss of five electrons. As each electron is lost the 
unsatisfaction as to the discrepancy between num- 
bers of protons and of electrons becomes more 
marked. As long as a net balance of satisfaction is 
attained by losing electrons there will be a tendency 
to do so. This balance of desires is generally met 
before all five are lost, for two and three are the usual 
valences of the vanadium system which we are con- 

Table II 

The Names and Numbers of the Atomic Systems 

18 Argon* A 37 Rubidium Rb 

19 Potassium K 38 Strontium Sr 

20 Calcium Ca 39 Yttrium Y 

21 Scandium Sc 40 Zirconium Zr 

22 Titanium Ti 41 Niobium Nb 

23 Vanadium V 42 Molybdenum Mo 

24 Chronium Cr 43 

25 Manganese Mn 44 Ruthenium Ru 

26 Iron Fe 45 Rhodium Rh 

27 Cobalt Co 46 Palladium Pd 

28 Nickel Ni 47 Silver Ag 

29 Copper Cu 48 Cadmium Cd 

30 Zinc Zn 49 Indium In 

31 Gallium Ga 50 Tin Sn 

32 Germanium Ge 51 Antimony Sb 

33 Arsenic As 52 Tellurium Te 

34 Selenium Se 53 Iodine I 

35 Bromine Br 54 Xenon* X 

36 Krypton * Kr 

♦Transition system 

The names of the atomic systems with numbers 
between 18 and 54 are given in Table II. From this 


it will be seen that the ^sterns corresponding to 
those with 8, 9, and 10 electrons in the fourth shell, 
namely, those of atomic numbers from 26 to 28, are 
those of iron, cobalt, and nickel, the three elements 
commonly known as mag^etic. They constitute a 
family of elements with much in common besides 
their magnetic property. Although they have about 
half as many electrons in their outer shells as is 
required for stability they have a sufficient number 
to form fairly symmetrical systems. Thus iron with 
eight electrons might have them disposed at the 
COTners of a cube like that of the outer shell in neon 
or argon. Nickel also may attain considerable 
stability with its ten electrons. Their valences, how- 
ever, would not be zero for the sheUs are incom- 
pletely filled. 

These substances are not inert and yet they 
possess certain structural advantages over their 
neighboring systems sufficient to foma an oppor- 
tunistic goal, toward which tiiese other systems may 
struggle in their quest of satisfaction in form. For 
this reason some of the systems on both sides of 
this group partake somewhat of their qualities. For 
this reason also, starting with the copper system, 
which is next higher than nickel, the valences again 
form an ascending series, being one (or two in some 
cases) for copper, two for zinc, tiiree for galUum, and 
four for the amphoteric germanium. 

Beyond germanium, where the sheU lacks only 
four electrons of its complement, satisfaction is most 
easily obtained by adding electrons and attaining to 
the form of the inert, stable system of krypton (36). 



The elementa from arsenic (33) to bromine (35) 
corresponds therefore, to those immediately below 
the other inert elements of neon and ai^on. Thus 
bromine belongs to the same family and reacts in 
the same general way to its electronic surromidings 
as do chlorine (17) and fluorine (9). 

In a similar manner the elements rubidium (37), 
strontium (38) and yttrium (39), which have atomic 
numbers immediately above that of krypton, tend 
to revert in configuration to that structure and thus 
to lose electrons just as do the corresponding ^jrstems 
of the preceding series, namely, potassium (19), 
calcium (20), and scandium (21). 

Between the atomic numbers of 40 and 50 the gen- 
eral characteristics of ihe atomic ^stems correspond 
to those of the previous series for which the numbers 
are 22 to 32. Again we find the structures of higher 
number tending to reach satisfaction in configuration 
by assiuning that of the next highest stable system. 
Thus iodine, the fifty-third system, would attain 
satisfaction in gaining an electron and becoming in 
form like xenon, the fifty-fourth, in the same man»- 
ner as chlorine, the seventeenth, would assume the 
form if not the substance of argon, the eighteenth 

Beyond xenon the names of the atomic systems 
are given in Table III. A new shell is now required 
and we imagine one with four times the diameter of 
the first, sixteen times its area, and a capacity for 
thirty-two electrons. The first six elements in this 
new series correspond to ihe first six in ihe two im- 
mediately previous series. The seventh, of atomic 


number 61, is as yet undiscovered. Of the last seven, 
the one with an atomic number of 85 is also undis- 
covered. Otherwise the higher elements of this series 
are like those immediately below the transition sys- 
tems of xenon and krypton. 

Table III 

The Names and Numbers of the Atomic System 

54 Xenon* X 74 Tungsten W 

55 Csesium Cs 75 

66 Barium Ba 76 Osmiuria Os 

57 Lanthanum La 77 Iridium Ir 

58 Cerium Ce 78 Platinum Pt 

59 Praseod5anium Pr 79 Gold Au 

' 61 — 81 Thallium Tl 

60 Neodymium Nd 80 Mercury Hg 

62 Samarium Sa 82 Lead Pb 

63 Europium Eu 83 Bismuth Bi 

64 Gadolinium Ga 84 Polonium Po 

65 Terbium Tb 86 

66 Dysprosium Ds 86 Niton* Nt 

67 Holmium Ho 87 

68 Erbium Er 88 Radium Ra 

69 Thulium Tu 89 Actinium Ac 

70 Ytterbium Yb 90 Thorium Th 

71 Lutecium Lu 91 Uranium Xii Ur Xii 

72 .. 92 Uranium Ur 

73 Tantalum Ta 

 Transition systems. 

Of the thirty-one atomic systems between xenon 
(54) and niton (86), the first seven (55-61) corre- 
spond to systems (37-43) and (19-25). The last 
seven (79-85) correspond in chemical properties to 
systems (47-53) and (29-35). Both the lower series, 
(19-35) and (37-53), have intermediate transition 
gfystems of whidi the iron-cobalt-nickel group (26- 
28) is the more noteworthy. These intermediate 
transition systems are believed to be somewhat 
analogous to the transition systems formed by the 


inert gases in that they have fairly stable electronic 
configurations, but they differ by being chemically 
active because they are not completely satisfied as 
to configuration. 

In the series which we are now considering there 
are two such intermediate transition groups, namely, 
(62-64) and (76-78). Of these the latt^, represent- 
ing osmium, iridium, platinum, is the more impor- 
tant. The other group contains three rare earths, 
namely, samarium (62), europium (63), and gadoli- 
nium (64). 

Between these two intermediate groups of transi- 
tion systems there are nine known and two unknown 
systems, (72 and 76). With the exception of tan- 
talum (73) and tungsten (74) these are all rare 
earths — ^metallic elements with positive valences of 
three. The pictiu'es of electronic configuration which 
have been proposed to account for the elements be- 
tween (62) and (77) are not as yet generally ac- 
cepted and need not be discussed. It is pM'haps 
sufficient to record the fact that chemical properties 
do not vary sharply with increase in number of 
planetary electrons when the shell has more than 
eight electrons, but is not within eight of its comple- 

Beyond the last inert system, that of niton, there 
are only a few known ^stems, and the series termi- 
nates with uranium from which by radioactive proc- 
esses many of the lower systems were imdoubtedly 
derived. These few remaining systems require elec- 
trons in a seventh shell, which we imagine to be 


Ehcfro Nwgaf/tng 

PiQ. 1 

Atomic systems at the periodic table. Place numbers corre- 
spond to atomic numbers. Systems similarly situated, as indi- 
cated by radial lines, have similar chemical properties. 



superposed upon the sixth and to have the same 

We may now make a schematic picture of the 
series of atomic structures as if there were a group 
of tables to be filled by guests.' These tables are 
roughly concentric as shown in Fig. 1. One by one 
the atomic systems are seated and the order of their 
seating is given by ihe atomic numbers attached to 
their places. The first table seats only two. The 
next table eight on each side. The third table, seat- 
ing eighteen on each side, must place some atomic 
systems in positions which do not correspond with 
any of those at the second tabla There is, however, 
a correspondence between atomic systems which are 
opposite one another at the same table. The fourth 
table differs in some ways from any of the inner ones 
and on one side it is only partially filled. 

In this representation atomic systems which have 
corresponding characteristics will be found to lie on 
the same radial line. That corresponding to the 
stable systems is marked zero. The others are 
marked with Roman numerals for the convenience 
of those who wish to compare with the usual tabular 
presentation of' the periodic series of the chemical 
elements. Intermediate transition systems are indi- 
cated by VIII. To a very large extent the elements 
correspond in positive valence to the Roman nume- 
rals, thus the elements of group I all have positive 
valences of one although copper may also have two 
and gold may have three as values of valence. For 
groups beyond IV, the exceptions become more 
frequent as is evident from Table IV, where the 



s ;? 





s ^■ 


B «- 




























» 5 























■a , 





« -t 





















« « 




















periodic series is tabulated. This table gives for 
each element, except for some of the rare earths, the 
atomic number, the diemical sjnnbol and the various 
observed valences. 



The physical matter of which we are composed 
and with which we deal whether as scientists or not 
is composed of discrete molecules which are but 
unions of smaller particles, the atomic systems. Of 
the latter, we have distinguished ninety-two tjrpes 
which differ in the nmnber of excess protons in their 
nuclei and consequently also in Hie number and con- 
figuration of the planetary electrons about their 
nuclei. Because these external electrons are all iden- 
tical, the various atomic systems form a progressive 
sales of geometrical patterns in which certain 
typical relations periodically reciu*. The series, 
therefore, contains groups or families of atomic 
types, which possess similar or common charac- 

Although the actual configurations are not known, 
the hypothetical scheme of disposition for the planet- 
ary electrons, which was. presented in the last chap- 
ter, accounts for a sufficiently large number of tiie 
known relationships of atoms to warrant its tentative 
acceptance. About the nucleus the electrons are 
grouped as if they occupied cells in shells of diam- 
eters which are related as 1:2:2:3:3:4:4 and of 
capacities for electrons, 2, 8, 8, 18, 18, 32 and 32 re- 



spectively. No electrons exist in outer shells unless 
those within are completely filled. Those systems 
whidb have no partially fiUed shdls are satisfied inert 
structures to whose configuration ihe unsatisfied S3rs- 
tems tend to revert or to progress. In this tendency- 
is the proximate cause of the chemical actions of 
various kinds of atoms. 

The basis whidi has been chosen for the classifica- 
tion of atomic gfystems is relative in that it depends 
upon the excess of protons in the nucleus over the 
electrons and not at all upon the total number of 
either kind of electrical element. It is therefore 
possible that two or more atomic systems may exist 
which classify as of the same tjrpe, that is are iso- 
topic at the Periodic Table, but differ in the total 
number of protons in their nuclei. In all chemical 
combinations or reactions these isotopes are indistin- 
guishable. They may be distinguished, however, as 
the result of an important physical property of elec- 
trical elements which is most pronounced in the 
case of protons. 

This property is that of inertia, the inherent un- 
willingness to change in state of motion which is 
common not only to the infinitesimal elements but 
to such larger aggregations as compose ponderable 
objects, whether human or otherwise. It is this 
quality which makes the flying missile so destructive 
and the stone wall or conservative so annojring. The 
first delivers a blow and the second resists our force 
and impedes our progress. 

Because of the phenomenon of gravitation we have 
become accustomed to measure inertia by weight 


and a popular misconception has arisen in which 
weight, mass and inertia are inextricably confused. 
The diflBculty is largely due to our instinctive ap- 
proach to scientific questions through our immediate 
but frequently misleading sensations. 

When we cause a body to alter its state of motion, 
either by changing its speed or its direction, we are 
conscious of exerting what we are pleased to call a 
force. When we observe the gravitational tractation 
of body and earth we speak of a force of gravitation 
as acting on the body. Bodies upon which ihe earth 
under similar conditions exerts equal forces we call 
equal in weight. Unfortimately weight is but a par- 
ticular kind of force and force itself is an entirely 
subjective concept without any objective reality. 
Whatever may be the character of the alteration in 
the relative motions of the bodies of a system the 
alteration is but the manifestation of a change in 
the disposition and availability of that uncompre- 
hended motive power of our universe which we call 

Energy and the electrical elements are the postu- 
lates of the new science, the entities in terms of 
which all explanations of scientific phenomena must 
be made. 

To our senses, whether aided by apparatus or not, 
this motive power, or energy, is evidenced only by 
changes in the state of motion of the electrical ele- 
ments. To every moving particle, whether electron, 
proton, atom, molecule, or more evident mass, we 
ascribe a portion of this imknown. The amount 
whidb we assign to any particle depends upon the 


speed with whidi it is moving and upcm its electrical 

As the unit by which to measure enei^ we may- 
take that energy which is associated with an electron 
under some definite and arbitrarily chosen condition 
of motion. For example, we might choose the speed 
of one centimeter a second as that at whidi an 
electron would be traveling when it had what we 
wish to call a unit amount of energy. Two electrons 
moving with this speed, obviously, represent two 
units of energy. 

When two bodies differ in kinetic energy^ even 
though their speeds are alike we say that they differ 
in inertia or in mass. In quantitative significance 
the two terms are interchangeable although the first 
represents the unwillingness of a body to change its 
state of motion and the second the quantity of mat- 
ter in tiie body. On the basis, for example, of experi- 
mental observations of the relation for the energies 
of any body and di an electron we may ascribe to 
the body a mass which is some definite number of 
times that of an electron. 

If we are to express quantitative relationships we 
shall need units. Three fundamental units are all 
thai are required and these have already been 
chosen. They are tiie units of distance, time, and 
energy. Our jmit magnitudes are then the centi- 
meter, the second, and the kinetic energy of an elec- 
tron which is moving one centimeter per second. 

The habit of reducing all quantitative expressions 

^That is, energy associated with a body as consequence of its 


to tenns of a very limited number of imits is not re- 
stricted to scientific procedure but holds in many 
other human activities. To a large extent we 
measure our desires and their gratification in terms 
of the distance we would go, the time we would 
consume, and the money we would expend. 

There is a wide range of choice in the selection of 
magnitudes upon which to base three fundamental 
units, but for present purposes the three previously 
mentioned are to be preferred. In terms of these 
we may define unit mass. First, however, we recog- 
nize that a speed of one centimeter per second is a 
speed of unit distance in unit time, that is a speed 
of unity. Double the distance in the same time or 
the same distance in half the time represents a speed 
of two units. In terms of imits of speed we now 
see that our chosen unit of energy is that associated 
with an electron which is moving with unit speed. 
The next step is to define imit mass as that of a body 
which has imitv energy when its speed is unity. 

It is to be noted against future reference that this 
definition carries no implication as to the constancy 
of mass and contains no indications as to the rela- 
tionship of mass, speed, and energy.^ The considera- 
tion of these matters may be omitted since our im- 
mediate discussion requires only the recognition of 
mass as a factor for expressing the relation of the 
energies of two bodies whose speeds are identical. 

We assume that energies are determinable and 
that speed is not only measurable but controllable 
so that we may determine the mass of a body by 

* For such a relation c/. p. 206 in the Appendix. 


finding its energy at unit speed. WKen so deter- 
mined the mass of an alpha particle is 7380 times 
that of the electron. The alpha partide, however, 
is merely the nucleus of the atomic ^stem known 
as helium. Wben associated with two planetary elec- 
trons it becomes an atom of helium. The mass of 
the atomic system of helium, therefore, is due almost 
entirely to this nucleus, 

Alpha particles are known to be constituents of 
liie nuclei of all radioactive atomic systems and are 
assumed to be present in all other systenoB except 
hydrogen. It seems highly probable, therefore, that 
within the nucleus of any atomic structmre the pro- 
tons are associated in groups of fgur, bound together 
with two electrons in the same manner as in the 
alpha particle. Whenever the number of protons 
in the nucleus is divisible by four we may, therefore, 
expect, although we do not yet know, that the 
nucleus is formed by an integral number of alpha 

Consider, for example, such a nucleus as would be 
formed by four alpha particles. Each constituent 
contributes four protons and two electrons so that 
the nucleus contains a total of sixteen protons and 
ei^t electrons. Its atomic number would then be 
eight, that is, its construction would correspond in 
valence and in other chemical properties to the atom 
of oxygen. Its mass would be due to four alpha 
particles and would be four tunes that of the helium 
atom, and this, in fact, is the experimentally deter- 
mined ratio for the masses of the oxygen and helium 
atoms. ' 


A nuclear composition of only alpha particles is 
not possible, however, where twice the atomic nmn- 
ber is not evenly divisible by four. In such cases we 
must afisume the nucleus to contain ^ in addition to 
alpha particles one or more protons. In the case 
of nitrogen, for example, it has been determined re- 
cently that protons are part of the nucleus for they 
may be knocked out from the nuclei of nitrogen 
atoms by impacts from other atomic systems which 
are moving with enormous speeds. 

In determining the mass of an atom we mtty 
neglect the electrons and assume that each proton 
contributes to the nucleus one-quarter of the mass 
of an alpha particle. For any nucleus, then, we may 
calculate the mass as some improper fraction of the 
mass of an alpha particle. For example, if an atomic 
system has twenty- two protons in its nucleus it has 
a mass of 22/4ths of an alpha particle. We may 
compare the mass also to that of an atom of oxygen. 
Since the latter is four times as heavy as the helium 
atom, the mass of the gystem which we are consid- 
ering is 22/16ths Uiat of an oxygen atom. In addi- 
tion to the system with twenty-two protons let us 
assume another whidi has twenty protons. Its mass 
will be 20/16ths that of an oxygen atom. Instead 
of working with fractions we shall let 16 stand for 
the mass of an atom of oxygen and then in terms 
of the new unit thus arbitrarily adopted we may ex- 
press the masses of the hypothetical systems as 22 
and 20 respectively. 

So far we have been concwned only with their 

*C/. footnote of p. 114, and also p. 111. 



ma£M3eB. Now let us aasume that they are of the 
same type^ eadi with an atomic niunba* of ten. The 
configuration of the ten planetary electrons will then 
be the same in both structures: the valence will be 
the same; the chemical properties will be the same; 
and the only difference will be in mass. The 
isotopes, which we are imagining, cannot be sepa- 
rated by chemical methods for they have identical 
behaviours in all reactions. 

Let us further suppose that this chemical identity 
has resulted during the ages past m such a mixing of 
these isotopes that wherever one obtains a sample.of 
this chemical element the sample will contain them 
in the same proportion. Suppose, for example, that 
there are nine atoms of the isotope with mass 20 for 
every one of that with mass 22. Any determination 
of the atomic mass will give the average mass, that is 
20.2, since on the average the total mass of ten atoms 
would be 9X20+1X22 or 202. 

We now turn to Table V in which are given for 
some of the chemical elements their so-called atomic 
weights, on the basis of 16 for the oxygen atom. 
For neon, which we know to have an atomic nimiber 
of ten, the atomic weight is 20.2. The gas which the 
chemists used to know as neon is not a homogeneous 
gas, composed of identical atoms, but is a mixture of 
two gases, the atoms of which are alike in atomic 
number but unlike in mass. 

These two isotopes, of atomic weights 20 and 22, 
have recently been isolated by physical rath«* than 
chemical methods. The methods used are made 
possible by the fact that systems which diff^ in mass 


will have different energy contents at the same speed. 
As we shall see later, however, the actual experi- 
mental determinations are based on the converse 
statement of this relationship ; if two particles of dif- 
ferent masses are given equal energies they will differ 
in speed, the smaller mass attainmg the greater 
The table of atomic weights, to which reference 

Table V 
Atomic Weiohtb of Somb Common Chemical Elements 

Hydrogen 1.008 

Helium 4.00 

Lithium 6.94 

Beryllium 9.1 

Boron 11.0 

Carbon 12.0 

Nitrogen 14.01 

Oxygen 16.0 

Fluorine 19.0 

Neon 20.2 

Sodium 23.00 

Magnesium 24.32 

Aluminum 27.1 

Saicon 28.3 

PhoBphonu3 31.05 

Sulphur 32.06 

Chlorine 35.45 

Argon 39.9 

Potassium 39.10 

Calcium 40.1 

Manganese 54.93 

Iron 56.84 

Nickel 58.68 

Cobalt 58.97 

Copper 63.57 

Zinc 65.37 

Arsenic 74.96 

Selenium 79.2 

Bromine 79.92 

Krypton 82.92 

Rubidium 85.45 

Palladium 106.5 

Silver 107.88 

Cadmium 112.4 

Tin 118.7 

Antimony 120.2 

Iodine 126.92 

Xenon 130.2 

Caesium 132.81 

Bariimi 137.4 

Tungsten 184. 

Osmium 190.9 

Iridium 1931 

Platinum 195.2 

Gold 1975. 

Mercury 200.6 

Lead 207.2 

Bismuth 208.0 

Note: The following elements have isotopes of the following 
atomic masses: 

Lithium, 6, 7 
Boron, 10, 11 
Neon 20, 22 
Magnesium 24, 25 
Silicon 28, 29 
Chlorine 35, 37 
Potassium 39, 41 

Bromine 79, 81 
Rubidium 85, 87 
Krypton 84, 86, 82, 83, 80, 78 
Xenon 128, 130, 131, 133, 135 
Mercury (197-200), 202, 204 
Lead, Bismuth— -/S^ Fig. 2. 


has beea made, gives the observed relation between 
the masses of the atoms of various chemical elements 
as determined by the weights of equal numbers of 
atoms. To facilitate the ei^ression of the relations 
or ratios of atomic mass the ratios are all referred to 
oxygen and a common denominator of 16 is used in 
their expression. The various numerators of the 
ratios then become the atomic wei^ts of the various 
el^nents in terms of oxygen as 16. The choice of 
this number was a more or less conscious anticipation 
of the facts of today. The unit of weight whidi is 
used in the expression of atomic weights is the weight 
of one-sixteenth of the oxygen atom. Today we 
know that this xmit is the wei^t, or more strictly 
the masS; of a proton which is associated with other 
protons and electrons in the nuclear structure of an 
atom. To a close approximation this unit of the 
table of atomic weights is one-quarter the mass of 
an alpha particle and hence is 1845 times the unit 
of mass which was chosen earli^ in this chapter. 

For reasons which are not yet evident the mass of 
an isolated proton is not exactly one-sixteenth of the 
mass of an oxygen atom. Relative atomic weights 
are capable of sufficiently exact determination so 
that the values in the table are not to be doubted. 
From that table the masses of the atoms of hydrogen^ 
helium and oxygen are respectively l.l!|p08, 4.00, and 

Why hydrogen is not unity is not known, although 
plausible explanations may be given in terms of 
electro-magnetic theory. When, however, we con- 
sider that mass is merely a factor in the expre^on 


of the relationship between energy and speed, it be- 
comes conceivable that the energy relations should 
be slightly different, depending upon whether or not 
the proton is nearly or entirely isolated or is inti- 
mately associated with otiier protons as in the nuclei 
of the atoms of large mass and large atomic number. 

Whenever the atomic weight of a chemical ele- 
ment is a whole number within the limits of the ex- 
perimental errors involved in its determination, as, 
for example, in the cases of lithium, nitrogen, so- 
dium, and sulphur, we have reasons to expect that 
the substances are actually chemical elements and 
not mixtures of atomic systems with equal atomic 
numbers but unequal nuclear masses. In all other 
cases isotopes are suspected and recent experiments 
have shown flie existence of the proper isotopes to 
explain the failures of some atomic weights to be 
whole numbers. The isotopes so far discovered are 
given in the note to Table V. 

One of the most interesting illustrations of the ex- 
, istence of isotopes is found in the case of lead, where 
a large number are known to exist. Except for bis- 
muth all the elements above lead in atomic number 
are radioactive ; and lead seems to be an end-product 
of several different series of radioactive disintegra- 
tions which we shall consider in the next chapter. 



Atomic systems which are chemically identical 
and non-separable occupy the ssune place in the 
periodic table which was described in Chapter III. 
The basis of selection for position is the atomic 
number. Systems with the same atomic numb^ 
may, however, differ in atomic mass, in previous 
history, and in inner tiendencies toward radioactive 
displays. When the atoms of such isotopic systems 
are different in mass they may be separated by 
physical means, but those of isotopic systems which 
differ in inner tendencies cannot be separated. 
When, howeva*, their divergent tendencies actually 
result in different radioactive transformations we 
may reason that isotopes do exist. 

Radioactive substances have been described as 
atomic systems which are dissatisfied in their nuclear 
structures. In an individual atom such dissatisfac- 
tion leads to a nuclear debacle, after which the atom 
is generally declassed. Ultimately all the individual 
atoms of a radioactive substance will undergo the 
same transformation. By some iAner economy, 
however, they so arrange that at any instant a defi- 
nite proportion of their number shall be engaged in 
the characteristic activities of the group, that is 




either hurliag alpha particles or shooting forth at 
high speeds the lighter beta particles. 

When an atom changes in its nuclear construction 
^ it must be reclassified and assigned to another place 
in the periodic table. By radioactive changes the 
atom jumps from one place in the table to another. 
The new atomic ^stem, which embraces the atoms 
whiah have jxmiped, differs in previous history and 
inner fendencies from the system which already oc- 
cupies the new place in the periodic table. With 
this older occupant it becomes isotopic but inot 

* The changes in position in the periodic table which 
accompany radioactivity are due to changes in the 
nuclear structure of the various atomic systems. 
The nucleus may lose an alpha particle or a beta par- 
ticle. A loss of an alpha particle reduces the number ^ 
of protons in the nucleus by four and the number of 
electrons by two. The excess of protons over elec- 
trons, which we express by the atomic number, is 
therefore reduced by two. Whenever a nucleus 
loses an alpha particle the atom is declassed, not to 
the class immediately below but to that two below 
in the scale of atomic numbers. ^ 

When an atom of radiiun loses an alpha particle 
it ceases to be radium, for its atomic number is re- 
duced from 88 to 86. This new substance is called 
niton, or "radium emanation." In a similar manner 
when an atom of niton loses an alpha particle it be- 
comes isotopic with all oUier systems of atomic 
number 84. 

Before discussing this series of changes it is de- 


sirable to consider for a mom^it what happ^is to the 
alpha particle which is ejected. It is the nucleus of 
a heliiun atom and needs two external electrons to 
become a satisfied, inert heliimi atom. In the first 
portion of its mad rush outward from a radioactive 
atom, an alpha particle seriously disturbs the otfa» 
atomic systems by which it passes, shaking and 
knocking loose some of their planetary electrons. 
Its effect is to ionize some of the atoms of the at- 
moi^here through which it passes, forming atomic 
systems which are imsatisfied in niunber of electrons, 
some having too few and others, which have ac- 
quired ihe loosened electrons of their neighbors, hav- 
ing too many. When the rush of the alpha particle 
has been stayed it, too^ becomes as the other atomic 
systems of the atmosphere and finds quantitative 
satisfaction by claiming two electrons from any 
system whidi has more than it needs for its own 

The subject of the ionizaticm of gases by alpha 
particles, and also by other methods, is one of con- 
siderable interest but it must be postponed. For 
the present it must be sufficient to say that in the at- 
mo^here of the earth there are always some atomic 
^stems which have either an excess or a deficiency 
of electrons. Whenever in the wanderings of these 
systems those of opposite kinds of imsatisfaction 
meet an electron is transferred. 

The fi^*c6 rush of the alpha particle, as it is ejected 
from the nucleus of the radioactive atom, is capable 
of dislocating the planetary electrons of the atom 
from which it proceeds just as well as those of other 



atoms which it meets later. Its departure from the 
nucleus leaves the nucleus a net escees of protons, 
two less than before, and the shells of planetary 
electrons would therefore hold an excess of two 
electrons if the alpha particle did not jar them loose 
into outer space. It is not content, however, with 
shaking loose enough planetary electrons to leave the 
remaining atomic structure neutral, that is satisfied 
in total number of protons and electrons. It appears 
to dislocate several dectrons and so to leave behind 
it an atomic structure reduced by two in atomic 
number and by more than two in number of planet- 
ary electrons. 

The effect is experimentally observable because of 
the phenomenon of recoil. When the alpha particle 
erupts, it kicks back the structure from which it pro- 
ceeds. Because of the larger mass of the system 
which is left the speed of its recoil is much less than 
that of the lighter alpha particle. It suffices, how- 
ever, to permit a segregation of the two products of a 
radioactive disturbance. 

The elecl3*ons, which the departing alpha particle 
drags from its own original atomic siuroundings, 
wander about as free electrons or are acquired by 
nei^bOTing atoms which thus become quantitatively 
unsatisfied. From them, or from other structures 
with excess electrons, the atomic system, which re- 
sults from the emergence of an alpha particle, may 
later acquire sufficient electrons to be quantitatively 
satisfied. The number which it thus adds will be 
such as to make the number of planetary elections 
equal to the new atomic nmnber. The disintegra- 


tion product^ therefcMre^ of an emisBion of alpha par- 
ticles is a substance with the atomic number and also 
the configuration of planetary electrons whidi cor- 
reqx>nd to a position in the periodic table in the 
second place below that occupied by the atomic 
sjrstem of the wiginal substance. The atomic mass 
of the disintegration product is, of course, four units 
less than that of the original atom, because each 
alpha particle removes four protons. 

An opposite type of diange occura when a beta 
particle is ejected from the nucleus of a radioactive 
atom. The atomic numbar is increased by one, since 
the excess of protons in the nucleus is .increased by 
the subtraction of an electron. In the planetary 
qrstem of the atom there is then an excess of one 
electron over the numba* necessary for quantitative 
satisfaction of the qrstenL The extra electron is 
loosely held and therefore it is shortly acquired by 
some atom whidi wanders into the nei^borhood. 
The net result is aa increase of one in the atomic 
number and a configuration of planetary electrons 
which corresponds to the new atomic number. The 
disintegration product of a radioactive change 
which is accompanied by the expulmon of an electron 
is therefore isotopic with the atomic sjrstem of 
number next hi^er than the original system. The 
expulsion of an electron, however, is unaccompanied 
by any appreciable change in mass, for we consider 
the mass of an atom to be due essentially to the pro- 
tons which enter into its nuclear construction. 

A glance at the diagrammatic representation of 
the periodic table which is given on page '3^ shows 


that the atom moves two places (clockwise) if there 
is expelled an alpha particle and one place (counter- 
clockwise) if a beta particle is expelled; Two suc- 
cessive expulsions of beta partides will therefore 
neutralize the effect of one expulsion of an alpha par- 
ticle so far Bs concerns position in the table. It wUl 
not neutralize the change in mass^ however, for the 
^TDeta ray^' change, as it is called, is without effect on 
atomic mass, while the "alpha ray" change produces 
a reduction of four units in atomic mass. 

It therefore happens that a radioactive substance 
may undergo such a succession of changes aa to pro- 
duce a substance isotopic with the original substance, 
chemically indistinguishable, but four units less in 
atomic weight. This is true, for example, in the case 
of uranium which ejects an alpha particle, forming 
Uranium Xj, as it is called. This substance ejects 
a beta particle, forming Uranium X jj, and the latter 
ejects another beta particle, forming Uranium II, 
so-called, which is isotopic with uranium. 

Altogether some thirty-eight radioactive sub- 
stances have been discovered. All these, however, 
find their places in the periodic table between urani- 
um, with an atomic number of 92, and lead, with a 
number of 82. All are products of the disintegra- 
tion of two elementary substances, uranium and 
thoriimi. Radium, the most famous, is a product 
in the disintegration series of uranium. In terms of 
these elements, uranium and thorium, modem 
science accounts for all the known radioactive 

The inner structure and history of the atoms of 


any radioactive substAnce are not the same for alL 
There are points in the aeries of uranium, for ex- 
ample, wha% two distinct disinte^ntiou products 
may be formed. The entire series with its sevea^ 
brandies is shown dia^mnmaticatly in Fig. 2. 
Changes produced by alpha rays are indicated by 
heavy arrows, and those of beta rays by lifter ar- 


\ 1 1 

*^^ MA 

Fia. 2 
Radioactive TraUBformations. Atomic aumbera are given by 
the vertical scale. Alpha my changes are indicated li^ heavy 
arroTB. These decrease atomic number by two, and atomic wei^t 
by four. Beta ray changes are indicated by light arrowa. These 
increase atomic number oy one, but do not aSect atomic weight. 

rows. All the substances in the same horizontal line 
have the same atomic number but may have diflfw- 
ent masses. 

fVom this diagram it appears that th»« is a rel- 
atively large number of isotopes of lead, for the end- 
products of the various Becies fall in the place at tiie 
pffliodic table which is occupied by lead with its 


atomic number of 82. Under ordinary conditions 
what we know as lead is a mixture of several of these 
isotopes and has an atomic mass which depends upon 
the atomic masses and proportions of its constitu- 
ents. ^ 

Several experimental studies have been made of 
lead derived from different mineral deposits to de- 
termine whether or not such differences in atomic 
weight actually existed and confonned to the prob- 
able radioactive antecedents. For example, an ex- 
amination of tiie lead derived from Ceylon thorite 
gave 207.69 as compared to 207.2 which is the ordi- 
nary value. This mineral contains 55 per cent of 
thorium, 1 to 2 per cent of uranium, and about 0.4 
per cent of lead, an amount so small as to be un- 
doubtedly of radioactive origin. The lead in this 
mineral should be largely due to thorium xmless the 
rate of disintegration of uranium is many times 
greater than that of thorium. Since it is only two or 
three times greater, the lead in this ore should be 
about ten parts of thorium origin for each part of 
uranium origin. Other similar experiments have 
been performed on samples of lead with different 
radioactive antecedents, and atomic weights have 
been obtained which range from 206.1 to 207.7. 

Such experiments are but a small part of the care- 
ful, ingenious, and thorough study ^ of radioactive 
substances which has been responsible for the 
modem theory of isotopes. This theory has been 
corroborated by the discovery of isotopes among the 

*To this study the chief contributions have been made by 
Soddy and Rutherford. To the former is due the concept of 


atomic systems of low^ atomic number. Some re- 
sults of such investigation were mentioned in the 
preceding chapter. The most potent method is that 
involving so-called "positive rays" but purely me- 
chanical methods sudx as diffusion have been used 
to produce a separation of isotopes. 

Within the last twenty years the whole basis for 
our conception of matter has changed. Today we 
know no matter but only electricity. Our atoms 
are no longer "imcut" but are compile structures of 
protons and electrons. Their masses are due to the 
protons and their chemical behaviour to the plane- 
tary electrons which encircle the nucleus. From the 
standpoint of chemical behaviour Hxere are only 
ninety-two possible types of systems and these are 
distinguished by the excess of protons in their nuclei. 
Some of these types include structures of radically 
different atomic mass, history, and stability of nu- 
cleus. Those of unstable nuclear construction change 
from type to type in conformity with a definite law, 
shifting their positions at the periodic table of eleh- 
mental types. 

Such is the matter with which the new science 
deals. All phenomena of matter, such as cohesion, 
vaporization, capillarity, elasticity, heat conductivi- 
ty, light and heat radiation or photochemical effects, 
must finally be explained in terms of a matter which 
is granular in structure and electrical in character. 
Unfortunately there remain today wide gaps in our 
knowledge. The first step, however, toward an ap- 
preciation of what is known is the consideration of 
those phenomena usually classified under the term 



In the preceding chapters the discussion of atomic 
systems has been limited ahnost entirely to those 
systems which are quantitatively satisfied, so-called 
normal or uncharged atoms. The abilities of 
various atoms to enter into molecular unions with 
other atoms has been attributed to the unsatisfactory 
configurations of their planetary electrons. In the 
formation of such unions configurations are attained 
which represent net increases in satisfaction or 
stability. The molecules so formed are, of course, 
satisfied also in equivalence of electrons and protons 
and are normal molecular systems. Under certain 
conditions, of which Chapter II contained an illus- 
tration in the dissociation of sodium chloride, a 
molecular system may split into two parts each of 
which preserves some satisfaction of configuration at 
the expense of a satisfaction in quantity. The 
separate parts are called ions; and one has an excess 
of protons while the other has an excess of electrons. 

Whenever any body has an excess of protons, 
whelher the body be of atomic size or as big as the 
earth, we shall say that it is "positively charged" 
with electricity ; and similarly we shall call a body 
with an excess of electrons "negatively charged." 



Of the various possible ways of chargmg a body with 
electricity we shall consider first the so-called fric- 
tional method which originally excited attrition to 
the peculiar properties of amber. 

Suppose two dissimilar substances are brought into 
close relations by rubbing. In g^ieral there will be 
an appreciable difference betwe». the substances in 
the matter of what constitutes a satisfactory con- 
figuration for the electrons of their molecules, for 
one may have a greater need for electrons than the 
other. Although the surfaces may appear smooth 
the structure of their atoms is such that the act of 
rubbing two bodies together is really the act of 
crowding one planetary ^stem into anoth^ or caus- 
ing one to pass through the other. There is ev&ry 
opportunity for some of the electrons to be displaced 
from their own planetary systems and to join those 
of other nuclei. The molecules of the system which 
has the greater need for electrons will gain or that 
which would more willingly assume a configuration 
with fewer electrons will lose. The net result when 
the substances are separated is that one has more 
than its normal number and the other less; the first 
is n^ative and the second positive in charge. 

The classical substances are glass and silk, or cat's 
fur and sealing wax. The first of each pair acquires 
a positive charge and the second a negative charge. 

The act of separating ^e substances is done 
against the attraction of ^e excess protons of one 
body for the excess electrons which are being left be- 
hind on the other body. The act requires wort for 
the charged bodies tractate. If free to move into 


contact they will do so, and the electrons which were 
foisted upon the unsuspecting electronegative 
systems of one body will return to the electroposi- 
tive systems of the other, restoring the quantitative 

In their motion of returning to each other the 
charged bodies manifest energy. This energy is con- 
tributed during the act of separation, is potential 
while they are held apart, and is converted into 
kinetic energy as they move toward each other. At 
the moment of impact t^e kinetic energy of the 
electrified bodies is passed on to their invisible mole- 
cules, atoms, and electrical elements, contributiag to 
them haphazard motions whidi we recc^nize as 
heat. Of such conversions or transferences of 
energy y however, more will need to be said later. 

Because two oppositely electrified bodies will so 
move toward each other and thus manifest energy 
we say that they possess when held apart a potential 
energy. Since we believe that energy is mdestructi- 
ble we measure this potential energy either by the 
energy originally required to produce the separation 
or by that which may be derived from a return of 
the electrical elements to the normal condition of 
equal numbers of protons and electrons. 

The return, however, need not be accomplidied by 
the actual motion of the two oppositely charged 
bodies, which may indeed possess billions of normal 
atoms for every one which is charged. Any method 
which will transfer electrons from the negative body 
to the positive will bring about the original stable 
condition. To all methods we give the general name 


of "electrical conduction" and to the medium 
through which conduction takes place we ascribe a 
charac^ristic of elecliical conductivity. With some 
of the methods of obtaining conductivity and with 
the corresponding medianisms for conduction the re- 
mainder of this chapter will deal. 

Whether by some adaptation of the crude method 
of electrification by friction, or by sudi more efficient 
means as dynamo-electrical machinery oflFers, we 
may give opposite electrical charges to two bodies. 
Such a condition is convenientiy evaluated as a 
magnitude, known as electrical potential, which 
represents the potential energy of the last electron 
to be added to the negative body, and hence the 
energy which is released by the return of this elec- 
tron to its former home. There is something of the 
idea of marginal utility in this concept of electrical 
potential for we always measure it by the energy 
corresponding to the last electron to be added. The 
comparison, however, is without stigma. 

Whatever path this marginal electron may travel 
in a return trip the total amount of energy thereby 
converted from potential into kinetic is always the 
same and its value is the electrical potential between 
the two charged bodies. The movement of an 
electron from a negative to a positive body is a 
descent from a height, from a place of hi^ potential 
energy to a place of zero possibilities in energy. As 
it falls it acquires kinetic energy and the potentiali- 
ties are decreased. In steep places the conversion is 
rapid, not necessarily with respect to time, but rather 
with respect to space. Just as we measure the 


grades of roads in feet of descent per mile of length, 
so we measure the "potential gradient" by the de- 
crease in potential for each centimeter. In all the 
phenomena of conduction of electricity the impor- 
tant magnitude is this potential gradient, for it is 
the space rate at which a body, carrying an excess 
proton or an excess electron, will acquire kinetic 

If conduction occurs between two oppositely 
charged plates it may take place, depending upon the 
conditions, in any one or any combination of three 
distinct manners. There may be a motion of elec- 
trons from the negative plate to the positive, a mo- 
tion of protons in the opposite direction, or a 
friendly service on the part of molecular or atomic 
systems which lie between the two plates. The last 
case is that of conduction through gases and also 
through conducting liquids such as the salt solution 
to which reference was made earlier in this chapter. 

Ordinarily an atom or a molecule of a gas is in- 
capable of assisting in electrical conduction. To 
serve, it must be ionized, that is be spUt into two 
parts which are quantitatively unsatisfied, one part 
positive and the other negative. 

In any gas the various molecules are always in 
more or less violent haphazard motion. The greater 
the temperature the higher the speed with which 
they are moving, for temperature is merely our con- 
ventional term for expressing the degree of thermal 
agitation of the molecules of a substance. Each 
molecule travels in a straight line until its approach 
to another, molecule causes it to swerve. There is no 


real coUisioii but rathw a req>ect for each other's 
sphere of influence which results in a mutual change 
of direction when these sph^'es are in dang^ of col- 
lision. On the average between successive adapta- 
tions to the presence of its neighbors a molecule 
travels a distance relatively large as compared to its 
own size. 

Now let us suppose that in the space between these 
widely separated molecules there are some free elec- 
trons, that is electrons which have been dislodged 
from their original atomic systems. These also 
wander about, choosing the easiest way and usually 
avoiding diifficulties although an individual electron 
may now and then strike into the planetary system 
of a molecule and become attached to it.^ If it does 
we have a n^atively charged molecule; if it does not 
we have a free electron. In either case we have a 
very different phenomenon as soon as this gas is 
placed between two plates which are oppositely 
charged. Then there is added to the haphazard 
motion of the free electrons, or of those molecules 
which have acquired a negative charge by adding an 
electron, a directed motion due to the charged plates. 
Only those molecular systems which are uncharged 
are uninfluenced. 

Each of the charged molecules or ions, as they 
should be called, now finds itself at some point or 
other along a path between the plates and starts to 
fall from this point toward tiie positively charged 

* Whether or not the atoms or molecules of the atmosphere 

acquire these wandering electrons depepds upon their tyjpe. Inert 

' gases certainly can not ; gases like oxygen, nowever, can because 

their atoms have external shells incompletely filled by electrons. 


plate. If the potential gradient is small the result 
is merely a drift of the negative ions and electrons 
toward this plate as a goal. A possible comparison 
is the guided drift of a herd of cattle whidi a rancher 
is leisurely driving across the plains. 

The larger the potential gradient at any point, 
that is the more rapidly a negative ion or an electron 
falls toward the positive plate, the greater is the 
possibility of its plunging into the atomic system of 
some molecule, which may be in its path, and gen- 
erally dislocating this system. If it falls far enough 
to acquire a certain definite amount of energy it will 
knock^ an electron loose from tiie molecule with 
which it collides, and then continue on its own way 
toward its positive goal. As soon as it has again 
fallen far enough to acquire the necessary energy it 
is ready to ionize another molecular system. 

Each time it does so it leaves behind a free electron 
and a positive ion, that is a molecular system which 
has lost ah electron and so has an excess of protons. 
These also take up directed motions, the electron 
moving toward the positive plate and the positive 
ion moving in the opposite direction. Both of these 
newly formed systems are able to ionize uncharged 
molecules with which tiiey collide provided that be- 
tween successive collisions they fall sufficiently far 
to acquire the necessary amount of energy. 

The process is obviously cumulative; and what 
starts as a drift of the occasional unemployed elec- 
tron becomes a stream of oppositely directed and op- 

*The word "knock" is convenient although "crowd" is more 
exact for there is no actual contact in a "collision." 


positely charged particles, botb ions and electrons. 
A current of electricity is now said to be flowing be- 
tween the two plates. The net effect of the motions 
of these ions and electrons is to carry protons to the 
negatively charged plate and electrons to the posi- 
tively charged plate. When a positive gaseous ion 
reaches the negative plate it acquires from it an 
electron which satisfies its own requirement and re- 
duces the unsatisfaction of the n^ative plate. Simi- 
larly the electrons which arrive at the positive plate 
join its atomic systems and reduce their unsatisfac- 

In describing this general phenomenon of the con- 
duction of electricity tkrough gases we have as- 
sumed, first, the presence in the gas of some free 
electrons or negative ions, and second, a potential 
gradient between successive collisions such tiiat these 
ions acquire suflSicient energy to ionize the gas mole- 
cules with which they collide. 

The first condition is always met by the atmos- 
pheric gases above the earth, for it so happens there 
is a suJBSciency of radioactive transformations^ al- 
ways going on within the earth to provide a fair 
number of electrons in each portion of the atmos- 
phere. These electrons are wrenched from their 
original atomic systems by the so-called gamma rays 
which usually accompany the beta rays. While the 
beta rays are not rays at all but are expelled electrons 
the gamma rays are strictly a radiation of en^gy 

^ Electrons are also freed in large numbers by the ultra-violet 
rays from the sun. This is a more important source. The 
phenomenon is mentioned later and also considered in detail in 
Chapter XI. 


similar to light radiation^ but most closely allied to 
X-rays. Ordinary matter is not very opaque to 
these radiations^ which are extremely penetrating 
and thus ionize gases far from their source. The 
second condition is usually within the control of the 
experimenter, for electrical potentials of a wide range 
of values are possible by the use of electric batteries 
or djoiamos. 

The amount of energy which must be acquired by 
an electron or ion in order, by its impact, to ionize 
a normal molecule or atom is dependent upon the 
character of the latter. It is obvious, for example, 
that the ionizing potential which is required for the 
disruption of an atom of helium, or of any other inert 
pB, into a free electron and an atomic ^stem which 
is positive by virtue of a lost electron, will be greater 
than that required for the ionization of some electro- 
positive element, like sodium, where the system electron more than its most stable con- 
figuration would require. The ionizing potential de- 
pends upon the electronic configuration of the atom 
or molecule in much the same way as does the 
chemical valence. 

There are many interesting phenomena connected 
with the conduction of electricity through gases 
which merit and will receive later some discussion. 
For example, the oppositely directed streams of posi- 
tive and negative ions may have collisions among 
themselves which result in the formation of un- 
charged molecules. On the other hand, the impacts 
of collision may be insuflficient to cause ionization 
and yet be sufficient to cause such a readjustment 



of the electronic constituents of the atom as to result 
in a radiation from it of li^t with a charact^istic 
color. The diaracteristic radiation whidi is emitted 
by the molecules of the gas is not entirely visible to 
the human eye for some of it lies beyond the violet. 
These ultra-violet radiations are capable of ahaking 
loose electrons of substances upon which they im- 
pinge. When, therefore, they strike the negative 
plate and so shake loose electrons from some of its 
atoms, the freed electrons are repelled from the plate 
into the surrounding gas where they take paths to- 
ward the positive plate. 

At the n^ative plate electrons may be freed if the 
impacts of the positive ions are suficient to disrupt 
the atomic sfystems of which the plate is composed. 
The bombardment of the plate results also in a gen- 
eral thermal agitation of its constituents which is 
manifested by a rise in temperature. 

Before discussing some of these phenomena in 
more detail a few words should be devoted to that 
type of conduction which occurs when molecular 
systems dissociate in solution. The example which 
was given earlier is that of sodium chloride. Quite 
a large group of chemical compounds wiU dissociate 
in this manner and these are known as ion(^ens or 
electrolytes. They may be divided further into three 
classes. The first of these, known as acids, give as 
one product of the dissociation positively charged 
ions which are nothing more or less than protons, al- 
though they are commonly known as hydrogen ions. 
They are hydrogen atoms which have each lost an 
electron to their previous partners in molecular 


union. An example would be hydrochloric add, 
HCl. The second type yields negative ions, OH, 
which are composed of one oxygen and one hydro- 
gen atom in a molecular union, but have retained 
one electron from their former associates. Such 
compounds are called bases. An example is sodium 
hydroxide, that is, caustic soda, which is symbolised 
as NaOH. The third type, known as salts, is the 
result of mixing solutions of an acid and a base. 
Under^ tJiese conditions the positive and negative 
ions, H and OH, combine, as often as they meet, to 
form HgO and the other ions when they meet form 
molecules of a salt which may or may not be soluble. 
Of this type NaCl is an example. 

The dissociation is not the result^ of collisions or 
of ionization in any way similar to that discussed 
above for gaseouis molecules. It is in the nature of a 
spontaneous parting of the molecular system because 
of the attracting influences of the neighboring mole- 
cules of water. The ions then pursue haphazard 
paths in the same way as do all the molecular 
systems which compose the liquid. If oppositely 
chai^ied plates are immersed in the electrolyte, the 


ions are given directed motions in addition to their 
own natural haphazard motions. The positive ions 
proceed to the negative plate and the negative ions to 
the other plate. When they make contact with 
these plates their quantitative unsatisfactions are 
appeased and they become uncharged atomic or 
molecular structures. In this form they are either 
deposited on the plates or liberated as bubbles of 


With certain electrolytes there may occur second- 
ary chemical reactions so that the substance whidi is 
liberated at the plate is not that which traveled 
through the solution as an ion. For example, when 
the electrolyte is dilute sulphuric acid, that is H2SO4 
and H2O, the two hydrogen ions, each H, travel to 
the negative plate and there areliberated as hydro- 
gen gas. The sulphate radical, SO4 after delivering 
two electrons to the positive plate, combines with a 
water molecule to form more sulphuric acid. The 
oxygen atom thus released then joins with another 
atom of similar experience to form a molecule which 
appears as oxygen gas, Og. By means, therefore, of 
the electric current and the secondary chemical 
action, water is decomposed into its ch^nical con- 



In solid bodies the molecules or atoms are re- 
stricted in their motions and do not wander from 
one part to another as do the molecules of liquids 
and gases. Through solids, therefore, the conduc- 
tion of electricity can occur only as the result of the 
motion of electrons. The solid substances which 
conduct electricity best are metals, tiie elements 
whose atoms are most prone to part with an electron. 
These require the smallest potential relative to the 
ensuing stream of electrons. 

The atoms of metals apparently do not form poly- 
atomic molecules, so that in conduction through 
metallic solids we have to do only with atoms. The 
close grouping of atoms in soUds is probably re- 
sponsible for a certain freedom on the part of their 
electrons since it may mean that some of the planet- 
ary electrons of one atom are at times within tiie 
sphere of influence of another atom. In that case 
they might serve a dual purpose of partially satis- 
fying the claim of their own nuclei and that of the 
adjacent atom. By such double service tiiey would 
release other electrons of their respective atoms for 
more or less free wandering throughout the sub- 



stance. The latter electrons would be akin in free- 
dom to the molecules of a liquid and would be 
restrained from excursions beyond the solid by the 
attractions of the nuclei of the surface atoms. Under 
certain conditions, as we shall see on page 73, some 
may pass beyond the surface and appear in ^ace as 
free electrons. 

We might form a picture of a solid oonductcw of 
electricity by imagining an enormous basket ball 
court on which there are disposed a laxge number 
of players. Eadi is assigned to a relatively small 
circular space within which he is free to move. The 
space may, however, overlap somewhat those as- 
signed to his nei^bors so that even within his own 
circle a player's movements are sometimes restricted 
by the necessity of avoiding a collision with a neigh- 
bor. A large number of basket balls are being tossed 
rapidly about from player to player. The latter 
correspond to the atoms and theballs to the wander- 
ing electrons. There is always activity but the balls 
only fly wild, beyond the boundaries of the court, 
when there is a very considerable (thermal) agita- 
tion, as will be explained later. 

Now suppose that each second we throw into the 
court at one end a large number of balls and with- 
draw an equal number from the opposite end. We 
do not alter the number within the court at any in- 
stant, but we do require that the haphazard motion 
shall be largely superseded by a directed motion. 
This in effect is what happens when there is a po- 
tential betwe^i the two ends of a solid 'conductor. 


Each atom-player must paas to one of his neighbors 
who is nearer the positive goal. 

Usually this is most effectively accomplished if 
the players are not dashing about too rapidly and 
moving too far. On ^he other hand, as the thermal 
agitation increases there seems to be more difficulty 
in securing the passage of the same current, that 4s 
the same number of electrons a second. A higher 
potential is required or there is a lower current for 
the same potential. Under these conditions we say 
that the conductor has a higher electrical resistance. 
For most substances the resistance increases as the 
temperature rises. 

Conversely, as the temperature is lowered the re- 
sistance decreases. The decrease is a definite frac- 
tional amoimt for each degree of temperature, and 
indicates an extremely low temperature, at which we 
should expect no resistance but instead perfect con- 
ductivity. This temperature, which is the absolute 
zero and is discussed on page 173, has never been at- 
tained, although closely approached. It represents 
a condition m which there is no thermal agitation of 
the atoms of the substance. Under these conditions 
the atoms would be closely packed together and an 
electron could be passed from one to the other with- 
out requiring that it should ever pass beyond the 
influence of an atomic nucleus. 

Under ordinary conditions it is believed that an 
electron shoots clear of its original atom and pro- 
ceeds across free space until it comes into the sphere 
of another atom, just like the basket ball of our 
iQustration. To free an electron from an atomic 


structure requires an expenditure of energy and ac- 
cording to the most recent theory, that of Bridgman, 
the solid ofFers resistance because the electron must 
travel gaps between atomic systems. Within the 
sphare of influaioe of an atom the electron is be- 
lieved to move freely. Upon this basis, and sup- 
ported by many expa^ents, Bridgmaa is develop- 
ing an apparently satisfactory theory of metallic 
conduction. According to this theory, when the 
atoms no longer dash to and fro they may be so close 
that an electron passes from one to the next essen- 
tially without crossing any gap. 

Some substances, however, usually relatively poor 
conductors, decrease in electrical resistance as their 
temperature is increased. In sudi a case it is prob- 
able that the electrons are not so easily shot from 
one player to the next and a sort of hand-to-hand 
transfer is required. If the player-atoms are already 
too far apart for sudi an operation it may be facili- 
tated by giving them greater amplitudes in their 
vibratory notions. This phenomaion occurs in the 
case of the carbon filament of the old-style electric 
lamp. When cold, and first connected to the electric 
light mains, it offers a larger resistance than it does a 
moment later when it is heated by the current. 

Any conductor is heated by an electrical current. 
A stream of electrons can only be passed throu^ a 
conductor as the result of an expenditure of energy 
upon the part of the system which establishes or 
maintains the potential. During the passage of a 
current the potential energy of the source is con- 
VKl«i into kinetic energy of the carriers of the elec- 


tricity — the electrons, in the case of solids. These 
by their impacts transfer to the intervenmg atomic 
structures the energy which they have acquired. 
Heat always results and sometimes light. In con- 
duction through solids, however, light is always an 
indirect result of the increased thermal agitation and 
is not the direct result of recombinations of electrons 
with positive atomic structures, as it is in the case of 
conduction through gases. Light occurs as the tem- 
peratiu'e rises, and even melting may occur if suffi- 
cient energy is expended in the conductor. 

Many d^rees below the melting temperature, 
however, when ihe solid is red hot or incandescent, 
there is evident a phenomenon which weU corrobo- 
rates some of the statements made above. Suppose 
we have a wire, or rather a portion of it, in an evac- 
uated vessel, as in the case of an incandescent lamp 
bulb, and heat the wire by an electric current. As 
the temperature increases the violence of the motions 
of the electrons, which serve for conduction, also in- 
crea^ies. Remember that these motions are hap- 
hazard although they have a component in the di- 
rection of the positive plate. The progress of an 
electron along its coursb resembles that of the golf 
ball of an erratic but powerful driver, for more and 
more frequently as the temperature rises will some 
electrons be driven out of bounds. Those with suffi- 
cient energy and the proper direction of flight pass 
beyond the influence of the nuclei of the surface 
atoms and appear in the space beyond as free or dis- 
lodged electrons. An electron which is emitted in 
this way is sometimes called a ''thermion." 


Its behaviour is quite analogous to that of a mole- 
cule of a liquid. We know that evaporation is in- 
creased as the temperature of a liquid is raised and 
are inclined to think that it is restricted by enclo^ 
ing the liquid. In a partly filled bottle, however, 
evaporation proceeds just as it would if the bottle 
were open except for the fact that the flighty mole- 
cules which evaporate have no place to go oth^ than 
that immediately above the liquid. Here th^ soon 
become so congested that in dodging each other some 
of them get directed back toward the liquid surface. 
Striking that surface they take up again the normal 
routme of molecules in a liquid. If the temperature 
is maintained constant a condition of so-called sta- 
tistical equilibrium is soon reached in which there ai^ 
just as many molecules evaporating each second as 
there are condensing back into liquid form. The 
same sort of a statistical equilibrium exists when 
electrons are being thermionically emitted from a 
heated wire in a very highly evacuated space. 

The equilibrium is displaced, however, if another 
wire or plate is inserted in the vessel and made posi- 
tive with respect to the heated wire by proper con- 
nection to a battery or dynamo. Then, the electrons 
stream across the space to the positive plate, pass to 
the positive terminal of the battery and there ap- 
pease to some extent the unsatisfactions whidi the 
activity of the battery elements manifest. At the 
same time other electrons from the battery pass 
along a wire to the heated electrode and thus main- 
tain in it a normal supply of electron& 


This phffliomenon was discovered by Edison many 
years ago although it was about thirty years before 
^Scient application was made of the principles in- 
volved. Today it is widely used in wire and wireless 
coimnunication, and also in electrical meaaur^noits 
in different types of industry, for the principle has 
be^i applied to the construction of an amplifier of 
electrical effecta whidi is a v^itable marvel of effi- 
ci^icy and delicacy. 

The Thennioaic Vacuum Tube. Electrons emitted by a heated 
filament, F, are dr&wn across a highly evacuated space to a 
plate, P. The stream is very sensitive to changes in the electrical 
potential of the grid, G. The device is widely used in the Bell 
System as an amplifier of telephone cuirents. 

It is evident that, by the thermionic emission of 
electrons at a heated electrode, dectrons are secured 
for the conduction of electricity through a vacuum. 
By the introduction of a third electrode the stream 
may be controlled with an inappreciable expenditure 
of MiM^. The result is that a very feeble electrical 
effect may manifest itaelf by a vwy pronounced 


change in the current which passes throu^ the 
vacuum. A device of this form is the "audion" — 9o- 
called by DeForest who introduced the third or con- 
trolling electrode. The combination of picture and 
diagram of Fig. 3 shows its practical features.^ 

We leave this phenomenon, however, to continue 
our discussion of electrical currents in wires and to 
develop some ideas which are essential to the lat» 
text. Except at hi^ temperatures, where the 
electrons may be "boiled out," the course of the 
electrons is entirely controlled by the wire. Wires 
serve much like pipes for the guided flow of electrons 
and thus permit distinct streams of electrons to be 
brought very close to one another without merging. 

This possibility is of great practical importance 
since parallel streams of electrons tractate. The 
tractation of parallel electron streams results in a 
tractation of the wires in which these streams are 
confined. Streams in opposite directions pellate and 
hence the wires which carry them are urged apart. 
If streams are at right angles there is no reaction be- 
tween them. The phenomena, unfortunately, are 
as completely without explanation as are the funda- 
mental phenomena of the tractation of proton and 
electron or the pellation of two electrons or two pro- 

The effect depends for its magnitude upon the 
length of the wires which are parallel, the intensities 
of t^e currents, and the distance between the wires. 

*'nie device has been highly developed both in structure and 
application by the research phsnsicists and communication en- 
janeers of the Bell Telephone System and of the General Electric 



The greater the lengths which are parallel and the 
greater the currents, that is the greater the numbers 
of electrons which stream through the wires eadi 
second, the greater is the effect of attraction. It 
therefore happens that tiie effect may be enhanced 
by arranging each wu^e in the form of a coil, the suc- 
cessive turns of which wiU carry the same electron 
stream. Two coils of this solenoidal form are, shown 
in Fig. 4. If they are supported so as to be free to 




Fia. 4 

Attraction of wires which cany parallel streams of electrons in 

the direction indicated by the arrows. 

move it is found that they rotate so that their loops 
are parallel and at the same time they move closer 
together so that they tend to form one long con- 
tinuous solenoid, the turns of which all carry parallel 
electron streams. 

The effect is very greatly increased by winding the 
coils on cores of so-called magnetic material, for ex- 
ample, iron, cobalt, nickel, or certain alloys for which 
the electronic configurations are generally similar to 
those of these elements. The effect of the currents 
in the coils upon the atoms or molecules of the mag- 
netic cores is easily explainable if we assume rota- 



tions for some or all of the planetaiy elecUx)n8 of an 
atom of a magnetic substance. Suppose some of 
the electrons are revolvmg about the nucleus. They 
constitute a stream of electrons around a loop just 
as really as do the streams which travel the larger 
loops of the solenoids which we have been consider- 

Each molecule or atom of a magnetic substance 
will then act like a current-canying loop and will 
tend to place itself so that its loop lines up with oth«- 





^ £i€cfron RofoHttn 

Fig. 6 

Equivalence of a bar magnet and a current-canying solenoid in 

phenomena of attraction. 

current-carrying loops. The effect of the current in 
the solenoid is to orient the individual atoms or mole- 
cules of the core so that as many as possible of their 
loops shall be parallel to those of the solenoid. 
Under this condition the core is said to be magnet- 
ized, and the combination of core and exciting sole- 
noid is called an electro-magnet. 

The orientation which the molecules of the core 
acquire by virtue of the magnetizing current in the 
solenoid is retained with more or less tenacity after 
the current has ceased to flow. The cor© is thus 
made into a more or less permanent magnet. If its 


ends are marked for refa^nce and it is then with- 
drawn from the solenoid it will be found to replace a 
currentHiarrying solenoid and generally to behave as 
if it were a coaxial series of current-carrying loops. 
(See Fig. 5.) In all pjienomena of mutual attrac- 
tion or r^ulsion, magnets and current-carrying 
eolenoids are equivalent. 

Fio. 6 

Interaction of magnetic field aod electron stream. The lai^e 

current-carryii^ loop and the solenoid tend to place themselves 

coaJiially. The effect is that the wire, AB, carrying the electron 
stream is pushed sidewise across the magnetic field between N 
and S. 

In the ca«e of magnetic materials we picture some 
or all of the planetary electrons as engaged in circu- 
lar or elliptical motions. Adjacent molecules would 
then tend to orient themselves so as to have their 
current looi^ in parallel. We might ^erefore ex- 
pect that in any piece of iron the molecules would 
of their own action have assumed such similar 
orientations as to have made the piece of iron a mag- 
net. Such, however, is not the case. The mole- 


cules have haphazaxxi orieatations, as may be vai- 
fied by placing one piece of ordinary iron near 
anoth^ and noticing that fhere is no attraction or 
repulsion as there would be if the molecular cur* 
rents were not flowing "every whidi way/' The ex- 
planation is that the molecules have already formed 
themselves into a large number of small and fairly 
stable groups. For this reason heating and jarring, 
which increase molecular agitation, facilitate the 
process of magnetization of an electromagnet or 
the process of "self-demagnetization" by which its 
molecules reform self-satisfied groups whidi neutral- 
ize each other's external effects. 

All so-called magnetic phenomena are merely the 
interactions of parallel streams of electrons. As far 
as possible current-carrying loops inta*act so as to 
place themselves parallel and coaxial and to have 
electron streams in the same sense, e.g. clockwise, or 
counter-clockwise, when viewed from a common 
point, not between the two loops. An application 
of this law, which is of importance in our later dis- 
cussion, is shown in Fig. 6. If a portion of a current- 
carrying loop of large size is placed between two 
coaxial coils, which are carrying currents in the same 
sense, then the portion of the large loop is ui^ed 
along a line at right angles to the axis of the fixed 
coils in a direction depending upon the direction of 
the current. The coaxial coils may contain cores 
and be electromagnets or may be replaced by per- 
manent magnets without prejudice to the expm- 

Usually there is said to be a magnetic field of force 



between the two coils or magnete. The direction of 
guch a field is taken as that in which the north-seek- 
ing end of a compaaa needle would point. The direo- 
tioD of deflection f(ff the stream of electrons in the 
large loop will then be related to this direction of the 
ma^etic field and to fiie direction of the electron 
stream as is the thumb of one's right hand to the 

Rg. 8 

Tie telative directicmB 
of magnetic field, F, of 
the motion, M, of a con- 
ductor, and of the iiH 
duced electron stream, 
C, ia the conductor. 

The relative directions of a magnetic field, F, of an electron 
Btre&m, C, and of the motion, M, of the stream relative to the 

fore and center fingers, respectively, when all three 
digits point at right angles to each other. 

In the appUcation of this rule, as pictured in Pig. 7, 
it must be remembered that so far as concerns this 
phenomenon a stream of positive ions ia equivalent 
to a stream of electrons in the oppo»te direction. 


Parallel currents undergo mutual deflectians at 
right angles to their directions. Does sudi deflec- 
tion alter the cmrOTits? Always, for every physical 
action has an equal and opposite reaction. The 
electron streams are momentarily affected by their 
deflection in such a manner as to oppose the change. 
If the currents in two parallel wires are in such direc- 
tions as to cause an attraction of the wires, then 
during their mutual approach the currents are mo- 
mentarily decreased. 

For simplicity let us concentrate our attention on 
a single current, choosing that of the portion of the 
large loop of Fig. 6 which we know is deflected across 
the magnetic field between the two solenoids. The 
wire is deflected in the direction given by the right- 
hand rule of Fig. 7. If there were flowmg in it a 
stream of electrons in the opposite direction there 
would be a tendency to the opposite deflection. If 
the actual deflection which takes place is to be ac-. 
companied by a reaction, this reaction may be ac- 
complished by the setting up of an opposing sfaream 
of electrons. Such a counter stream will result in a 
reduction in the net number of electrons which are 
being transferred along the wire. The current, 
therefore, is reduced momentarily, that is as long as 
there is a deflection of wire. 

Now suppose that the wire carries no current and 
that by some external means it is caused to move 
across the field between the two solenoids of Fig. 6. 
Let its direction of motion be the same as before. 
The original stream of electrons no long^ exists but 
the induced stream comes momentarily into exist- 


ence just as before and its direction is such as to op- 
pose the cause inducing it. 

The relations of direction of motion, direction of 
field, and direction of the induced stream of electrons 
will be identical with that pictured in Fig. 7, except 
that the direction of the electron stream is reversed. 
By using the left hand, however, as shown in Fig* 8, 
the directions may be represented by the same sym- 
bols as before. We may call the left-hand relations 
those for the induction of electronic streams and the 
right-hand relations those for the deflection of elec- 
tronic streams. 

It is this phenomenon of the induction of elec- 
tronic streams which is used to such industrial 
advantage in the so-called "generation of electricity" 
for power purposes. By rotating machinery, coils of 
wire are kept in motion across magnetic £elds and 
thus there are obtained streams of electrons which 
may be guided by wires to points where the energy 
of the moving electrons may be utilized. 

The utilization may involve the phenomenon of 
the attraction of parallel streams of electrons in 
motors where the electron streams cause coils of wires 
to rotate relative to electromagnets. In many cases 
the utilization involves the release of the energy of 
the electron streams in the form of the heat and 
light which results from the impeded progress of the 
electrons through wires which offer high resistance. 



Our knowledge of the interactions of magnets 
dates from Gilbert, the Elizabethan physician; our 
knowledge of the interactions of a magnet with an 
electric current, or of current with current, started 
with Oa^ted in the early nineteenth century; and 
our knowledge of electronic structures has been al- 
most entirely a twentieth-century development. It is 
natural, therefore, to say that electric currents pro- 
duce magnetic effects. Magnetic properties were at- 
tributed to currents m order to explain their inter- 
actions. Today, however, we incline toward the 
explanation of the properties of so-called magnetic 
substances in terms of revolutions of the electrons 
within their atoms, although we do not know defi- 
nitely the nature of these revolutions. 

The chemical properties of atoms, which were dis- 
cussed in Chapter III in connection with the periodic 
table, are most easily explained if we assmne the 
planetary electrons to be located in fairly definite 
positions. The magnetic properties are best vizual- 
ized if we assume electrons to be rotating. The 
emission of light, as we shall see later, requires that \ 
the electrons shall be in rotation and that their orbits ^ 
shall change under various conditions. So far no , A 




satisfactory picture ha^s been presented, although for 
the simpler atoms of hydrogen and helium there have 
been suggested atomic models which would have 
properties in agreement with those observed for 
these substances. 

Although we are in ignorance of the exact form 
of the paths pursued by the electrons in atoms we are 
perhaps justified in assuming that rotations do occur 
and in explaining so-called magnetic attractions by 
the interactions of electrons which are moving in 
parallel paths. If the paths are at right angles there 
are no attractions. For intervening directions the 
attraction depends upon the components of the mo- 
tions which are parallel. The idea of a component 
is easily grasped when one realizes that if two bodies 
are not going in directions exactly at right angles to 
each other, they must to some extent be going in the 
same direction, and, with equal truth, to some other 
extent at right angles to each other. The extent to 
which one body is moving in the same direction with 
a second is the component of the motion of the first 
in the direction of the second. 

The magnetic attraction which occurs between 
electrons with components of motion in the same 
direction is very probably one reason why such mu- 
tually repulsive entities as electrons can form a group 
about an inner nucleus. The magnetic attraction 
' may partially offset the tendencies of the electrons 
to pellate and may thus assist jthe nucleus in retain- 
ing them within atomic limits. It may also be liiat 
the protons and electrons within the nucleus are re- 
strained from flying apart by similar attractions. 


To make these attrax^Uve forces commensurable 
with the natural repulsions of similar electrical ele- 
ments would require hi^ speeds for the elements 
which are rotating and thus represent large energies. 
This would fit with the observed facts as to the high 
energies possessed by alpha and beta particles. The 
actual geometry of the atomic nucleus/ however, is 
far in the speculative twUi^t, although present 
scientific progress is so rapid that the whole matter 
might well be explained within a few years. 

In dealing with the interactions of electrical cur- 
rents it is usual to speak as if one current acted on 
the other and to neglect the reaction of the second 
on the first. To the acting current we attribute a 
magnetic field and then speak of this field as acting 
upon the current in which we are intwested. It is 
in this terminology that one will find described the 
classical experiments which established the electron 
theory with which modem science starts. Through- 
out all the original reports one will find the idea of 
fields of force, not only magnetic but so-called elec- 
trostatic fields. The latter are the regions near 
charged bodies and the direction of the field is taken, 
unforturtately, as that in which a positive charge 
would move. 

By applying magnetic and electrostatic fields of 
force to ike streams of particles which are expelled 

* The most recent evidence is that of C. J. Darwin (February, 
1921) who worked with Professor Rutherford in the latter's 
experiments on the collision of alpha particles with hydrogen 
nuclei. The evidence seems to support the idea that an alpha 
particle has a shape something like a plate or disc ^th a diameter 
of 2.7x10-** cm. The evidence comes from experiments simi- 
lar to those described on page 113. 


from radioactive bodies, there was obtained the first 
information that these were streams of particles or 
corpuscles instead of radiations as intangible and 
imponderable as those of light. In a magnetic field 
a stream of alpha particles is deflected in the opposite 
direction from a stream of beta particles, and the 
same is true for an electrostatic field such as exists 
between two oppositely charged plates. The proof 
of the existence of electrons, however, was reached 
largely by the study of so-called "cathode rays," 

The origin of the latter phrase is explained as fol- 
lows: In the study of electrolysis, that is the con- 
duction of electricity through liquids which was dis- 
cussed in Chapter II, two terminal plates are inserted 
in the liquid. The positive plate was called the 
anode and the negative the cathode since it was 
assumed that electricity flowed up to one and down 
to the other. The tJerms have been retained and ap- 
plied to the terminal plates in conduction through 

We remember also from our discussion of gases 
that electrons are liberated at the negative plate 
when there is a suflBciently severe bombardment of 
this plate by positive ions. If the tube containing 
the gas through which conduction is taking place is 
not too highly exhausted a relatively large number of 
gas molecules are present and may be ionized. On 
the other hand, if it is not so little exhausted that a 
gaseous molecule is stopped by collision before it 
travels a distance, representing a potential difference, 
suflScient to acquire the necessary energy, then the 
impacts of the positive ions wiU liberate electrons 


from th^ cathode. These shoot off into spaxse, re- 
pelled by the negative plate from which they are 
derived. Their ena^gy comes from the battery 
which keeps the cathode negative, by forcing upon 
it electrons far in excess of its possibilities of getting 
rid of them. Electrons may be freed from the 
cathode and so made available for conduction 
through the tube only by the bombardment of the 
positive ions (or by other agencies, like ultra-violet 
light, which do not concern the present case). 

Fia. 9 

Cross-section of apparatus for examination of cathode rays. 
The cathode stream from C passed through the tubular anode, A. 
It was deflected by the magnetic field into the vessel, V, for 
which an electroscope, E, then indicated a negative charge. 

The result is a steady stream of electrons, flying 
from the cathode with velocities which may be al- 
most as enormous as that of li^t. These constitute 
the "cathode rays," as they were first called. Where 
they impinge on the glass of the tube they cause it 
to phosphoresce, and thus their paths may be traced. 
Many of the electrons travel straight for the positive 
terminal, or anode. If the latter is made hollow, or 
perforated, many wiU pass straight through with al- 


most no regard for its attracting excess of protons 
for they are going too fast to stop. The result is 
that a "beam" of cathode rays is available for experi- 
mental study in the space beyond the anode, as 
shown in Fig. 9. 

Through Ihis space the beam travels straight 
except as deflected, for example by magnets set out- 
side the tube so as to establish a magnetic field at 
right angles to the stream. In one of the original 
experiments of J. J. Thomson the beam was deflected 
into the hollow metal vessel, V, shown in the figure. 
The du-ection of deflection indicated that the beam 
was a stream of negative particles. Further evi- 
dence came from the charge which the beam gave to 
the vessel 7, for the latter was found to be negative. 

You wiU remember, however, that it should also 
be possible to deflect the beam by placing above and 
below it oppositively charged plates. If the upper 
plate is made positive the stream of electrons should 
be attracted toward it and repelled by the lower 
negative plate. By subjecting the beam to this in- 
fluence the effect of the magnetic field can be 
counteracted, provided that there is maintained a 
certain relation for the intensities of the electrostatic 
field which deflects upward and the magnetic which 
deflects downward. It happens that the ratio of 
these intensities depends only upon the velocity with 
which the particles in the stream are moving. By 
such a balancing of deflections, therefore, Thomson 
was able to determine the velocity of the particles. 
His apparatus is shown in Fig. 10. 

Up to this time the electron was unknown and 



electricity had been meaaured in other units than 
this natural unit. He next sou^t in terms of exist- 
ing units to measure the charge whidb each particle 
carried. However, it waa not then known how to 
measure this quantity directly, and the method he 
devised gave the relation of the chiu:^ on l^e particle 
to its mass (inertia). 

He found this ratio by observing the deflection 
which was produced when only the electrostatic field 
was active. Each electron in the stream behaves 


iPtctf^s for 
\,ihcfrfG FMcf 


$ide View 


Cross Section at XX* 

Fia. 10 

Apparatus used by J. J. Thomson for determining properties of 
cathode rays. Electrons from C pass through A to the screen, P. 
The magnets and the plates deflect the stream up or down, 
depending on their respective polarities. 

like a bullet shot in a horizontal line and the plate 
toward which it is attracted acts like the earth with 
its gravitational pull. The constant pull gives the 
particle an acceleration toward the plate just as in 
the case of a bullet and the earth. The acceleration, 
however, depends upoja the diarge, for it is by virtue 
of the charge that the particle is attracted toward the 
plate, and upon the mass or unwillingness to be ac- 
celerated. From the horizontal and vertical dimen- 
sions of the parabolic path whidi the particle pur- 
sued Thomson determined the ratio of its charge to 


its maas. It was found to be about 1700 times the 
similar ratio for the hydrogen ion which takes part 
in electrolytic conduction. 

An approximate value for the mass of the particle 
in a cathode ray was then obtained upon the assump- 
tion that the ion of hydrogen is essentially the same 
in mass as the hydrogen atom and that the charge of 
electricity which it carries is equal but opposite in 
kind to that of the particle under examination. 
Upon this assumption the mass of the imknown 
particle was obtained as one-seventeen-hundredth of 
a hydrogen atom, since its mass must be that much 
smaller in order to make the ratio of charge to mass 
correspondmgly larger. 

Methods for determining the unknown charge on 
the particle were soon devised and one by Townsend 
was widely used. The latter knew that not all the 
gas which escapes at an electrode in an electrolytic 
action, like that described at the end of Chapter VI, 
is composed of neutral uncharged molecules. Once 
in a million times or so a molecule may carry away a 
charge, the result, apparently, of hasty cpmbination. 
Whether the molecule gets out into free space with 
one too few, or one too many, electrons is not acci- 
dental but is characteristic and depends upon the 
electrolyte from which the gas rises. 

If the air above the electroljrte contains moistm*e, 
that is molecules of water wandering about like 
molecules of ordinary gas, then the charged mole- 
cules act as centers of attraction for the water mole- 
cule& The latter aggregate about the charges, 
forming small drops which appear as a cloud. The 



natural assumption is that in such a condensation 
the number of droplets is equal to the numba- of 
centers about which drops can form. Townsend 
therefore calculated the number of drops in the 
cloud, measured the electrical charge involved, and 
thus found the charge per drop, Hiat is the desired 
elemental charge. 

The number of drops was obtained by calculating 
the amount of water m each drop and then dividing 
this into the total weight of the entire cloud. The 
latter was found by passing the cloud through tubes 
filled with chemicals, which took up the water, and 
observing their increase in weight. The volume of 
the drops was calculated on the basis of earlier work 
by Stokes who had expressed quantitatively the law 
for the descent under gravity of small drops. The 
smaller the drop the more slowly does it fall. Such 
drops as formed the clouds with which Townsend 
worked will take about half a minute to fall throu^ 
an inch of air. By observing the rate of fall of the 
entire cloud the average size of its drops could be 
computed and hence their weight obtained. 

To measure the total charge which the cloud car- 
ried there was used a calibrated electroscope, or elec- 
trometer, as it is called. This instrument has proved 
of great usefulness in most of the experiments which 
have led to the present state of our knowledge of 
electrons and radioactive substances. In simplest 
form it consists of a vertical metal strip to which is 
attached a light gold leaf. The metal strip is insu- 
lated from the protecting case through which it pro- 
jects to an external knob. 


If a charged body is brought in contact with the 
knob there is a transfer of electrons either to the 
knob or from it. Let us suppose the body negative. 
Then electrons pass to the knob and because of mu- 
tual repulsions pass down into the metal strip and 
its gold leaf. There their repulsions result in the de- 
flection of the gold leaf which stands out at an angle 
from the vertical. When the charged body is re- 
moved some of the electrons at the bottom of the 
strip are repelled back to the knob and the leaf drops 
a little to a new and final position which it maintains 
except as the charge on the system is neutralized by 
stray ions in the air about it. 

If now another charged body is brou^t near but 
not iQto contact with the knob two different actions 
are possible. If the new body is negative the 
electrons are again repeUed mto the extremities of 
the strip and gold leaf and there results an increased 
deflection. On the other hand if the new body is 
positive its excess of protons attracts electrons to- 
ward the knob and the number at the bottom of the 
system are no longer sufficient to maintain the 
former deflection so that the leaf falls back. 

The same effect is, of course, produced if a charge 
is added to the gold leaf system by direct contact of 
the charged body with the knob. The only difficulty 
is that if the charge is of opposite kind to that al- 
ready on the system it may neutralize that charge, 
allowing the leaf to drop, and instantly recharge the 
electroscope with the opposite kind of electricity, 
causing the leaf again to stand out from its support. 
By proper care, however, the change in deflection of 


the gold leaf may be made not only to indicate the 
kind of charge but also to measure its amount. By 
such a method Townsend determined the total 
charge on his cloud. 

The series of expmments described above w^^ 
sufficient to establish the fact that cathode rays are 
streams of negatively charged particles, eadi with a 
charge like that of the hydrogen ion in electrolysis, 
and a mass about one 1700th of that ion, and also to 
determine in terms of the standard imits the charge 
on individual particles. With the conclusion of this 
series the existence of the electron was established. 

Experiments of this character are obviously com- 
plicated since they generally involve a number of 
necessary subsidiary experiments as well as mathe- 
matical formulation and a careful use of units. In 
this book we shall describe only a few. One, which 
deserves immediate attention, is Millikan's method 
for determining the value of an electron in terms of 
the earlier accepted units for electrical charge. 

Millikan's work, extending from 1907 to 1917, was 
a series of ingenious experiments, each more simply 
direct than the precedmg and adapted to givmg more 
precise results. In one of these, instead of a cloud, 
he used a single drop under conditions which elimi- 
nated the properties of the drop itself and of the 
medium in which it was placed juid gave direct indi- 
cations of the electrical charge which the drop 

The principal features of his apparatus appear in 
Fig. 11. Between the two parallel plates, M and iV, 
a droplet was introduced by spraying oil from an 



atomizer into a chamber above. Drops about one- 
ten-thousandth of an inch in diameter were thus 
fonned. As these fell slowly through the chamber 
one would find its way through the small hole at p 
into the space between the plates. Here it was 
made visible as a bright speck, by a powerful stream 
of light, just as particles of fine dust in the air are 




Fig. 11 

Cross-section of Klillikan's apparatus for measuring the ele- 
mental charge of electricity (the electron) . An electrified oil drop 
between the plates M and N falls or rises, depending upon the 
electrical condition of these plates, and this is controllable by the 
battery, B, and the switch, /8. 

made visible by a transverse beam of sunlight. Its 
motion was observed through a small telescope and 
was timed by a stop watch or a chronograph. 

Between the plates an electrical potential was ap- 
plied by a battery, By so arranged with switches, S, 
as to permit making either plate positive and the 
other negative. The drops acquired charges by fric- 
tion as they left the atomizer. The plates, however, 


were not charged until a drop was seen in the field of 
view of the telescope. As long aa the plates remained 
uncharged the drop would fall slowly, about one thir- 
tieth of an inch a second. Connecting the plates to 
the battery would result in a change of speed. If 
the charge on the drop was the same kind as that of 
the upper plate it would fall more rapidly, but if op- 
posite to that of this plate it would eith^ rise or re^ 
main practically at rest, depending upon whether or 
not the potential applied to the plates was sufficient 
to do more than neutralize llie gravitational effect. 

The drop was caused to rise and allowed to fall, 
alternately, and the times were observed. Some- 
times the drop would suffer collision with some ion 
of the atmosphere betwe^i the plates and then be- 
cause of its dianged electrical condition its time of 
rise would be changed, but its time of fall, when the 
plates were uncharged, would not change. A fair 
supply of ions for such collisions were provided by 
bringing radium near the apparatus or by exposing 
the air between the plates to X-ray& 

The drop could be caused to collide with either 
positive or negative ions by the following method: 
Suppose it was desired to add positive charges to the 
drop. It would be brought near the n^ative plate 
and then kept from falling by properly adjusting the 
potential. Then the space would be exposed to ion- 
izing radiations from the radium. The negative 
ions, thus formed, would move toward the positive 
plate and away from the drop. All the positive ions, 
however, would move toward the oth«r plate and the 
drop would thus be in a veritable shower of positive 


ions. In this way the charge originally held by the 
drop could be increased or neutralized and reversed^ 
if desired. 

A change in the velocity with which the drop rose 
would indicate a change in the charge it carried. If 
there is an elemental charge tiiere should be a defi- 
nite minimum change in velocity corresponding to 
adding or subtracting this charge from the drop and 
all other charges should be small exact multiples of 
this minimum. On the assumption that the electri- 
fied condition of the drop is due to a certain excess 
or deficiency of electrons, this is what we should ex- 
pect, and this is what Millikan found. His experi- 
ment constitutes a beautiful proof of the existence 
of a definite elemental quantity of electricity. 

By a proper correlation of his quantitative data he 
arrived at a very exact determination of the value 
of this elemental charge in terms of the usual units 
for measuring electricity. In the Appendix we shall 
consider the numerical value for this important 
physical magnitude. For the moment, however, we 
quote an illustration from Millikan to relate the 
electron to a familiar magnitude. He says that the 
niunber of electrons which pass every second through 
a common 16-candle power electric-lamp filament is 
so large that it would take the two and a half miUion 
people in Chicago, counting at the rate of two each 
second, twenty thousand years of 24-hour working 
days to count an equivalent number. 

It made no difference how the electrification was 
produced or the charge transferred. Millikan used 
thousands of drops in various media, experimenting 



with drops of non-conductiiig substances like oil, 
poor conductors like glycerin, and excellent metallic 
conductors like mercury. He states that ^^in every 
case, without a single exception, the initial charge 
placed upon the drop by the frictional process, and 
all the dozen or more charges which resulted fram 
the capture by the drop of a lai^r or smaller niunber 
of ions, were found to be exact multiples of the 
smallest charge caught from the air." 

His experiments w^e a beautiful demonstration 
of the correctness of the concept of an electron. 
They "placed beyond all question the view that an 
electrical charge, wherever it is found, whether on an 
insulator or a conductor, whether in electrolytes or 
in metala, has a definite granular structure, and that 
it consists of an exact niunber of specks of electricity 
(electrons) all exactly alike, which in static phe- 
nomena are scattered over the surface of the charged 
body and in current phenomena are drifting along 
the conductor." 




That there is an elemental quantity of electricity 
was definitely shown by the experiments of Millikan 
which were described in the last chapter. Hib ex- 
periments are apparently the most accurate and con- 
vincing because of their simplicity. They constitute 
a final proof in a long series of independent investi- 
gations by various physicists. Some had experi- 
mented with cathode rays, proved that they were 
formed by small charged particles and found the 
mass and charge of the particles (electrons) . Others 
had carried out similar investigations of the beta 
rays from radioactive substances, proved their gran- 
ular nature, and found for their particles the same 
value of electrical charge. In beta rays, however, 
the electrons move with high velocities, very nearly 
that of light, and usually much higher than in 
cathode rays. The investigators found that while the 
quantity of electricity represented by an electron in 
a beta ray was the same as that in a cathode ray, the 
mass was in general much greater, that it depended 
upon the velocity and was enormously greater for 
velocities nearly that of light.^ ,- ; 

The quantity of electricity which cotistitutes tKe 

* Cf. p. 205 of the Appendix. 



elemental charge had also been determined from a 
knowledge of electrolytic phenomena and by deduc- 
tion from certain phenomena of radiation. It was 
determined also from measurements of alpha rays 
by experimental methods similar to those used for 
cathode rays. In the case of gaseous ions the ele- 
mental charge had been determined by variations of 
the "cloud" method which was described in the 
preceding chapter. 

The net result of ail these experiments has been 
the common acceptance of the idea of a definite ele- 
mental quantity of electricity, and its identification 
with the electron which appears in cathode rays and 
beta raya For some years, however, nothing very 
definite was known about the complement of the 
electron, the equivalent positive charge of electricity^ 
which we are calling the proton. At first all that 
could be said was that an atom consisted of electrons 
which could be isolated and a nucleus which must 
have a positive charge equal to the negative charge 
represented by the electrons which surrounded it. 

Knowledge of the elemental positive charge has 
come partly from a study of radioactivity and partly 
from a study of conduction through gas^. The 
earlier determinations of the elemental charge by the 
cloud method had employed the ions of conducting 
gases, sweeping them aside from their normal course 
by highly chatted plates and thus collecting similar 
ions for measurement. Determinations of the num- 
: ber of ions in these experiments were baaed upon 
:':'t * file phenomenon discovered by C. T. R. Wilson tiiat 

* Which is usually known as the "positive electron." 

i. • 


ions act as centers for the condensation of water 

This phenomenon Wilson used also to obtain some 
interesting pictures of the progress of swiftly-moving 
charged particles. When an electron is shot through 
a gas^ in which there is a large amount of water 
vapor, its progress is recognizable by small drops, 
formed about the ions which result from its collisions 
with the molecules of the gas. One of Wilson's pic- 
tures of the path of a high-speed electron, a beta par- 
- tide, is reproduced in Fig. 12. Drops due to several 
ionizing particles are seen but those produced by the 
particular particle under consideration appear as a 
straight line lengthwise through the center of the 
picture. This beta particle moved so rapidly through 
the atomic systems of the gas and the free spaces 
between that only rarely was it long enough in the 
neighborhood of any particular electron to displace 
it permanently from its colleagues in an atom. It 
ionized only about one of every 10,000 gas molecules 
through whose systems it passed. 

In Fig. 13, on the other hand, appear the paths 
of some alpha particles from radium. Although 
these heavier particles ionized millions of gas mole- 
cules in each centimeter of their progress they were 
rarely deflected from straight-line paths. In two 
cases in this figure there may be seen sharp changes 
in th^ir directions. These occurred near the ends 
of their paths, when their energies were much re- 
duced by their previous activities, and are believed 
to represent collisions with the nuclei of gas mole- 
cules. In the earlier parts of their paths there were 


undoubtedly some siinilar coUifflons but the number 
was relatively small and the momenta of the. alpha 
particles were such that they su£f»ied inappreciable 
deflectiona Probably they drove before tiiem the 
molecules of gas with whose nudei they had head-on 
coUiaiohs much as does the cue ball in a well-played 
''follow shot" in biUiards. The smaUness of the alpha 
particle and of the nuclei of atoms, in general, ex- 
plains, howev^, the infrequency of deflection in 
those later portions of their paths when th^ abnor- 
mal energy is almost entirely absorbed and they are 
becoming as the oth^ atomic systems through which 
they pass. 

As early as 1011 Ruth^wd applied this phe- 
nomenon, of the deflection of the positive alpha 
particle by the positive nucleus of an atom, to a 
quantitative determination of the charge on the 
nucleus of various types of atoms. That on the alpha 
particle was, of course, known from previous work 
as equal in amount but complementary in kind to 
the diarge of two electrons. He computed the 
chance that an alpha particle would suffer a given 
deflection by being shot through thin sheets of foil 
of gold and other metals. The method of the experi- 
ment involves a principle which is widely appUed 
in the study of radioactivity. 

The method is that of counting scintillations. 
When alpha particles strike a screen of zinc sulphide, 
for example, they give rise to bright specks of li^t. 
Each partjide apparently sets into vibration the elec- 
tronic systems of several atoms and these vibrations 
the eye recognizes as light. The phenomenon is 

FiQ. 12. The trails of beta particlea (electrons), moving swiftly 
through humid air, as shown by drops of water which formed 
about the ions produced by the impacts of the electrons. (Re- 
produced from original memoir of C. T. E. Wilson.) 

Pic. 13. The trails of alpha particles as shown by the con- ' 
densation of water vapor on the ions which were formed by their 
impacts. (Original in scientific memoir of C. T. R. Wilson.) 


similar to that involved in the recognition of the 
impact of cathode rays by the fluorescence of the 
glass of cathode ray tubes. 

The particular experiment involved finding what 
fraction of a thousand alpha particles, which were 
shot through a sheet of foil, produced scintillations 
at a location on the screen corresponding to the given 
angle of deflection. It was determined by calcula- 
tion based on this experimental method that the 
number of elemental charges on the nucleus of an s 
atom is approximately equal to half its atomic 

This was the first determination of atomic num- 
bers. Although the method is not capable of very 
exact indications and although the values obtained 
are necessarily only indicative, the experiments im- 
plied a definite granular structm^ to positive elec- 
tricity such that nuclei of different atomic systems 
differ by whole niunbers of elemental positive 
charges. It gave no hope of isolating the elemental 
positive charge (proton). 

Further indications and very exact quantitative 
results on atomic niunbers were obtained about three 
years later by Moseley. His method, however, in- 
volved X-rays and will be discussed in the following 

The next evidence as to the proton came from 
experiments on so-called positive rays. In the con- 
duction of electricity tiirough gases, as we have seen, 
the term "cathode rays" was applied to the stream 
of electrons which proceeds away from the negative 
electrode. In the preceding chapter we have seen 



how expmmenta^ arranged a hollow anode so that 
a pencil of these rays mi^t pass beyond the anode 
and be subject to examination or use. In mudi the 
same way the term ''positive rays" has been applied 
to the positive gaseous ions which are ui^ed toward 
the cathode. By making the latter a hollow cylinder 
these positive ions may be passed into the space 

Fig. 14 

Cross-section of apparatus for positive ray analysis. (Dlustrat- 
ing method of J. J. Thomson.) The stream of positive ions passed 
through the hollow tubular cathode, C, to the photographic plate, 
P, It was deflected by an electric field (due to a battery con- 
nected at +, — ) and by an electromagnet, N-S, and thus acted 
to trace a parabolic curve on the plate. Tube L connected to the 
vacuum pump. 

If the cathode is a long cylinder of small cross sec- 
tion like that of Fig. 14, there is relatively little 
diffusion or mixing of the gases of the two parts of 
the vessel. For this reason the gas pressure within 
the conducting portion of the tube may be main- 


tained at the proper value to secure the optimum 
density of gas molecules for the formation of ions 
and the remainder of the enclosed system may be 
practically a vacumn and thus contain few mole- 
cules to impede the progress of the ions which con- 
stitute the positive rays. At the end of this second 
portion of the tube a photographic plate, P, permits 
a record of the stream, for each ion, as it strikes, 
disturbs the electronic composition of £he neighbor- 
ing atoms of the plate, much ae does light in ordinary 

In one sense, of course, alpha rays are positive 
rays. They are helimn ions, identical with helium 
atoms which have lost two electrons each. They 
differ from helium positive-rays, which would be 
formed if the tube of Fig. 14 contained helium in 
its conducting chamber, in their origin, for alpha 
rays arise from radioactive disturbances. They 
differ also in velocity, at least in the early portidn 
of their progress, for they may have original veloci- 
ties as high as a tenth that of light. In conduction 
through gases no such high velocities are attainable. 
They may differ also in the niunber of ions which 
are lost, since ionizing impacts in a conducting gas 
usually remove only a single electron from such 
stable structures as the inert atoms, although they 
frequently remove two from substances like nitrogen, 
or more than two from metallic atoms like those of 
mercury vapor. 

It was this high velocity and hence high penetra- 
tion of alpha particles which permitted Rutherford 
to make his classical demonstration of the fact that 


alpha particlee are really helium iona He used a 
very thin-walled tube like that diown at A in Fig. 
15. He first showed that there was no connection 
between A and the larger tube, B, by filling A with 
helium and obearing that thwe was none of the 
spectroscopic charaotwistics of helium gas when a 
current passed between the electrodes of C. Nest 

Fia. 15 
CroBs-section of Rutherford's (qiporatus for ahowing that alphft 
particieH are helium. Ad electric cuireot through C gives a 
radiation characteristic of the Bubetaace in B. When radium 
emanatioa was placed in A, the spectrum of the radiation from C 
showed traces of helium. 

he removed the helium from A and substituted 
radium emanation. After a few houra the spectro- 
scope showed that helium was present in the dis- 
charge path between the electrodes of C. The only 
way heliimi could get into B and C was by brang 
identical with the alpha particles which aite emitted 
by radium emanation. The high velocities of these 
particles are sufficient to carry them through the 
atomic systems of the glass walls just as well as 
through less closed pa^ed atomic systems of gases. 


The velocities of the positive iona from a gas which 
is conducting electricity are insufficient, as we have 
said, to produce some of the effects of the swift alpha 
particles. The ions do, however, affect photographic 
plates and may, therefore, be easily studied. Sup- 
pose, for a moment, that all the ions which form the 
positive rays, from such a tube as that of Fig. 14, 
are of the same mass. They will differ in velocity 
because th^ have been formed at different points 
in the tube, have fallen through different potentials 

Fia. 16 
Parabolas formed on the plate, P, of Figure 14. 

and have suffered different coUisions. Because the 
beam of positive rays is not homogeneous in velocity 
the various particles which compose it will suffer 
different deflections under the influence of a field of 
force, whether magnetic or electrostatic. 

If a magnetic system is so placed as to deflect the 
particles upward some of them will be deflected but 
little, others more and the result will be a line of 
pomts on the photographic plate. Such a line is 
represented as ab in Fig. 16. If, now, an electro- 
static field is established which produces a deflection 
at right angles to that of the magnetic field, each 


component particle of the beam will be deflected, 
say to the rig^t, by an amomit which d^p^ads upon 
its velocily. The result is a smes of qiots whidi 
lie, as shown at mn of the figure, on a portion of a 

For positive ions of some different mass there will 
be formed on the photographic plate a different para- 
bolic curve, says pq. From the dimensions of these 
parabolas there may be calculated, as was first done 
by J. J. Thomson, the ratio of the masses of the 
types of particles which r^gist^ these curves. If 
the tube from which the positive rays are derived 
contains a mixture of gases the atomic (or molec- 
ular) weights of the various particles may be de- 
rived from the various traces on the photographic 
plate. If, however, the particles diff^ not only in 
their masses but also in the charges whidi they 
acquire by ionization, then the analysis becomes 
more complicated or even impossible. Two par- 
ticles, one having twice the mass of the other, and 
carrying twice the charge, wiU give the same trace 
on the plate for the method separates particles only 
when they differ in their ratios of mass to charge. 

In one of Thomson's experiments he studied at- 
mospheric air, which contains in addition to nilrogen 
and oxygen small amounts of ina*t gases like neon 
and argon. From the tap-grease which was used to 
seal the valves leading to the vacumn pump there 
was added to this mixture traces of carbon dioxide 
and carbon. In addition, since mercury was used in 
the pump, there was a trace of mercury vapor. In 
the photograph of the deflected positive ra3r8 from 

Flo. 17. Parabolas obtained in positive ray analysis by 3. J. 
Thomson, Neon gave two parabolas, A and B. (A retouched 
photc^aph of the illustration in the original memoir.) 

Fia. M. Moseley's phoK^apha of the X-ray spectra of various 
metallic anti-cathodes. The different photographs are placed 
approximately in register in the t^rc. 


this mixture of gases and vapors Thomson recog- 
nized molecules of nitrogen and carbon dioxide which 
had lost one electron; atoms of nitrogen, oxygen, 
carbon, neon, and argon which had lost one electron 
each; and atoms of mercury which had lost re- 
spectively one, two and three electrons. 

The appearance of the curve for neon was much 
like that of Fig. 17, which is not an exact copy of 
the original photograph but was retouched to ex- 
aggerate slightly a peculiarity of the original. 
Apparently there are two curves, A and B, close to- 
gether. From the more prominent curve, A, the mass 
of the particle was found to be 20 and from the other 
22. In this way the isotope of neon was discovered. 

The most recent and reliable series of analyses of 
the so-called chemical elements by the method of 
positive rays is that of F. W. Aston. He discovered 
isotopes of other chemical substances, like chlorine, 
which were formerly supposed to be elementary. In 
his method the electrostatic and magnetic fields are 
arranged so that their deflections occur subsequent 
to each other as the ray progresses instead of simul- 
taneously. The precision of his results is remarkable 
as compared to other positive ray analyses for the 
probable error of his determinations is only about 
one-tenth of one percent. 

Our present interest in his work is due to the fact 
that he not only isolated the proton, that is the posi- 
tive hydrogen ion — for Thomson had done this in 
his analysis — ^but he made for its mass a very precise 
measurement. Aston compared the mass of the pro- 


ton with that of the hydrogen molecule and the mass 
of the latter with that of the helium atom. 

You will remember that tiie ordinary chemical de- 
t^minations by weighing had resulted in atomic 
wei^ta of 1.008 for the hydrogai atom, twice as 
much for the diatomic hydrogen molecule, and 4.00 
for the helium atom. Aston's determinations are 
corroborative and indicate definitely that the mass 
of the proton, when free or when constituting the 
nucleus of a hydrogen atom, is eight-tenths of a per- 
cent greater than when it is combined with electrons 
in a nucleus. 

His method was as follows: If the photographic 
plate is exposed successively to impacts of ions of a 
given mass and to ions of twice that mass which, 
however, are deflected by an electrical field of twice 
the intensity, then the two traces should be coinci- 
dent and indistinguishable. If, on the other hand, 
the field is not quite doubled the line for the atoms 
of -double mass will lie very near but not coincident 
with that for the atoms of single mass. Similarly by 
taking a third exposure for the atoms of double mass, 
but using for deflection an electrostatic field as much 
greater as it had formerly been less, another line is 
obtained equally spaced on the other side of that 
recorded by the atoms of single mass. 

In applying this method he exposed a plate to 
positive rays containing molecules of hydrogen which 
had been ionized by the loss of an electron. Then 
using first slightly more than double the potential 
on the deflecting plates and second an equal amount 
less than this double potential, he obtained two 


records for heUum ions. These are shown in Fig. 
18a which is a drawing based on the photographs of 
his original paper. It is evident that the tra<5e for 
the hydrogen molecule is not midway between these 
bracketing lines as it would be if the mass of Hg 
•were just half that of He. On the other hand from 
Fig. 18b it is seen that the line for molecular ions, 
H2, is equally bracketed by the lines of tlie atomic 
ions, Hj. 

II Ml II 1 11 

He Ha He Hi H* Hi 

Fig. 18a Fia. 18b 

Drawing based on the positive ray photographs by means of 
which Aston compared the atomic weight of the hydrogen mole- 
cule with that of the helium molecule (Figure a), and of the 
hydrogen atom with that of the hydrogen molecule (Figure b). 

Since the work of Aston it becomes possible to 
speak definitely of an element of positive electricity, 
complementary to the electron, and when isolated 
equivalent in mass to the hydrogen atom. When 
the proton is not isolated it is apparently secreted 
in the alpha particles which are known constituents 
of the nuclei of the radioactive elements and by in- 
ference constituents of all others. In one case, that 
of nitrogen,^ there seems to be direct evidence that 
the proton is a constituent of the atomic nucleus. 
The evidence was obtamed during 1918 by Ruther- 

*In a letter to the Editor of Nature, March, 1^1, Rutherford 
announced similar phenomena for boron, fluorine, sodiiun, 
aluminum and phosphorus, and said. "While we have no ex- 
perimental evidence of the nature 01 these particles, except in 
the case of nitrogen, it seems likely that the particles are in 
reality H atoms." 


ford but he was in doubt as to whether it indicated 
a single proton or a particle composed of two such 

The isolated positive particles of which he ob- 
tained evidence were produced from nitrogen by 
bombarding its molecules with alpha particles. As 
it happens alpha particles have very definite ranges 
through which they wiU penetrate before losing their 
ability to produce scintillations. For each radio- 
active substance there is a thickness of normal 
«|tmosphere which its alpha rays can penetrate. For 
those from radium the range is 3.5 centimeters but 
for radium C it is twice as much. However, if the 
screen whereby scmtillations are to be observed is 
placed more than seven centimeters from radium C 
there are still occasional scintillations. These have 
been shown to be due to ions produced and driven 
forward by the impacts of the alpha particles with 
atoms of the gas through which they pass. For ex- 
ample, if the atmosphere is hydrogen scintillations 
are observable at a distance from the source effec- 
tively four times as great. 

According to Rutherford about one time in a hun- 
dred thousand an alpha particle will come so near 
to hitting the nucleus of a hydrogen atom as to 
propel it along the line of its own motion. His cal- 
culations show that smaller increases in range should 
result if the alpha particles are projected into other 
gases than hydrogen ; thus for nitrogen and oxygen 
the range in centimeters should be extended only 
from 7 to 7.8 and 9 respectively. From air, there- 
fore, there should be produced a few long-range 


particles which should not however be visible beyond 
about 9 centimeters. 

He found that the actual number of scintillations 
was in excess of that expected and that the range 
was practically that of the hydrogeti. particles. 
When pure nitrogen was substituted for air there was 
an increase of twenty-five percent in the number. 
Since, by volume, air is four-fifths nitrogen we 
should expect the effect in pure nitrogen to be five- 
fourths as large if it were solely a phenomenon of 
nitrogen. Rutherford showed conclusively that it 
was such ; but he was unable, with the small number 
of long-range particles which were formed from the 
nitrogen, to determine whether their atomic mass 
was 1 or 2. As he said, "From the results so far ob- 
tained it is difficult to avoid the conclusion that the 
long-range atoms arising from collision of alpha par- 
ticles with nitrogen atoms are not nitrogen atoms 
but probably atoms of hydrogen, or atoms of mass 
2. If this be the case we must conclude that the 
nitrogen atom is disintegrated under the mtense 
forces developed in a close collision with a swift 
alpha particle and that the hydrogen atoms which 
are liberated formed a constituent part of the nitro- 
gen nucleus." 

What becomes of the rest of the nitrogen nucleus? 
Nobody knows. The determination of the fact of 
its disint^ration was an experiment requiring a 
delicacy of operation, an imagination, and a persist- 
ence of which only a master is capable. If he failed 
to detect the by-product of the disintegration it must 
await other experiments in which alpha particles of 


greata* energy shall be used for bombardment. The 
guess may be made, however, that the nitrogen atom 
is disrupted into two long-range particles (protons), 
three alpha particles, and an electron.^ 

With the experiments of Thomson, Aston, Ruther- 
ford, and others we may, however, take as definitely 
settled a granular structure for positive electricity 
and an atomic nucleus composed of these grains in 
close combination with their complementary elec- 

* Rutherford, apparently, is inclined to believe that nuclei in- 
volve particles of mass 3 and charge 2 (that is, of three protons and 
one electron) which would form normal atoms, isotopic with 
helium (mass 4, nuclear charge 2). In this connection the work 
of W. D. Harkins is specially impOTtant. The latter has shown 
that for all known atoms (excepting atoms with only a transitory 
existence, such as those produced by Rutherford) the atomic mass 
and atomic number can be explained on the basis of a nuclear 
structure in which there are never less than half as many electron^ 
as protons. For atoms of even atomic number, the ratio is 
exactly %. Such atoms as analyses have shown are most abundant 
in meteorites and in the surface of the earth. They are apparently 
the stable atomic forms. Atoms of uneven atomic number have 
slightly higher ratios for the numbers of electrons and protons in 
the nucleus. Rutherford's nuclear corpuscles would have a ratio 
of 1/3, which is not in conformity with the other evidence. Until 
further evidence is presented the general reader may, perhaps, be 
safe in assuming atomic structures to be composed of alpha 
particles and in some cases to include extra protons. 




Experiments on the scattering of alpha rays by 
their collisions with the nucl^ of atoms in passing 
through thin sheets of metal early indicated an ap- 
proximate relationship of nuclear charge to atomic 
weight of one to two. The exact determination^ 
however, of the excess of protons in the nucleus of 
each type of atomic system was the result of work 
by Moseley and others who applied and extended 
his methods. To understand the experiments we 
must consider X-ray phenomena and the construc- 
tion of crystals. 

X-rays, or Roentgen rays as they were once called 
after their discoverer, arise from the impacts of a 
stream of swiftly moving eleclrons with ordinary 
matter, as, for example, with a plate of platinum. 
From the atoms which are struck by the electrons 
there proceeds a radiation which we now know to 
be identical with visible light except for the fre- 
quencies which are involved. 

Heat rays, light, ultra-violet rays, X-rays, the 
gamma rays which have been mentioned as some- 
times accompanjdng electron streams from radio- 
active substances, and the Hertzian rays used in 
radio-communication are all radiations of the same 



character except for differenoes in the frequenQr of 
the vibration3 from which they originate. Except 
for heat rays, which are believed to be due to mo- 
tions of atomic systems, and except for Hertzian 
waves which are due to the surges back and iiyrih of 
electrons in wire systems which are conducting alter- 
nating currents, all other radiations are due to 
vibrations of the electrical elements wiUiin atomic 

Vibration and oscillation are synonymous t^ms. 
Both imply that a body moves back and forth 
through an equilibrium position. The farther it 
moves from this position the greater is its tendency 
to return. A simple ca^e of oscillation is that of the 
pendulum bob of a clock. We start it by swinging 
it aside from its equiUbrium position and thus lifting 
it further from the earth. The tractation of earth 
and bob then results in a motion of the bob toward 
its unstressed position. As it swings back it moves 
faster and faster. When it reaches the bpttom of its 
swing it has an energy (kinetic) which is equal to 
that contributed in raising it, except, of course, for 
subtractions by friction with the air. By virtue of 
this kinetic energy it continues in motion. It can 
rise, however, only to the height of its original sepa- 
ration in the opposition direction. At any greater 
height it would have greater potentialities of energy. 
It rises, therefore, until the kmetic energy which is 
associated with it in the equiUbrium position is con- 
verted into potential energy. At this point it pauses 
and reverses its motion. The time required for one 
complete trip, that is the interval between two sue- 



cessiye motions in the same direction through the 
same point of its path, is called the period of its 
oscillation. The number of periods per second is the 

Oscillations in general are not restricted to a 


Pig. 19 
Illustrating oscillations due to three restoring forces. 

linear path as in this simple case where there is but 
a single restoring force, namely that of gravitation. 
Suppose, for example, that a body is constrained by 
forces which have components at right angles in the 
three directions represented by the springs of Fig. 19. 
If it is displaced from its equilibrium point in the 


direction of the arrow all three forces will be active 
in its restoration and it will execute the most gena:^ 
type of vibration. Its frequency, which is still de- 
fined as above, depends upon the inertia of the body 
and the nature of the restoring forces. 

In the case of molar bodies, like the pendulum of 
the preceding illustration, there is always a gradual 
dissipation of energy from the vibrating system to 
surrounding systems. Energy is given to the adja- 
cent molecules of the air and by them passed on to 
more distant molecules. If the frequency of a vibrat- 
ing mechanical system is within a certain range the 
vibratory motions of the air molecules may set up 
vibrations within the human ear which are recog- 
nized as sound of a definite pitch or vibration-fre- 
quency. Above 20,000 vibrations per second, how- 
ever, the vibrations are usually inaudible for the 
human ear is but little sensitive outside the impor- 
tant frequency range of the human voice which ex- 
tends from about 200 to about 5000. 

Between the vibrations of molar bodies, which are 
observed as sound, and those of electrons witiiin 
atomic structures, which are observed as light, th^e 
are several important difiPerences. In one case the 
vibrating litems are aggregates of molecules and 
in the other discrete electrons. The restoring forces 
are usually due to elasticity in the case of sources 
of sound, and hence to intermolecular forces, but 
for light they are intra-atomic. The medium by 
which energy is transmitted from the vibrating 
source is molecular in one case; in the oth^ it is at 
best a mere postulate, as to which more shall be 


said later. The frequencies involved in sound are 
expressed in hundreds or thousands, while those for 
light are expressed in millions of millions, extending 
from 375 million million at Hie red end of the visible 
spectrum to 750 million million at the violet end. 

The difference, however, which is most incompre- 
hensible is that involved in the phenomena of ab- 
sorption and emission of energy. When a violin string 
is set into vibration the energy with which it starts 
depends upon what energy was contributed to it in 
producing its initial displacement. As the string is 
continuously displaced there is added continuously 
the energy with which it shall engage in vibration. 
In its subsequent vibration this energy is continu- 
ously dissipated in truly infinitesimal amounts to 
the surrounding molecules. Both the absorption and 
the emission of energy are conceived aa contmuous 
phenomena, just as if there was a flow of a fluid 
energy which is infinitely divisible. 

There is no such phenomenon as occurs in our 
money economy where human energy is conceived 
to be expended in quantities adequately represented 
by monetary units. Our stored energy grows by 
dollars or by pennies but the energy of the system 
we are considering increases or deceases continu- 
ously by amounts which are infinite! / small parts of 
any of our usual units for energy. 

In the case of electronic oscillators, on the other 
hand, there is evidence that they emit energy only 
in definite quantities the values of which depend 
upon the frequencies of their oscillations. Wheth^ 
or not the operation of absorbing energy also takes 


place discontinuously by similar units is still de- 
batable and awaits further evidence. It may be that 
the elecUx>nic systems can absorb continuously in 
infinitesimal amounts but can emit only discon- 
tinuously in definite "quanta," just as warlike na- 
tions may tax the tiny energies of their citizens to 
expend in dreadnoughts. 

Unlike the vibrating systems of mechanics, 
whether actual or theoretical; the vibrating systems 
of the electrons within an atom do not radiate 
energy continuously but emit it in definite quanta. 
According to liie present accepted picture the elec- 
trons may vibrate in orbits without loss of energy to 
surrounding i^stems. (This in itself is an argument 
against an all-embracing ethereal medium, for if it 
M4,'P ^ f> was capable of absorbing energy at all from a vibrat- 
ing electron we should expect it to do so contmu- 
ously.) When, however, there is a change in the 
orbital motion of an electron, then a quantum of 
energy is shot out. This quantum travels with the 
enormous velocity of 30,000 million centimeters a 
second, that is with the velocity of light. 

The quantum itself is not a unit of energy but 
rather a specific amount. It is specific for any given 
frequency of vibration and in terms of the ordinary 
unit of energy is numerically equal to the product 
of the frequency by a fixed number, known from 
the originator of Ihe "quantum theory" as "Planck's 

For any type of atomic system there appears to 
be a fairly large number, for example nearer to a 
hundred than to ten, of possible orbits for the planet- 


ary electrons. Radiation occurs when an electron 
passes from a less stable to a more stable orbit. By 
interactions with other atomic systems, if they are 
in violent motion, or with swiftly moving electrons, 
a planetary electron may be displaced into a less 
stable orbit. During its return energy is radiated. 

Violent interactions give rise to higher frequencies 
than do those which can contribute less energy. The 
gamma rays from radioactive substances and the 
X-rays which arise from impacts of swiftly moving 
electrons with atomic systems have the highest fre- 
quencies so far observed. 

As to their relations of energy and frequencies 
more will be said later after considering the physical 
means for the production of X-rays. The latter may 
always be produced when a stream of electrons im- 
pinges on a plate, provided that the individual elec- 
trons have siifficient kinetic energy. In the original 
X-ray tube the electrons were obtained in the form 
of a cathode stream which arose from the cathode 
as the result of its bombardment by positive ions. 
The modem X-ray tube avoids the difficulty of con- 
trol which is inherent in the use of a gaseous 
conductor and obtains the cathode stream by thermi- 
onically emitting electrons in a manner similar to 
that described for another vacuum tube device in 
Chapter VII. 

The Coolidge X-ray tube, in which this principle 
is applied, is shown in Fig. 20. A spiral timgsten 
wire, C, serves as the cathode and is heated by pass- 
ing through it a current from a battery. The anode, 
il, is a massive block of tungsten. The anode is 



maintained positive with respect to the cathode by 
a source of w&y high potential There is thus drawn 
across the intervening vacuum a stream of swiftly 
moving electrons which are furtha: encouraged to 
focus upon the auode by enclosing the cathode in a 
tube of molybdenum, shown in cross section at M. 


FzG. 20 

Cross-section of Coolidge X-ray tube. Electrons, thennionicaUy 
emitted from the cathode, C, are drawn across the highly evacu- 
ated space to the anti-cathode, A, from which X-rays arise. High 
voltage is applied between + and — . 

The electrons of this stream violently displace 
from their orbits some of the electrons of the atoms 
upon whidi they fall. The bombardment appar- 
ently affects not only electrons more or lees loosely 
held in the outer shells of the atoms — ^those whidi 
account for valence and ionization — but affects also 
electrons in the inner shells. These are displaced to 
new orbits from which they return to their original 
onea The return is accompanied by an emission 


of energy. Because these inner electrons are closely 
bound by the nucleus the restoring forces are large 
and the frequencies high^ in much the same way that 
tightening a violin string increases the pitch of the 

For X-rays the frequency may be twenty thousand 
times that of visible light, which is apparently pro- 
duced by electrons further from the nucleus. On 
the other hand, even hi^er frequencies are obtained 
when the displacement of an electron is caused by 
the ejection of a beta particle from the nucleus it- 
self. For gamma rays which arise in this way the 
frequencies are ten to a hundred times as hi^ as for 

The emission and absorption of X-rays are com- 
plementary phenomena. As just stated, their emis- 
sion results from the displacement of electrons by 
foreign electrons which violently intrude into the 
inner circles of the atom. When, in turn, these 
X-rays impinge upon atoms they eject electrons and 
disturb the quiet orbital motions of the inner circles. 
Two different phenomena are, therefore, involved 
when a body is exposed to X-rays, first, the ioniza- 
tion of some of its atoms, a ph^iomenon which will 
be discussed later in connection witii other cases of 
ionization by radiant energy, and, second, the pro- 
duction of orbital changes which are of the same 
general character as those occurring in the atoms of 
the anode from which the rays arose. 

The second phenomenon is one of re-radiation. 
The electrons of atoms which are exposed to X-rays 
are displaced from their normal orbits and in their 


return they radiate en^^. The X-rays whidi arise 
from a body exposed to X-rays are so-called second- 
ary X-rays. The re-radiation may involve X-rays 
different from those incident upon the body. Some 
of the re-radiation will be of the same character as 
the original X-rays whidi are then said to be ^'scat- 
tered" by the body. 

The last term is well diosen^ since ord^ly reflec- 
tion, to which we are accustomed in the case of 
polished niirrors and li^t rays, does not occur. Such 
reflection is possible only if the surface irregularities 
of the Fleeting body are negligible in comparison 
to ''the wave length/' so-called, of the incid^it radia- 
tion. By wave length is meant the distance whidi 
radiant energy travels during eadi pmod of the 
vibrating source. For X-rays this distance is just 
about half the diameter of an ordinary diatomic 
molecule. No surface, tha:^fore, can be smooth to 
X-rays and reflecting in the ordinary sense. For 
this reason the re-radiation of X-rays is usually 
irr^ular and disorda'ly. 

It was pointed out, however, by Laue in 1912 that 
X-rajrs would be reflected in an (ntl^ly mann^ by 
Ihe regularly spaced molecules of crystals^ and fur- 
ther that by this means the wave l^igth of various 
X-rays could be det^mined, provided that the dis- 
tances between the molecules of the crystal were 
known. The experimental method was pa^ected 
shortly after by W. L. and W. H. Bragg. 

The principle involved may be explained by the 
following analogy: Imagine the points in fig. 21 
to represent widely separated gjrmnasts who are to 


perform identical sequences of motions at the orders 
or counts of a distant captain, C. Because the energy 
vocally emitted by the captain takes a finite time to 
travel to the gjrmnasts each receives the order an 
instant later than his next neighbor who is nearer 
the source. Therefore, they do not perform in step. 
Suppose that each gymnast counts aloud as he 
executes the characteristic motions. There will be 
some point, as X, where an auditor would hear" the 
counting of all as if they were actually counting in 
unison. This point must be so located that the time 

Fia. 21 

Diagram to show the principles involved in the spectral analysis 

of X-ra3rs by a cr3rstal grating. 

required for the sound to travel over the path aX 
is greater than that for the path bX by just the 
amount of time which gymnast b is behind gymnast 
a in his counting. On either side of X the auditor 
will receive a jumble of unintelligible and interfering 
sounds. At X, however, the sounds reenforce each 
other. If the gymnasts are mechanically perfect in 
their tasks and in their rhythm the point X will be 
sharply defined by absolute silence on either sidQ 
of it. Such precision is attainable in tiie case of 
electronic gymnasts. 
There will be other points also, like X' and X", 



whare there will be similar sharp maxima of re- 
radiated en^gy. The first of these will be the point 
where the counts heard from a are one whole series 
behind those of b. Under these conditions the dis- 
tance aX' is a whole wave length greater than the 
distance bX\ % 

The actual location of these points depends upon 
the wave length of the radiant energy and upon the 


Fig. 22 

Representation of a cubic crystal. If the crystal is that of 
common salt, sodium atoms are as represented l^y black circleB 
and the chlorine atoms by light circles. 

spax^ing of the re-radiating center& If the latter is 
known the wave length may be determined. Now 
in crystals of certain types, namely cubic, only cer- 
tain relatively simple arrangements of the molecules 
are possible. For example. Fig. 22 shows the simple 
arrangement for NaCl and similar substances. The 
molecules, however, are diatomic and the crystal 
structure is built primarily with reference to the 


atoms, as we would expect from our knowledge of 
the opposite valence of sodium and chlorine. Adja- 
cent to each atom of sodium is one of chlorine. The 
black circles in the diagram represent the sodium 
atoms and the other circles the chlorine atoms. 

Each atom of each kind must be shared by eight 
small contiguous cubes, which are indicated by 
dotted lines. However, each small cube has asso- 
ciated with it four atoms of each kind. We are, 
therefore, correct m assigning to each small cube 
of a rock-salt crystal four-eighths of the mass of each 
kind of atom. From a knowledge of the mass of 
each type of atom and from the measured mass and 
volume of such crystals very accurate data are made 
available as to the dimensions of these small cubes. 

Measurements of the tiny wave lengths involved 
in X-rays are, therefore, made possible by the use 
of crystals for which the dimensions of the "lattices" 
are known. The frequencies corresponding are then 
obtainable by simple arithmetic. 

In sudi measurements the crystal is merely a por- 
tion of the instrument and there is no further con- 
cern with the physical mechanism whereby it 
operates. Such was the use to which Moseley put 
crystals in his famous investigations of 1914 before 
his life was sacrificed to a World War. He used the 
crystal grating which we have described above for 
the determination of the characteristic X-ray fre- 
quencies of various substances. The oscillators of 
the crystal will respond to radiations of a wide range 
of X-ray frequencies and re-radiate the same fre- 
quency as that with which they are excited. 



Substaaoes, however, which give rise to primary 
X-rays, instead of secondary, that is those which are 
bombarded by electrons, emit rays which have fre- 
quencies characteristic of their atomic structure. 
Each t3rpe of atom emits a characteristic group of 
X-rays. For example, when silv^ is used as the anti- 
cathode of an X-ray tube the point X' of Fig. 21 
appears not as a single point but as two near-by 
points, for two slightly different frequencies of X- 
rays are simultaneously emitted. 

Fig. 23 

CrofiSHsection of an X-ray spectrometer. X-rays from the anti- 
cathode, F, pass to a crystal grating, C. The spectrum there 
formed is detected by a photographic plate, mounted beyond Uie 
screen, i>. 

In the examination of X-rays by means of a 
crystal, instead of using a point source as in Fig. 21, 
a narrow line source is used. To obtain such a source 
the X-rays from the tube are cut off by lead plates 
in which there are slits, shown in cross section at 
A and B in Fig. 23. A narrow rectangular beam is 
thus allowed to fall on the crystal C of this figure. 
The crystal may be rotated, sa may also the tube 
marked D. The re-radiated beam traverses this tube, 


passes through another slit in a lead plate and falls 
upon a photographic plate. 

Moseley took photographs successively of the 
X-radiation from various types of anti-cathodes. 
Some of these are reproduced in Fig. 24 (Plate II, 
opposite p. 108). 

A series of similar photographs taken by Si^bahn 
are reproduced in Fig. 25. (Plate III.) Consider 
the left-hand series. As the substance from which 
the rays are emitted is changed from arsenic (As) to 
selenium (Se), or from rubidium (Rb) to strontium 
(Sr), there occurs the same shift in the spectrum 
which is of common characteristic form for all the 

This particular spectrum is that of the K type of 
X-rays. Of the different t3T)es more will be said 
later. For the present it may be noted that they 
differ in their origin, and that the K type is excited 
only by more swiftly moving electrons than will give 
rise to the L tjrpe. Characteristic spectra of the L 
type are shown on the right-hand side of Fig. 25. 

For both types there was found a simple relation- 
ship between the frequencies of the characteristic 
radiations of a large number of elements. The fre- 
quencies progressed according to a simple rule as 
successive elements in the periodic table were ex- 
amined. When the elements were arranged in order 
of their characteristic frequencies it was found that 
each was obtainable from its predecessor by simple 
addition. Apparently each element of the periodic 
series differs from the next lower by the addition of 
a definite amount of electricity which is accom- 



paoied by an increase in frequ^icy of the charac- 
teristic radiation. It is the nuclear charge which 
increases and thus gives rise to greats restoring 
forces and more rapid vibrations when the inner 
electrons are displaced. 

Moseley's discovery of a simple numerical rela- 
tionship between charactmstic frequencies did not 
involve measurements on all the known elements. 
Below aodium^ for example, there are ten elements 
for which no X-ray spectra have yet been obtained. 
The inert elements also must of necessity be omitted. 
Thus you will notice that krypton (atomic number 
36) is omitted in Fig. 25. His work and conclusions, 
however, have been corroborated by many other 
tests and may be considered the first definite proof 
of the structure of the atomic nucleus by grains of 
positive electricity (protons). 

Part of the corroboration has come from measure- 
ments on the characteristic absorption which ele- 
ments show for X-rays. This work was done in 1916 
by DeBroglie although the discovery of sudi absorp- 
tion dates from Barkla's work in 1909. 

In an X-ray beam there is present, in addition to 
the characteristic frequencies which arise from the 
vibrations of electrons within the atoms of the anti- 
cathode, more or less radiation of other frequencies 
below those which are characteristic. A haphazard 
jmnble of disturbances of all d^rees of suddenness 
accompanies the impacts of the various electrons of 
a cathode stream. These are analysed by the crystal 
spectrometer into a consecutive s^ies of recurring 
disturbances which then have the appearance of 







radiations of definite frequencies. A continuous 
spectrum is thus formed. The appearance, however, 
is due entirely to the regularity of structure of the 
crystal or other instrument of analysis and is not 
inherent in the X-rays themselves. 

. The amount of this general or so-called "white" 
radiation is relatively small and does not obscure 
the more pronounced characteristic radiation. At 
the top of Fig. 26, for example, there appears a 
photograph of the X-radiation from tu^gsten as 
taken throu^ a crystal spectromet^, like that of 
Fig. 23, except that the slit D is omitted so that a 
wide range of frequencies may reach tlie plate. In 
addition to the continuous spectrum of X-rays two 
series of characteristic lines are visible, namely, the 
K series near the central black band, and the L series 
further to the right. 

The central black image corresponds to X of Fig. 
21. Each of the other lines corresponds to X' of this 
figure for there is a different location of X' for each 
frequency involved in the beam of X-rays. The 
separation of X and each X' is greatw ^ the smaller 
tie frequency of the vibratory motion which the 
crystal spectrometer is detecting. For tungsten with 
its high atomic number of 74 the K lines are due 
to radiations of correspondingly high frequency and 
are very close to the central image. The L series 

* In the photographs of Fig. 25 the central image corresponding 
to X appears at the extreme left. Prom these, it is seen that the 
higher the frequency, that is the higher the atomic number, the 
closer to the central image will be the spectral line corresponding 
to X'. 


which have about one-seventh the frequencies of 
the K lines are well separated from the oeat&r. 

The second photograph of Fig. 26 was made by 
ins^ting in the path of the X-rays from tungsten a 
thin sheet of molybdenum. The K lines are no 
long^ visible. In fact, above a definite f requ^icy all 
the radiation from the tungsten has been absorbed 
and for a c^tain region to the ri^t of the central 
image, the photographic plate has been unaffected. 
If antimony, of atomic numba: 51, replaces 
molybdenum, of atomic number 42, the absorption 
band does not extend to as low frequencies. In gen- 
eral it has been found that the limiting frequencies 
at which absorption b^ins are sharply marked, • are 
diaracteristic of the atom of the absorbing material, 
and increase with the atomic nimiber. 

Before carrying the discussion further an explana- 
tion must be given for two edges of li^t and dark 
which occur in the first photograph of Fig. 26. These 
are marked Ag Ka and Br Ko. They are the 
boundaries of absorption for silver and bromine. 
They were obtained by inserting a thin film in- 
volving atoms of these substancea X-ray absorp- 
tion is a function of the electrons withm an atom and 
hence without prejudice an atom may be a partner 
in any sort of molecular union. In this particular 
case the film of silver bromide, AgBr, was the sensi- 
tized film of the photographic plate itself. 

An element will absorb radiation of frequency 
higher than that of its own characteristic X-ray 
radiation. If, therefore, a given radiation is im- 
pressed successively upon the elements of the 

Fic. 26. X-ray absorption spectra. The upper photograph 
shows X-raya from s tungsten anti-cathode. The lower photo- 
graphs show absorption of this radiation by plates of molybdeniiin, 
cadmium and antimony. (Reproduced from memoir of DeBrogiie.) 

Fig. 28. The path of an X-ray through humid atmosphere It 
is marked by the ionization trails of the electrons which it ejects 
from the gas molecules. (Reproduced from memoir of C T R. 

Fig. 31. A line spectrum of hydrogen. The hydrogen spectrijm 
ia bracketed by an iron spectrum which furnishes a comparieon^ . 
scale. (A section of photograph from memoir of H. B. Lemon.): : 

* •< 

to * 



periodic table there will be absorption by all elements 
of atomic numbers lower than that from which the 
radiation arises. 

The phenomenon is further illustrated in Fig. 27. 
A series of elements were exposed to the K radiation 
of nickel (atomic number 28). For each element 
the height of the curve represents the absorption. 

40 80 120 160 200 

Atomic Weight of Absorbing Element 

Fia. 27 

Relation between absorption of X-rays and atomic weight of 
absorbing element. The K type radiation from Ni (atomic 
weight 58.7) was successively impressed upon various elements. 
For elements below Ni it excited K, L and M radiations. For 
elements of extremely high atomic numbers it excited only M 
radiations; for the intervening elements L and M radiations. 

In each of the elements below nickel there is an 
absorption of the K radiation from nickel, for in 
each element the X-ray energy is absorbed by the 
electronic systems which then vibrate naturally to 
give oflF their own radiation, not only K type but also 
L and M types. The higher the atomic number 
the greater the Amount of energy required to emit 
the characteristic radiation and hence the greater 
the absorption. 


When nickel is reached^ absorption abruptly ceases 
so far as it is due to energy whidi is convai;ed inta 
characteristic K radiation. There remains, how- 
ever, a cause of absorption in t^e L and M types of 
radiation. These vibrations are of low^* j&requency 
and require less energy. As elements of still higher 
niunbers are examined the absorption increases. The 
''rare earth" elements have not been examined, so 
that for this r^on the probable form of tiie curve is 
indicated by dots. For some element in this range 
the nickel radiation is unable to excite the L series 
but may excite a series of still lower frequencies 
known as M. Again the absorption mcreases as in- 
dicated in the figure. 

Studies of absorption phenomena by DeBroglie 
and others are largely responsible for our knowledge 
of the atomic numbers of the elements of higher 
atomic weight. A great deal of evidence, however, 
besides that which has been presented in this chapter, 
confirms the modem physicist in his concept of 
atomic numbers. 



In one of Stevenson's fables the charactet^ of 
"Treasure Island" come forth between chapters to 
discuss the author's plans for them. For writers of 
less ability the characters adopt tactics of heckling 
between chapters. In the preseni book there are 
only two characters if one does not include the form- 
less and intangible spirit of energy. The burden of 
their complaint is the author's selection of their 
characteristics. For some time Proton and Electron ^ 
have been objecting that they were incompletely 

Proton and Electron: Why haven't you told how 
large we are? 

Author: I have by implication. You are too 
small to see anyway. 

Electron: We don't believe you know. 

Author: What if I don't know exactly? You can't 
be greater in diameter than 0.000,000,0 — 

Voice of Energy: Stop! You are not paid by 
space rates. If you will degrade me and decrease 
my availability, wasting wood pulp by liie page, re- 
fusing even to make the small conservation of my 
potentialities which simplified spelling offers, you 
might at least stop writing noughts. Can't you use 
powers of ten? Write it as 2X10-" or a^ 2/W\ 

Author: Yes, I know; but it will make my pages 



look mathematical and inhibit the General Reader. 

General Reader (by ether waves): Don't mind 
me; I am about throu^ with you anyway. 

Scientific Reader (thrcmgh the same hypothetical 
medium) : I am through with you, too. You have 
approached the subject in an (Hxler which is imprac- 
ticable for pedagogical purposes, starting with im- 
known electrons and then describing how they wane 
discovered. Just take your laist chapter. You beat 
all around the subject and didn't say that what 
Moseley found was a proportionality between the 
square root of the frequency and the atomic number. 

Voice of Energy: Don't mind that fellow. I am 
the only important entity in the entire physical uni- 
verse. He doesn't really know me. He speaks of 
me glibly at times but when he gets into a pinch he 
says its due to some kind of a force — that's his way 
of referring to me when I am getting a bit run down. 
Now, as to you. You tell me when you are going to 
give me a whole chapter to myself. You are ready 
to do it now. In fact, you got yourself in for it by 
flirting with my Quanta in the last chapter. 

Electron: Oh! please, Father Energy, you know 
how my every motion conforms to your first and 
second laws. Don't insist. I feel sure he was going 
to discuss emission spectra of lower frequencies and 
then he would be discussing oscillations within the 
visible spectrum. And you know I just love to be 
seen of men. Or, perhaps he was intending to de- 
scribe how swiftly I can fly when I receive from 
X-rays or ultra-violet light just one tiny quantum. 
And you know. Father Energy, he couldn't write 


half a chapter on the photo-electric effect without 
saying something about these quanta in which you 
are so much interested. 

Proton: That argument cuts both ways. Why 
shouldn't he treat us both alike? You know its our 
joint motion as atoms to which he referred once as 
thermal agitation. If he will write now about that 
subject he can't get far without introducing quanta. 
Father Energy himself knows that Planck's theory 
of quanta might never have received the attention 
it has if Einstein hadn't applied it to the problem 
of specific heats. If he starts with the motion and 
energy of molecules and atoms he is bound to give 
more ideas of their sizes and to explain how scientists 
know how many molecules there are in any volume 
of gas, and what Avogadro's constant is, anjrway. 
And then he can't help emphasizing my point that 
even if you are larger than I am, stiU I am much 
more massive. 

Electron: Yes, you are more massive, but what 
he said about you was that you had 1845 times as 
much inertia as I had. I don't believe he appreciates 
personalities like yours with too much inertia. 
Didn't he give you a new name? That shows he's 
radical and insulted you, too, hanging on you one 
of those newfangled names which some Engilish 
scientists have only just suggested. If he thought 
so much of you why wasn't he respectful enough to 
call you a "positive electron" as all good scientists 

Voice of Energy: Stop quarrelling. You are dis- 
sipating energy. All that you have said merely 


fiihows the close interrelation of any one phenomenon 
of physical science to a large number of others. What 
does it matter to whidi portion of the subject he 
jumps next? Don't you realize that radioactive 
phenomena and now my quanta have shown that 
nature proceeds per witumf Really, it isn't nearly 
aa important where he jumps as how he lands. 

Proton: Do you mean that I must go back and 
live with this electron in some dark atomic struc- 

Electron: If it isn't dark my activities will pro- 
vide the light. 

(Exeunt Proton and Electron.) 

Author: Well, they're gone. But what was that 
last remark of Energy as to how I am going to land? 




Two phenomena are observable when X-rays im- 
pinge upon a substance. X-rays are re-radiated and 
electrons are ejected. The first phenomenon, which 
was discussed in the last chapter, has served to estab- 
lish the quantitative relations between the nuclei 
of different types of atomic ^yBtems, It is charac- 
teristic of radiant energy of all frequencies. Ac- 
cording to the frequency of the original vibration 
and according to the oscillating systems of the sub- 
stance upon which it falls, radiant energy, whether 
li^t or heat, is absorbed and re-radiated with or 
without change of frequency. Of re-radiation with 
change of frequency an illustration in the visible 
range of frequencies is furnished by so-called fluores- 
cent substances. 

Just as substances exposed to X-rays give off their 
own characteristic vibrations when these are of lower 
frequency, so fluorescent substances when exposed to 
the invisible ultra-violet radiations will give off 
visible radiations. Electric arc-lights are quite rich 
in ultra-violet radiations, so that fluorescent sub- 
stances exposed to such light will glow with their 
characteristic radiations. The effect is easily ob- 



served also with simlight, if a beam is allowed to fall 
on a glass vessel of k^x>sene. If the vessel is viewed 
at right angles to the beam the charactmstic blue 
fluorescence of the k^osene may be obs»*ved. 

The second phenomenon^ that of the ejection of 
electrons, is also charactmstic of all radiaticAis within 
certain limits of frequency. Gamma rays, X-rays and 
ultra-violet li^t will all eject electrons from the 
substances upon which they fall. The limiting fre- 
quencies below which such ejection cannot occur lie 
in the range of ultra-violet and even visible li^t and 
depend, as we shall see, upon the atomic ^jrstems of 
the substance. 

A picture of the phenomenon as it occurs in the 
case of X-rays may be quoted from a popular lec- 
ture^ by Sir William Bragg. "Suppose that the 
target (anti-cathode) of an X-ray bulb were magni- 
fied in size until it was about as great as the moon's 
disk, that is, magnified a hundred million times. The 
atoms in it would be spheres a centimeter or so in 
diameter, but the electrons (and the nuclei, as well) 
would stiU be invisible to the naked eye. The actual 
distance from earth to moon would now correspond 
roughly to the corresponding magnification of the 
distance that ordinarily separates the bulb from the 
observer's apparatus (the substance under examina- 
tion). We now shoot electrons (a cathode stream) 
at the moon with a certain velocity. Let us say that 
every second, each square foot or square inch, it 
doesn't matter which, receives an electron. A radia- 

* The Twelfth Kelvin Lecture before the Institution, of Elec- 
trical Engineers, 1921 (not literally quoted). 


tion starts away from the moon, which immediately 
manifests itself by causing electrons to spring out 
of bodies upon which it falls. They leap out of 
the earth, here one and there one; from each square 
mile of sea or land, one a second or thereabouts. 
They may have various speeds but none exceed, 
although some will just reach, the velocity of the 
original electrons that were fired at the moon. That 
reduced again to normal size is the process that goes 
on in and about an X-ray bulb. It is part of a 
universal process going on wherever electron or wave 
falls on matter and is one of the most important and 
fimdamental operations in the material world.'' 

The electrons which are ejected when an X-ray 
passes through a substance start off with speeds and 
energies like those of the cathode rays whidh origi- 
nated the radiation. As they pass through the sub- 
stance they disturb other electrons and hence ionize 
large nxunbers of the atoms. Except for such dodging 
as may be required to avoid adjacent systems the 
ejected electrons move at ri^t angles to the direc- 
tion of the beam. Their paths have been photo- 
graphed by C. T. R. Wilson, using his discovery of 
cloud formation in humid atmosphere. In Fig. 28 
is shown the path of an X-ray through a gas. It is 
marked by the activities of the electrons which it 
ejects. Their trails of ionized atoms, as shown by 
the drops, start at right angles to the path of the 
ray, which is lengthwise through the center of the 

The phenomenon of the ejection of electrons, when 
the exciting radiation is ultra-violet or lies within the 


visible range, is known as the photo-electric effect. 
It promises to be of wide scientific interest, for it is 
apparently the cause of photo-chemical effects like 
those utilized in photography, of photo-synthesis in 
the formation of carbohydrates in plant life, and 
even of the effect of light on the retina of the eye. 

When light of a certain minimum frequency is 
incident upon a substance electrons may be ejected. 
The phenomenon was first noticed by Hallwachs in 
1888, who found that a metal plate became posi- 
tively charged, or lost its negative charge, if it w^:^ 
originally n^ative. This is what should happen if 
electrons are emitted by the plate. 

Present-day theories as to this effect are the re- 
sult of observations by a large number of experi- 
menters, to which a valuable addition was made by 
Einstein in terms of the quantum theory. This 
theory, which received some mention on page 119, 
was propounded by Planck about 1901 to explain 
certain phenomena of radiation with which we shall 
deal later. In 1905 Einstein applied it to photo- 
electric effects and predicted that the emission of 
electrons would conform to a simple relation. 

He assumed that the electron, which is emitted, 
leaves the metal as the result of its absorption from 
the incident radiation of one quantum of energy. A 
quantum, as has been said, is a small amount of 
energy, numerically equal to the product of Planck's 
constant, h, and the frequency, n, of the radiation, 
and hence symbolized as hn. The energy with which 
the electron leaves the surface is lees than the ab- 
sorbed energy, hn, by the amount expended in get- 


ting free from the atom, much as the energy of a 
bullet at the muzzle of a gun is less than that con- 
tributed to it by the explosion because of the 
frictional losses in the barrel. For any substance 
there will be, then, a frequency of radiation, Uq, such 
that the quantum contributed to the electron just 
represents the energy required to set it free of its 
former associates. For a quantum at this frequency 
it becomes free but is too exhausted to move beyond 
the threshold. For any exciting frequency, as n, 
which is higher than this threshold frequency, Uq, the 
electron wiU have a net balance of kinetic energy 
which it may expend beyond the confines of its 
atomic home. This balance is always equal to the 
diflference of two quanta, one of value hn and the 
other hnQ, 

This is Einstein's relation. At the time he made 
his prediction there was no experimental evidence 
that the kinetic energy with which electrons are 
emitted should increase proportionately with the 
frequency, n, of the light. The relation has been 
verified since and this successful application of the 
quantum theory is strong evidence for the correct- 
ness of the hypothesis of quanta. 

One of the most exhaustive investigations^ of Ein- 
stein's expression was carried out by Millikan. Not 
only did he verify the relationship but he obtained 
from his experimental data a very exact value for 
Planck's constant, h. He measured frequencies and 
energies and hence h, the other magnitude involved 
in the relationship, was determined. The fact that 
it was constant, independent of the frequency of 


the exciting lig^t, was the proof of the correctness 
of the relation under examination. The method fol- 
lowed was essentially that of previous investigators 
of the photo-electric effect. The accuracy of Milli- 
kan's determination of h lies partly in the precision 
of his obs^vations and partly in his use, for the 
calculation of h, of the modem value for the charge 
represented by an electron, which he had determined 
by the oil-drop method. 

The quantity of electricity represented by an elec- 
tron enters into the relationship because of the ex- 
perimental method which was followed in determin- 
ing the en^^ of the emitted electron. Suppose the 
plate or electrode which is to be exposed to the radia- 
tion is made positive with respect to its surroundings 
by connecting between them a battery. The plate 
then starts with a deficiency of electrons and its sur- 
roundings have an excess. If an electron is moved 
from the positive plate to a nearby object it wiU 
acquire a certain amount of potential energy. In 
order that it shall of itself perform s)idi a motion 
it must leave the plate with a kinetic en^gy at least 
equal to this potential energy which it will have at 
the completion of its journey. By adjusting the 
potential applied by the battery to a value just be- 
yond the possibilities of the emitted electron the 
latter may be just prevented from reaching any 
of its n^ative surroundings. The value of the po- 
tential energy of an electron on the negative body 
then measures the kinetic energy of the emitted 

Into the evaluation of this potential energy there 


enters the charge on an electron. You will remem- 
ber that for simplicity we took the electron as the 
unit of electricity and the potential energy of an 
electron as the miit of electrical potential. The pres- 
ent accepted units of charge and potential were 
adopted, however, before the electron was discovered. 
The unit of electrical potential is the potential 
energy of unit charge, but unit charge is not the 
electron. Hence, to express the potential energy of 
an electron in the accepted units one must know the 
relation between imit charge and the electronic 
charge. This relationship Millikan had determined 
very accurately by the method described on page 94. 

The photo-electric experiment was performed in 
a highly evacuated vessel for collisions with gas 
molecules would mask the effect. The substances 
used were the alkali metals, lithium, sodium, and 
potassium, which are very markedly electropositive. 
Their atoms each have one more electron than is 
desirable for a stable configuration and probably 
for this reason they are most sensitive. They will 
respond to the frequencies of the visible spectrum 
as well as to the ultra-violet frequencies. 

Cylindrical plates of these materials were mounted 
as shown in Fig. 29, so that one at a time could be 
studied. By magnetic control from outside the ves- 
sel a plate could be turned to the knife S, which re- 
moved a thin paring and left a fresh surface. The 
plate with its clean surface was then turned into con- 
tact with electrode C, so as to determine what por- 
tion of its potential was due to the so-called "con- 
tact electromotive force," that is to differences in 



potoitial which are ahrays pre&eaat between 
lar gubstanoes. It was thai turned to face the wire 
gauze cylinder G, which effectively constituted its 
surroimdingB. Whether or not any electarons reached 
this cylind^ was determined by observing an elec- 
trometer connected to it at B. 

Fia. 29 

Croae-eection of Millikan*s apparatus for measuring photo- 
electric emission. Light entering at O ejects electrons from the 
disc Na. If these reach the wire gauze cylinder, G, a deflection 
is produced in an electroscope connected to the terminal B. 

The value of h which was obtained will be given 
in the Appendix with other important physical 
magnitudes, since statements of magnitude involve 
choices of units and in the case of scientific units con- 
siderable explanation is usually required. 


Millikan also verified a phenomenon, first ob- 
served by Lenard in 1902, which was implicitly 
covered by our earlier discussion of Einstein's appli- 
cation of the quantum theory to photo-electric emis- 
sion. The energy with which the electron is ejected 
depends only upon the substance and the frequency. 
It is independent of the intensity of the light which 
causes the ejection. If the light is intense more 
electrons are emitted but none leaves with greater 
energy. This same phenomenon also occurs in the 
case of X-rays and of gamma rays. The amount of 
light determines the number of electrons which are 
ejected but does not affect their individual energies. 

For X-rays the converse phenomenon has been in- 
vestigated. Duane and Hunt and also Hull have 
studied X-ray radiation and found that the highest 
frequency in the general or "white" radiation corre- 
sponds to that which should arise according to the 
quantum theory. The product of this highest fre- 
quency by Planck's constant is always equal to the 
energy of the individual electrons in the cathode 
stream which causes the radiation. 

Prom all these experiments it seems certain that 
whenever electronic impacts give rise to radiation 
the energy associated llierewith is always propor- 
tional to the frequency and the factor of propor- 
tionality is Planck's constant, h. Similarly, it appears 
from all measurements where electrons are emitted 
by radiant energy that the energy associated with 
the individual electrons is always related to the fre- 
quency of the radiation by this same constant. The 
result is that the scientific world has quite unani- 


mously accepted it to be a fact that ext&rgy is quitted 
in quanta. 

When an electronic ^stem expends en^-gy it does 
so in definite amounts. Is ^lergy granular or atomic 
in character? Must we think of it as transmitted 
through space like a corpuscle? And then, is eadi 
corpuscle of energy received in toto by a single elec- 
tron? Since an electron can emit only definite 
quanta of energy, can it receive energy in amounts 
less than a quantum? If it receives and emits only 
by quanta, presumably its own total enwgy at any 
time is some integral number of quanta. What in 
any case is the mechanism which is involved? 

Such are the questions which confront the scien- 
tist of today. Evidence as to the correct answers is 
lacking but it may well be forthcoming in the near 
future. Such evidence as now e3dsts only makes the 
problem more complicated. Consider, for example, 
the question as to the absorption of energy. 

The moment a substance is exposed to light of the 
proper frequency the photo-electric emission b^ins. 
This would appear to indicate that Hiere was a hop- 
perful of energy in some electronic system which 
was tripped off, as by a trigger, and allowed to dis- 
charge. The energy which is released was either ob- 
tained from the beam of light, despite the short time 
of exposure, or was already stored in the atomic sys- 
tem. The further fact that the energy of the emitted 
electron is the same whether the intensity of the 
light is large or small would seem to indicate such a 
storage. Photo-electric phenomena occur in such 
feeble light as would correspond to an ordinary 


candle at a distance of three miles. (The number 
of electrons whidb are emitted each second is greater 
for greater light intensity even though the energy of 
each is a function only of the frequency.) Through- 
out the entire range of intensities, which would corre- 
spond to bringing the candle from miles away to 
within an inch of the plate, the energy of an emitted 
electron is always one quantum. 

For the moment, then, the evidence adduced seems 
to favor a theory of continuous absorption of energy, 
its storage, and release in quanta when the electronic 
oscillator is disturbed. But if there is such a trigger 
action why should the action, and the amount of 
energy which is released, depend upon the exciting 
frequency? One might think of a tuned system 
which responded only to a single note, but why 
should the amount of the response depend upon the 
note? It should make no difference what frequency 
of radiation disturbs the hopper and allows it to 
dump its load of energy. Why, also, should the out- 
put depend solely upon the frequency and not upon 
the type of hopper, that is upon the type of atom? 
It does, although the amount of energy which is ex- 
pended by the emitted electron in passing through 
surrounding systems does depend upon the atomic 
natm-e of the substances. The analogy of the hopper 
which is released by a trigger action seems to be 
contrary to the observed facts. We are forced, there- 
fore, to the conclusion that the energy of the escap- 
ing electrons is derived from the incident li^t. 

But this conclusion brings us back to the difficulty 
as to thp intensity of the light which excites the 


effect. According to ihe theory of radiation whidi 
is commonly accepted, the energy leaving a source is 
uniformly distributed over a spherical surface which 
increases constantly in size as the radiation proceeds 
outward. The effect may be seen in the widening 
circle of a wave caused by dropping a stone into 
water. An object upon which sudi a wave front 
impinges subtracts from it only the energy corre- 
, spending to the proportion of the total wave front 
which strikes the object. The effect is well known 
to sailors of small boats who have received the wash 
of a steamer before its wave front was much en- 
larged. If we calculate on this basis the amount of 
radiant energy which in one second should reach a 
tiny atom we find cases where the amount ia so 
small that billions of seconds would be required be- 
fore the atom could acquire the quantum of energy 
which it radiates so promptly. 

This diflBculty would be solved if enei^ were not 
resident in the medium, as it is in the obvious me- 
chanical case of the water wave, but had a corpuscu- 
lar structure. On this basis, when a body radiated 
energy it would really be shooting out in all direc- 
tions a shower of invisible particles, small bundles 
of energy. The electron must then receive or reject 
a whole bundle. The picture of the ejection of elec- 
trons by X-rays which was quoted on page 140 would 
be ejcplained if the X-rays were really small bullets 
of energy which followed radial paths outward from 
the anti-cathode. What appears to us as a continu- 
ous distribution of energy in a wave is probably not 
really continuous but conforms in analogy to a fine 


shower of rain such aa one experiences when a fog 
blows m. 

Matter which origmally appeared to mankind a^ 
continuous and infinitely divisible has been shown to 
be atomic. Electricity, whose phenomena appeared 
those of an invisible fluid, has proved to be granular 
in structure. Why should we not expect that energy 
also should prove to be not infinitely divisible but 
transmissible only in finite amounts? There are 
three objections: First is the incompleteness of the 
evidence, second the subconscious effects of our sci- 
entific traditions and training, and third, a definite 
piece of evidence against the hypothesis which as 
yet has not been explained away. 

A corpuscular theory for^light was commonly ac- 
cepted in Newton's time, despite a growing mass of 
evidence and theory in favor of a wave motion 
through an ethereal medium. Reflection was then 
explained as due to an attraction of the reflecting 
surface which bent toward itself the swiftly moving 
corpuscle, which the human eye later apperceived as 
light. As it happens, our present concept of reflec- 
tion as re-radiation would also accord with a corpus- 
cular theory for the transmission of energy through 

The evidence which finally dispossessed the 
corpuscular theory arose in connection with the phe- 
nomenon of interference.^ In its simplest form in- 
terference phenomena take place as illustrated in 

*We have already implicitly applied the theory of this phe- 
nomenon to the case of the crystal grating for the spectral 
analysis of X-rajrs. 


Fig. 30. Imagine a source of radiant en^gy to trans- 
mit to two ^ts, shown in ccobb section at a and b. 
IVom these two slite the energy spreads throu^ the 
ether just as if the slits were separate homogeneous 
sources. For simplicity we imagine the light to be a 
single frequency. From these slits there then spread 
out a succession of wave surfaces. In cross section 
these have much the appearance of surface waves 



Fia. 30 
Diagram illustrating interference of wave trains. 

which are produced in liquids by regularly recurring 
disturbances. Where the trough of one meets the 
crest of another, interference occurs. Where trougji 
coincides with trough, or crest with crest, there is re- 
enforcement and a greater displacement. The figure 
represents an instantaneous view of the transmission 
and shows crests as full lines and troughs as dotted 
It is easy to pick out a succession of points wh«« 


either type of interference phenomenon is occurring. 
At some point like Y, for example, the disturbance 
from a is three whole wave lengths ahead of that 
from 6, and reenforcement occurs. 

In the present caee there is a definite limit to the 
number of wave lengths by which the two disturb- 
ances can differ. With the interferometer, however, 
which was devised by Michelson, large differences in 
path may be obtained. Differences of as much as 
several thousand wave lengths have been instituted 
between the paths of the beams from two homo- 
geneous sources and still the phenomenon of inter- 
ference haa been observable. 

The objection of the necessity of conforming to 
the known facts of interference is not, however, un- 
surmountable.^ It would seem to demand that the 
bundle of energy should have a length which might 
be large in terms of wave length but would be small 
as compared to the distance the energy travels in 
each second. In some way this bimdle might also 
contain within itself something of the structure of a 

^ It may well be that the two aspects of radiant energy which 
we recognize as ''quantum" and as ''wave motion'' are not 
mutually incompatible. Such a possibility is noted by way of 
illustration in that most interesting book on relativity, Profesfsor 
Eddington's "Space, Time and Gravitation." He sajrs, "Physical 
reality is the S3mthesis of all possible physical aspects of nature. 
An illustration can be taken from the phenomena of radiant 
energy or light. In a very large number of phenomena, the light 
coming from an atom appears to be a series of spreading waves. 
In many other phenomena the light appears to remain a minute 
bundle of energy, all of which can enter and explode a single atom. 
There may be some illusion in these experimental deductions; 
but if not, it must be admitted that the physical re^ity cor- 
responding to light must be some synthesis comprehending both 
these appearances. How to make this S3mthesis has heretofore 
baffled conception.' But the lesson is that, . . . reality is only ob- 
tained when all conceivable points of view have been combined." 


train of waves which would produce mterference 
e£fect6 with bundles which had been dispatched by 
otl^er routes. 

In the absence of direct evidence some incline 
toward one side and some toward the oth^ of this 
question. Perhaps the lay reader will have less to un- 
learn in the futiu^e if he accustoms himself to think 
of there being shot about in the physical imiverse 
bundles of energy, the arrival and departure of whidi 
are manifested by changes in atomic i^stems. 



TsE concept of an atom with a nucleus was due 
to Rutherford whose experiments on the scattering 
of alpha rays were explainable^ as we have seen on 
page 102, by liie assumption of such an atomic struc- 
ture. In terms of this structure it then became 
necessary to explain other known phenomena^ par- 
ticularly that of the radiation of light from atoms. 
' The attempt was made by Bohr in the years imme- 
diately following 1913. 

He started by pointing out that the planetary elec- 
trons of the Rutherford atom-model would be un- 
stable, according to the recogniz^ laws of mechanics, 
if their rotation was assumed to be the cause of light 
radiation. Rotating electrons, as was mentioned on 
page 78, influence other electrons. In so doing they 
impart some of their energy. Consider for a moment 
what the efifect would be if the rotation of the planet- 
ary electrons was accompanied by a radiation of 

Electron and nucleus tractate,, but the kinetic 
energy of the electron prevents its falling into the 
nucleus, just as planets maintain stable paths about 
the sun by virtue of their kinetic energy. If, how- 
ever, this energy is gradually subtracted by radia- 




tion, tiie electron will fall in towards the nucleus. 
Due to its dbanged orbit it will have a changed fre- 
quency of rotation. A continuous change in fre- 
quency, therefore, should be noted in the light from 
a tube of gas like hydrogen throu^ whidi an electric 
current is being passed by the motion of the ionized 
gas molecules. No such change is noted, for the 
spectral lines of the chemical elements are d^nite, 
unvarying, and characteristic. 

So-called classical electro-magnetic theory is in- 
capable of accounting for radiation in terms of 
planetary electrons rotating about a nucleus. Bohr, 
therefore, applied to the phenomenon the quantum 
hypothecs which had already served good purposes 
in other fields of inquiry. His radical assumption is 
the possibility of non-radiating orbits. In the 
Rutherford-Bohr atom-model a planetary electron 
rotates without the emission or absorption of energy. 
It has a steady orbital motion which represents a 
condition of equilibrium so far as concerns changes 
in energy. 

An electron may, howevw, be caused to change 
its orbit and the emission or absorption of enei^ is 
assumed to accompany this change from one 
equilibrium state to another. During the change of 
an electron from a larger to a smaller orbit radiation 
of a definite frequency is emitted and the amount 
of energy involved is always one quantum. By such 
a theory it was presumed that the spectral lines of 
the various elements could be accounted for. Char- 
acteristic spectra are emitted by the various ele- 
ments, as we have seen in Chapter XI, when liie 

■'i.ii. ■r^'"" 


electronic structures are disturbed by the impacts 
of a cathode stream. Vibration frequencies of 
smaller values, corresponding to the ultra-violet and 
visible range, arise from less violent disturbances, 
such 83 occur for example in the ionized gas or vapor 
of a highly evacuated tube which is conducting elec- 

When an electric current is passed through a gas 
light is emitted.^ By using a spectrometer or a grat- 
ing, involving the principles of interference which 
have been mentioned in previous chapters, this light 
may be analysed into a series of spectral lines, simi- 
lar to but more numerous than those appearing in 
an X-ray spectrum. It is found that any element 
produces a spectrum in which lines recur at intervals 
throughout a given frequency range. These lines 
form a series, the frequency of each member of which 
may be calculated from that of the highest frequency 
by very simple arithmetic. In the case of incandes- 
cent hydrogen three such series are known: one in 
the visible range of frequency called the Balmer 
series; one in the region of lower frequency, the 
infra-red region, which is known as the Paschen 
series; and the third, known as the Lyman series, in 
the ultra-violet. 

When one knows the highest frequency of a series 
of spectral lines the calculation of the other fre- 
quencies is a piece of arithmetic which impresses one 
with the probability that the order of nature is in- 

^ Energy is absorbed from the source of electric current in the 
act of ionization and radiated when recombination occurs. 


herent in the granular structure of electricity and 

Start with the simple senee of numbers, 1, 2, 3, 4, 
5 and so on. Write the reciprocals of these, thus, 
1, 1/2, 1/3, 1/4. Then write the squares of these 
reciprocals, thus, 1, 1/4, 1/9, 1/16. Now assume 
that we know for any atomic system its hi^est 
possible frequency of radiation. As a matter of fact, 
it is a little over three million, million, million, and 
is known as the Rydberg constant. To find the 
lowest frequency we take the diflFerOTice between 1 
and 1/4 and multiply it into this constant frequency. 
We thus obtain the line of longest wave length. For 
the next line of this same series we multiply the 
Rydb^i^ constant by the difference between 1 and 
1/9, and so on for the other lines of the Lyman 

The Balmer series, whidi has its head (highest 
frequency) in the visible spectrum, is found by tak- 
ing the second numb^ of the series of squared 
reciprocals, namely 1/4 and subtracting from it the 
next, namely 1/9, and ihefa proceeding as before. 
For the third series, which has a head of still smaller 
frequency, we start with the third term, and subtract 
from it successively the iowrthy fifth, and succeeding 

These series involve a relatively large number of 
terms. For example, in the spectra of certain celestial 
bodies thirty-three hydrogen lines have been ob- 
served which correspond to those calculated for the 
Balmer series. Fig. 31 (Plate IV, opposite p. 131) 
shows a photograph of a hydrogen spectrum. In the 


laboratory, however, only twelve lines of the series 
are reproducible by discharging electricity through 
a tube containing a little hydrogen gas. 

According to the Bohr theory the higher the num- 
ber in the series the greater will be the radius of the 
electronic orbit. The greater this orbit the greater 
is the apparent size of the atom, as was pointed out 
on page 13. If, therefore, atoms are to have large 
electronic orbits their centers must be widely separ 
rated, and hence the gas density must be small. 

At ordinary atmospheric pressure, however, the 
molecules in a gas are relatively close together. As 
the number in any enclosure is reduced the pressure 
which they exert, or, what is equivalent, the external 
pressure necessary to constrain them to this volume, 
is correspondingly reduced and the average distance 
between molecules is increased. With the modem 
vacuum pump the number of molecules in a given 
vessel may be so reduced that on the average indi- 
vidual molecules will travel twenty miles between 
collisions with other molecules within the tube. (Of 
course we are not considering reflecting collisions 
with the molecules of the walls.) Under these con- 
ditions, despite the fact that the tube will still con- 
tain about a thousand million molecules in each 
cubic centimeter, the average distance between mole- 
cules is enormously greater. 

Only in a highly evacuated tube would there be 
the possibility of large electronic orbits. The cor- 
responding spectral lines are not visible, however, 
because the whole mass of the gas in the tube 
is insufficient to give sufficiwit intensity of ra- 


diation to permit detection. In tibie neighborhood 
of stars, on the other hand, the mass of the ga& is 
sufficient and its rarefied condition meets the re- 
quirement as to gas density so that lines correspond- 
ing to larger orbits may be observed. On the basis 
of the Bohr theory, therefore, the failure of experi- 
menters in the laboratory to reproduce or to observe 
the higher frequencies of the Balmer series becomes 

Apparently, also, there is no normal size for any 
atom. Its effective diameter depends upon the larg- 
est orbit of its electrons. Whether or not an electron 
moves into a larger orbit depends upon the restrain- 
ing effect of neighboring systems and upon the 
violence of the disturbance to which it is subjected. 

The smaller orbits are more stable because of the 
greater tractation between nucleus and electron. 
Hence an electron which has been displaced to a 
larger orbit returns to one of smaller size and greater 
stability. In so doing it radiates a quantum of 
energy and the value of the frequency which de- 
termines that quantum is apparently that of the or- 
bit which it assumes. For large displacements the 
electron may assume successively smaller and smaller 
orbits and thus give rise to a succession of lines in a 
spectral series. 

When a large number of atoms are involved, as 
there must be if a measiu^able effect is to be observed, 
individual atoms may be emitting different charac- 
teristic frequencies. To the observer, however, there 
appears a number of lines of the series, just as if they 
were simultaneously produced by a single atom. The 


fact that they are mtermittent and originate in 
separate atoms is obscured, since he deals with them 
statistically in terms of average effects. 

Bohr's method and its successes may now be 
briefly summarized. He dealt most successfully 
with the hydrogen atom which has only a single 
electron and, therefore, the simplest possible struc- 
ture. Upon the assumption of non-radiating or- 
bits he was ablie to apply to the motions of electrons 
in such orbits the same mechanical principles as hold, 
in the case of planetary rotations in celestial systems. 
By the adoption of the quantum hj^othesis he was 
enabled to calculate the energy changes involved in a 
change from one non-radiating orbit to another. In 
calculations he had at his dii^x>sal previously ob- 
tained values for the mass of an electron, for its 
charge; and for Planck's constant. In terms of these 
he calculated the diameter of a hydrogen atom and 
the corresponding frequency of an electron revolving 
in this orbit. He also calculated the amount of 
energy required to displace an electron completely 
from the hydrogen atom and thus found the poten- 
tial necessary for the ionization of hydrogen. His 
values agreed very well with those obtained by other 

He further calculated, on the basis of his theory, 
the Rydberg constant for hydrogen. The value thus 
derived differed only one per cent from that obtained 
by a study of spectra. At that time the head of the 
Lyman series had not been discovered, and its exist- 
ence was in effect predicted by the Bohr analysis. 


Similar successes ^ also accompanied the thecH^cal 
study of the frequencies whidi were to be expected 
in the case of helium. 

In the Bohr formuke there are implicitly contained 
a large number of statements which have since been 
checked. His expressions for hydrogen and helium 
show the entire range of possible frequencies. The 
theory, howevw, has been extended by Sommerfeld 
who endeavored on the basis of an ellipticily in some 
of the orbits to account for th^ fact that the charac- 
teristic lines are not always single^ as would be re- 
quired by the simple theory of circular orbits. 

It has already been stated that three series of char- 
acteristic lines appear in the X-ray spectra of the 
elements above sodiimx and that the X-ray spectra 
of the elem^its below sodium have not yet been de- 
termined. On the basis of the Bohr theory, which 
implicitly includes the relation determined experi- 
mentally by Moseley, it is now possible to assert that 
the Lyman, Balmer, and Paschen series for hydrogen 
are the K, L and M series of its X-ray spectrum. 
As the atomic number decreases, the frequency of 
the diaracteristic X-ray spectrum also decreases. If 
this relation is extended by extrapolation to hydro- 
gen it gives for each of the three X-ray series the 

*0n the other hand, there are several observable phenomena 
which have not been amenable to treaUnent on the Bohr as- 
sumptions. The Bohr atom is, at present, largely a convenient 

' It haa also been suggested by A. C. Crehore that the multi- 
plicity of fine lines which appear in spectra is due to the nature 
of the paths which displaced electrons follow in their, return 
toward the nucleus. 


head line (highest frequency) in one of the three 
hydrogen series. 

It appears, therefore, that the mechanism for the 
production of light is fundamentally the same as that 
for X-rays and that the only difference is one of fre- 
quency. The X-ray spectra are merely the highest 
frequencies for atoms of large atomic number. Be- 
low each of these highest frequencies there is a series 
of terms representing frequencies some of which may 
not be visible under experimental conditions. 

In the case of the metals the spectra which are ex- 
cited, when an electric arc is formed in the metallic 
vapor, are complicated by hundreds of lines. An- 
alysis has not yet been accomplished for these cases 
but it seems safe to consider that the lines in these 
arc-spectra represent lower frequencies in series 
which are headed by the characteristic X-raya 

Bohr's formulae implied between the different 
series of X-ray spectra a simple relationship which 
goes far to indicate the fundamental correctness of 
his assumptions. The relationship was verified by 
reference to the experimentally determined facts. 
In the K series which is shown in Fig. 26, the line of 
longest wave length (smallest frequency) is desig- 
nated by alpha, and the next by beta, after the con- 
ventional manner for aU spectral series. According 
to Bohr's theory the difference in frequency between 
the beta and the alpha lines in the K series of any 
element should be the frequency of the alpha line of 
tiie L series. 

This is understandable if we think of Ihe alpha line 
in the K series as due to jumping from orbit 2 of Kg. 


32, to orbit 1 ; of the higher frequency beta line, with 
its larg^ quantum, as due to jumping from orbit 3 
to orbit 1 ; and of the alpha line of the L series as due 
to jumping from orbit 3 to orbit 2. The same idea 
may be obtained also by reference to the arithmetical 
operations of page 158. 

The permanent configuration which is reached 
when an electron changes in orbit is always one in 
the formation of which the maximum amount of 

Fig. 32 
Simplified diagram of electronic orbits in the Bohr atom-model. 

energy is emitted. The extreme case occurs wh^i 
an isolated electron joins a nucleus in the formation 
of an atom or neutralizes the negative charge pos- 
sessed by an atom which by ionization has already 
lost an electron. For this reason radiation of line 
spectra occurs only in the case of an ionized gas. It 
does not accompany the process of ionization which 
absorbs energy but only the process of recombination 
when this energy is released. 

For the basic ideas involved in the Bohr atom- 
model there is a large amoimt of evidence. It will 


be noticed, however, that it does not conform to the 
picture of atom structure which was given in our 
early chapters, where the electrons were assumed to 
occupy relatively fixed positions in the atom. The 
concept of definitely localized electrons is highly 
satisfactory to the chemists who have found it to ex- 
plain not only valence in chemical combinations but 
also many phenomena like the miscibility of different 
liquids, tendencies to vaporize, and hence melting 
and boiling temperatures. In such matters mole- 
cules which are believed to have like shells of elec- 
trons are found to have similar properties. 

Between the chemists who are int«:'ested in molec- 
ular combinations and such phy^cists as are con- 
cerned with radiation there is at present established 
a gulf. Each finds his own atom-model most con- 
venient and satisfactory. The chemical model is 
due to a number of scientists, chief of whom are 
Lewis, who first suggested its general features, and 
Langmuir, who has elaborated and extended it. It 
requires that the electrons effective in valence re- 
lations shall be relatively fixed. The Bohr atom re- 
quires that some, at least, of the electrons shall be in 

It seems quite probable, nevertheless, and indeed 
more or less inevitable, that the two conditions are 
not hopelessly conflicting and mutually impossible. 
According to the chemists' construction the valence 
electrons in all except a few of the atoms are in ex- 
ternal shells within which are other shells of elec- 
trons. Perhaps these inner shells contain the ro- 
tating electrons which determine the radiation of the 


ionized atom. In the case of the elements between 
lithium and argon, however, all except two electrons 
are in a single shell. It is possible, therefore, that 
future investigations^ of these elements will lead to 
evidence upon the basis of which a reconciliation 
may be possible, and the salient features of both 
models may be retained. 

That the electrons of an atom are in rotation at 
least while light is being radiated is well proved by 
other phenomena which antedate our knowledge of 
electrons. Zeeman in 1896 discovered that a spec- 
tral line which origmated from a gaseous source, 
placed in an intense magnetic field, appeared as three 
lines when the magnetic field was at right angles to 
the direction of the propagation of the light. The 
central line had the original position. The other 
two lines appeared on opposite sides of the original, 
one representing a slight increase in frequency and 
the otiher a corresponding decrease. 

For simplicity of discussion let us imagine the 
source to consist of only three atoms, in two of which 
the electronic orbits are coaxial with the electronic 
streams whose motions establish Ihe magnetic field. 
Suppose the directions of rotation in these two or- 
bits are opposite. Now apply to these rotating elec- 
trons the laws stated on page 83 and it will be seen 

* Characteristic X-rays are produced by the return of an electron 
which a cathode particle has knocked out of its normal position 
in an atom. Upon assumptions as to the distribution and orbital 
conditions of the electrons in an atomic system, it is possible to 
calculate for any eleitnent the "critical absorption" frequency for 
any given type of rswiiation, e.g., the K-type. Calculations were 
made by Duane (1920) upon the assumption that the distribution 
of electrons was that of the LewiskLangmuir "static" atom. These 
agree very well with the experimentally observed frequencies. 


that one is urged in toward the center of its orbit 
and the other is urged out. The result is that one 
acquires a slightly larger orbit and smaller frequency 
while the other acquires a smaller orbit and higher 
frequency. The orbit in the third atom we assume 
to be in a plane at right angles to the orbits of the 
other two atoms and it is unaffected by the magnetic 
field. The result is the three lines described above. 



In preceding diapters there have been mentioned 
two tjrpes of emission spectra, line and continuous. 
Of liiese the line spectnun is the more interesting. 
It is emitted by elementary substances which are in 
the state of a gas or a vapor, when the electrons have 
been displaced to new orbits or completely detached 
from the atoma The return of an electron is ac- 
companied by a radiation of which the frequency is 
characteristic of the element and the energy equal 
to one quantum. Line spectra are due to the 
natural vibrations of electrons and atomic nuclei. 

A continuous spectrum, on the otiier hand, is a 
phenomenon of substances in the soUd or molten- 
liquid state where the atoms are packed relatively 
close together. The atomic systems no longer func- 
tion as untrammelled individuals but as members of 
a large and unorganized crowd. Each is limited in 
the expression of its tendencies (line spectrum) by 
the interrelations and reactions with the other 
systems of its milieu. Energy, imp'arted to the atomic 
systems under these conditions, results in chaotic f 
motions on the part of all, which then proceed 
to jostle and crowd each other. Instead of a clear 
individual expression, which is characteristic of the 



atomic type, there. arises a roar of notes, expressive 
only of conflict and chaos. No longer are types 
easily distinguishable by characteristic lines for the 
spectra are continuous. Of this phenomenon aU in- 
candescent solids are examples. 

When the disturbance is excited by impacts, as in 
the case of "white'' X-rays, the highest frequency 
which is radiated is determined by the quantum of 
energy which is brought to the radiating substance 
by an impinging electron. A quantum relationship 
is also involved in radiations of lower frequency. 

Under the conditions where a continuous spectrum 
is produced the normal oscillating systems of nuclei 
and planetary electrons are altered by the close 
presence of other systems. An electron is no longer 
concerned only, or even primarily, with its natural 
oscillation, for the electrons of each atom are forced 
to adapt their motions to the external influences. 
To all effects and purposes, therefore, the radiating 
body contains at any instant a very large number of 
oscillating ^stems which differ markedly from one 
another in form of vibration and in frequency. Mole- 
cules and atoms, as well as the intra-atomic elements, 
enter into oscillation. It is a mad dance, in which 
the partn^s are changing from instant to instant, 
each pair dancing to its own time. Where molecules 
and atoms are vibrating, frequencies of infra-red 
radiation are produced. Where an electron is a part- 
ner the frequency is that of tdtra-violet light. In 
the visible range fast vibrations of atoms or slow 
vibrations of electrons are presumably the cause of 
the radiation. 



When we speak of atoms as reqx)nsible tor radia- 
tion we do not mean neutral atoms, but, instead, 
those which are electrically chained as by the tem- 
porary loss or gain of an electron. That such atomic 
Gfystems exist in solids we have seen m considering 
conduction of electricity throu^ metala Hig^ tem- 
perature, with its increased molecular agitation, also 
favors the formation of such atomic osciUatc^B. 




Fig. 33 

Cross-section of a uniform temperature enclosure, showing at p 
a peep-hole for studying the radiation within. A circulation of 
steam maintains the temperature. Screens 88 shield the measur- 
ing instrument /. 

Due to close packing of molecules, atoms, and elec- 
trons, any solid body possesses a large number of os- 
cillators of different electrical and geometrical di- 
mensions and hence of various frequencies. Such a 
body, therefore, emits or absorbs a continuous band 
of frequencies. The ^nission is a commonly ob- 
servable phenomenon. As a metal body, for ex- 
ample, is caused to rise in temperature it radiates 
heat and finally, becoming dull red, starts to radiate 
visibly. As the temperature is still further increased 


it radiates still higher frequencies, beoaming incan- 
descent when its spectrum includes the visible lange. 
The absorption phenomenon is not so easily ob- 
served. Let us suppose, however, that a radiating 
body is placed in an enclosure, as that of Fig. 33. 
Let the body be in equilibrium with the walls of its 
enclosure, that is with its surroundings, receiving 
from them by radiation just as much energy as it in 
turn is radiating to them. If either partner in this 
exchange were to absorb more radiation than it emit- 
ted its temperature would rise. The assumed con- 
dition, therefore, is one of temperatiu"e equilibrimn 
and the body is said to be in a uniform temperatm^ 

The assumption of an equality of exchange means 
that the radiation at any point is not affected by the 
nature of the body or its surroundings, nor by their 
relative location. For example, if part of the surface 
is covered with lampblack it absorbs nearly all of 
the radiation which falls upon it, but it must radiate 
an equal amount to satisfy the condition of equilib- 
rium.- Similarly, if part of the surface is covered 
by polished metal it will reflect most of the radiation 
and hence need radiate less to equal what it absorbs. 
The radiation within a uniform temperature en- 
closure is thus everywhere the same. 

For this reason it is impossible by the radiation to 
distinguish one part from another. Within a cave 
all objects are equally black imless there is light from 
an entrance, or unless the condition of equilibrium 
is violated by the presence of a tordi, which is an ob- 
ject of higher temperature, not in equilibrium with 


its surroundings. Similarly if one looks into a cru- 
cible or into a large furnace when conditions are 
stable. There is a glare of light, but the inner sur- 
faces are just aa indistinguishable as are those of the 
cave where the temperature is Iowot. 

Within a imiform temperature enclosure the ra- 
diation is altered in intensity and in quality only as 
the temperature is altered. For this reason such ra- 
diation is usually called "temperatiune radiation.'' 
The enclosure itself is a more or less artificial con- 
dition, an ideal or limiting case of equilibrium, which 
has been adopted by scientists because it permits 
them to concentrate their attention on the medium 
within the enclosure. In general, bodies are not in 
temperature equilibrium wiUi their surroundings, 
and particularly not when these include a human ob- 
server. By his temperature sense he is frequently 
able to detect a lack of temperature equilibrium be- 
tween himself and his surroundings. 

Two important laws as to temperature radiation 
have been known for many years. To appreciate 
them we must decide upon a method of measuring 
temperature. In scientific work temperature is 
measured in degrees centigrade, each nine- fourths of ^-i 
a degree Fahrenheit, but the zero is the so-called ' 
"absolute zero." 

This is based upon a phenomenon of gases. When 
a gas is heated one degree it is found that the hap- 
hazard molecular motion of its molecules is increased 
and that the pressure which it exerts upon tiie walls 
of its container is also increased by about one-273rd 
part of the pressure which this same volume of gas 


would exert at zero degrees centigrade (32° F.). 
Conversely, if it is cooled by an equal amount there 
is a similar reduction. The explanation of the pres- 
sure is found in the impacts of the molecules on the 
sides of the container, battering it like a steady rain. 
The effect of temperature changes is explained on 
the basis of additions of kinetic energy to the mole- 
cules of the gas or of subtractions and hence of corre- 
sponding alterations in their average speeds. ^ 

Actual gases condense into liquids and freeze into 
solid form at low temperatures (and under high pres- 
sures externally applied). The scientist, therefore, 
establishes an ideal thermometer by using an ideal 
and imaginary gas which will retain throughout all 
possible ranges of temperature the characteristic 
which actual gases like hydrogen show at ordinary 
atmospheric temperatures. Except for the low tem- 
peratures his ideal thermometer is identical in be- 
haviour with an actual hydrogen gas thermometer. 
From the ideal gas, however, he may imagine the 
energy to be successively subtracted until the kinetic 
energy of the molecules is reduced to zero and the 
pressure which they are capable of exerting is also 
zero. Since each degree decrease in temperature, be- 
low zero on the centigrade scale, reduces the pressure 
by 1/273 of its value at zero centigrade it will only 
take 273 such decreases to arrive at an absolute zero 
of temperature. On this thermodynamic scale of 
temperatiu"e ordinary room temperature is obviously 
a little less than three hundred d^rees. 

In terms of absolute temperatwes we may now 
express two important empirical laws of radiation. 


The first of these is known as Wien's law. Id any 
temperature radiation there is some frequ^icy which 
has more radiation than is associated with any oth^ 
frequency. This frequency becomes greater as the 
temperatxire is made higher; and it is directly pro- 

Curves Bhowing relation of intensity of radiation and frequency of 
radiating source at different temperatures. 

portional to the absolute temperature. There is 
thus a di^laoement of the frequency of maximum 
radiation toward the ultra-violet portion of the con- 
tinuous spectrum as is shown graphically in the 
curves of Hg. 34. 


The other law^ due to Stefan and Boltzmaon^ 
states that the total radiation from a heated body 
varies as the fourth power of the absolute tempera- 
ture; thus if the temperatiu'e is doubled the rate at 
which energy is emitted is increased sixteen times. 
It is also illustrated by the curves of Fig. 34. 

We are now ready to consider the occasion for 
Planck's development of the quantum theory. Up 
to the beginning of this century^ when he made his 
contribution, no adequate theory had been developed 
to explain, or to picture, the experimental relations. 
These had been observed by careful experiments on 
enclosiures the radiation from which was measured 
through a small peephole by delicate devices sensi- 
tive to heat. 

There was, however, no theory on the basis of 
which formulflB could be logically developed which 
contained the relations of actual experiment. 
Planck solved the diflBculty by reasoning the steps of 
which have never met with general approval but the 
conclusions of which are firmly established in the 
science of today. 

The chief difficulty in the way of the existing 
theories concerned the manner in which a radiating 
body shares energy with its ethereal surroundings or 
absorbs it from them. It was commonly assumed 
that energy must be, or rather ought to be — ^for the 
condition was contrary to fact — ^interchanged in a 
continuous manner. A radiating surface was recog- 
nized as composed of a number of oscillators, but 
these were supposed to absorb or emit continuously, 
that is, in truly infinitesimal successive amoimts, 


from or to the ether. For such assumptions there 
was a recognized basis in theories of mechanics and 
electrodynamics. Of this a mechanical illustration 
may be quoted from Jeans. 

Suppose we construct a vibrating system by con- 
necting a number of corks together by elastic bands. 
Imagine a complicated system, if you will, with a 
large number of cross connections between various 
corks. Now disturb this by pulling some of the corks 
from their equilibrium positions and then allow the 
natural oscillations to occur. Let this system with 
its several different oscillations be placed on water. 
The corks simulate a vibrating system. The water, 
with its almost infinite niunber of tiny molecules, 
and hence mfinite possibilities for forms of vibration, 
simulates the ether. We know what happens. 
Equilibrium between these two ss^stems is impossi- 
ble. The energy of the corks is all absorbed by the 
water. It goes into vibrations far more rapid than 
those of the corks, for it goes to increase the motions 
of the invisible molecules of the water. 

If the ether were like this in b^aviour all the 
energy of the bodies in a temperature enclosure 
would be abstracted by it. And the energy in the 
ether would be distributed mostly in the vibrations 
of highest frequency instead of having a distribution 
with a definite maximum as is shown in Fig. 34. 

In effect Planck's solution of the di£B[culty con- 
sisted in postulating a condition whidi would fit the 
observed phenomenon. 

To an economist or an actuary eadi experimental 
curve of Fig. 34 looks something like a so-called 


probability curve, such a curve, for example, as one 
would plot if the vertical distances represented 
numbers of men and the horizontal distances repre- 
sented corresponding lengths of life. If the various 
oscillators in the radiating body differ in their abili- 
ties to absorb or emit radiant energy, each being 
capable of only a definite amount, then the frequency 
of maximum radiaticwi should depend upon the char- 
acteristics of these oscillators just as the maximmn in 
a plotted curve of mortality statistics depends upon 
the characteristics of the class for which it is con- 
structed. To a very large extent, as we shall see, 
Planck's theory constituted a theory of probability 
for electrical oscillators. 

As you remember, he assumed that an oscillator 
could handle only a quantum of energy; and by 
quantum he meant an amount proportional to the 
frequency of vibration, the amount hn. Oscillators 
of low frequency, even if relatively numerous, will 
handle but a small portion of the total energy and 
contribute but little because the amount which each 
individual oscillator may handle is small. On the 
other hand, oscillators of large frequency will respond 
only if there is available a relatively large amount of 
energy since their quanta are greater. To function, 
however, the higher frequency oscillator must re- 
ceive its quantum all at once; it cannot make it up 
from several successive smaller quanta. Since large 
quanta will probably occur only infrequently, this re- 
quirement means that there will be little total energy 
associated with the oscillators of higji frequency. 
The maximum radiation, therefore, will occur in the 


middle range of frequencies, as the experimental 
sulta indicate. 

Upon the assumption of quanta Planck's relations 
are calculable under the ordinary laws of probability 
as was shown by Jeans some time later. For pur- 
poses of following the latter's method one limits his 
consideration to a narrow region of frequencies. The 
quantum will be essentially the same for all the fre- 
quencies within this narrow band. It is then pos- 
sible to calculate the probability that any given os- 
cillator of this frequency will have zero enei^ or the 
en&rgy of one quantum or that of two, and so on. 
Siunming up the energy which a large niunber of 
similar oscillators would probably have at this fre- 
quency, Jeans obtains the basic expression of 
Planck, namely, an expression for the probable 
average energy of an oscillator at any desired fre- 

It was Einstein, as a discrete, or indiscreet, elec- 
tron remarked between chapters, who applied this re- 
lationship with considerable success to the problem 
of the specific heat of solids. 

Different substances, but equal quantities by 
weight, are found to require different additions of 
heat, that is energy, to produce equal increases in 
temperature. The amount is specific to each sub- 
stance, and hence, the term "specific heat" is applied 
to the amount of heat required to change by one de-* 
gree the temperature of unit mass of a given sub- 
stance. The common imit for expressing tliis mag- 
nitude is tlie calorie which represents approximately 
the amount of energy necessary to raise one gram of 


water one degree Centigrade, and exactly, that re- 
quired for the degree increase in temperature be- 
tween 15 and 16 degrees Centigrade. 

Temperature, of course, is a numerical answer to 
the question "how hot." As has been implied above, 
it measures the difference in hotness of substances 
the molecules of which differ on the average in tlie 
kinetic energy which is associated with their hap- 
hazard motions. If body "A" is hotter than body 
"B," the molecules of "A" have, on the average, more 
kinetic energy than those of "B". It is for this 
reason that a hot and a cold body when placed in 
contact come ultimately to a common temperature. 
By molecular collisions at the contiguous boundaries 
a portion of the energy of "A" is imparted to "B" 
until finally the molecules of both substances have 
the same average value of kinetic energy. 

Because of differences in molecular structiu'e one 
may predict at once that different substances will 
have different specific heats. A fairer basis of com- 
parison, however, than amounts of heat for equal 
masses would be the amount required for equal num- 
bers of molecules. Molecules of similar structure 
should require equal amounts of energy for equal 
changes in temperature, tiiat is, they should have 
equal "molecular heats." Thus we should expect 
monatomic molecules to be alike in this respect. 

In a monatomic structure the mass is almost en- 
tirely concentrated in the nucleus, which is tiie center 
about which any molecular rotation must occur. 
From the familiar example of flywheels, we know, 
however, that if a rotating body is to have associated 



with it large amounta of energy, the mass must be 
separated from the axis of rotation by a lai^ dis- 
tance. Because monatomic molecules are not con- 
structed on the plan of flywheels, for the planetary 
electrons are n^ligible in mass as compared to the 
nucleus, they have no appreciable en^gy of rotation. 
When heat is added to monatomic gases it all goes to 
iuCTeese the kinetic energy of translation of the mole- 

A diatomic molecule, howe\3r, would be expected 
to acquire and to store ^lergy m a rotation or sp fi- 
ning of its figure-eight-shaped structure and particu- 
larly in a vibration of the component atoms with re- 
spect to each other. In the haphazard motion of 
such molecules when collision occurs, the atomic 
partn^is may be set spinning, or they may mom^i- 
tarily be crowded together, and thus vibrations may 
be set up within the molecular system itself. It ap- 
pears evident that collisions will lead to sudi trans- 
fers of energy, and hence that some of the specific 
heat of diatomic substances will represent spinning 
and vibratory motions, in addition to the haphazard 
translations of the individual molecules. 

The molecular specific heat of a substance i^ould, 
therefore, depend upon the molecular structure, 
being greater for structures whidi have greater 
variety in possible types of motion — ^more degrees of 
freedom, as it is technically said. There is nothing, 
howev^, to indicate that the molecular specific heat 
should be different at different temperatures. We 
should expect that it would require the same fraction 
of a calorie to change a substance from 100 to 101 


degrees as from 200 to 201 degreea Of course, if a 
change in molecular state occurs as, for example, 
from liquid to vapor, the number of degrees of free- 
dom may be changed and we may be dealing in effect 
with a different substance. As long, however, as 
there is no change of state, it would appear that the 
specific heat of any substance should be constant 
without r^ard to temperature. 

For inonatomic gases it is; also for metals in a va- 
por state; but for all other substances the specific 
heats are found to be markedly decreased as the tem- 
peratures at which th^ are measured are lowered. 
Here again no adequate theory had been presented 
prior to the application of the quantum hjrpothesis. 
The theory is still too incomplete to account for any- 
where near all experimental facts, but the successes 
of the quantum hypothesis are sufficient to Indicate 
that the final solution must involve its use. 

Planck had derived an expression for the probable 
average energy, involvmg a large number of similar 
oscUlators. This Einstein applied to the study of 
the specific heats of solids. The formula is too com- 
plicated for complete discussion, and it must suffice 
to say that it involves the absolute temperature of 
the substance. A mathematical operation was then 
required to find the rate at whidi this energy changed 
with temperature, that is to find the specific heat, 
which is the change in energy content of a body per 
degree of temperature. The expression so obtained 
was in form to permit the calculation of the specific 
heat of solid substances at any desired temperature 
if the frequency of the oscillators was known. 



Several methods were then devised by Einstein 
and others for obtaining this frequ^icy experi- 
mentally. Of these^ only one will be discussed. This 
depends upon a numba* of principles which have al- 
ready been mentioned. In the derivation of Hie for- 
mula for specific heat it had already been assimied, 
for simplicity, that all the oscillators of a homog^ 
neous body were essentially alike. It remained to 
excite them in such a way that their characteristic 
or natural oscillations could be detected and their 



EiG. 35 

OossHsection of apparatus for studying residual i«ys. Radiation 
from a source T is successively reflected from bodies of the same 
substance, The residual rays are analyzed by the spectrometer, 
diagrammatically indicated at L. 

frequency measured. You will remember that re- 
flection is really re-radiation. Any reflected radia- 
tion must then include most prominently those ra- 
diations which are of the same frequency as the os- 
cillators would themselves naturally emit. The 
phenomenon is one of resonance, so-called — ^that 
is the phenomenon of greatest response when the ap- 
peal strikes the proper personal note. 

If, therefore, a substance is illuminated by a con- 
tinuous spectrum of radiation, such as would arise 



from a black body which is emitting temperature 
radiation^ the reflected radiation will contain more 
intensely the frequencies natural to the oscillators 
of the body. Now let this reflected radiation fall on 
another body of the same substance as the first. The 
general scheme is illustrated in Fig. 35^ where the 
progress of the beam of radiation is indicated by the 
dotted lines. (A mirror, M, is interposed at one point 
to deflect the beam.) At the second reflecting sur- 
face there is a further selection of the natural fre- 
quencieS; and a furUier discrimination against all 
others. By successive reflections there are thus ob- 
tained so-called "residual rays," which are those 
natural to the oscillators under examination. 

When the natural frequency is known the calcula- 
tion of specific heat by Einstein's method may be 
completed. For certain substances his formula was 
found to give results wonderfully in accord with the 
experimental findings. For other substances there 
was an unsatisfactory lack of agreement. Neverthe- 
less, the formula agreed in such cases with the general 
trend of the relations between specific heat and tem- 
perature. It indicated a certain correctness of the 
general method of approach which other investi- 
gators have been rapidly extending. Thus inquiry 
in another field of physical science was stimulated 
and is being advanced by the fruitful hjrpothesis that 
energy is transferred in discrete bundles, the magni- 
tudes of which are dependent only on the frequencies 
of the atomic and electronic oscillators which are 



In the earlier diapters of this book the c»tlerly 
structure of matt^ was emphasized. In the later 
chapters some evidence was presented which favors 
a concept of "atomicity" for energy. Throu^out, 
it is to be hoped that the text has conv^ed an idea 
of the inherent structural order of nature. Now we 
must distinguish between order in structure and 
order in process. The processes of nature are orderly 
only in the sense that they constitute phases of an 
inevitable sequence of events. They may and in- 
deed always do result in a certain disorder which we 
shall now consid^. Of chaotic conditions we have 
had some intimations from the motions of molecules, 
particularly those of gaseous substances, and fh>m 
the electrical elements which are responsible for con- 
tinuous spectxa. 

The orderly processes of nature whereby disorder 
results have been formulated in a law commonly 
known as the second law of thermodynamics. It 
would be preferable to speak of a first and second law 
of energy rather than of thermodynamics, but they 
retain the titles, descriptive of their evolution, for 
both arose at a time when the relation between heat 
and energy was inadequately conceived. Both laws 



express relations which have been grasped more or 
less intuitively^ particularly the second law. 

The first law states an equivalence between work 
(enei^) and heat; and in mathematical ^mbols it 
contains an empirical constant for converting units 
of heat into units t>f energy. Prior to the statement 
of this law heat and mechanical work had seemed 
unrelated phenomena and different units had been 
adopted for the two magnitudes. Of these the 
calorie has akeady been defined ; the other imit is the 
erg. Whenever, under experimental conditions 
energy, associated with molar bodies disappeared, 
theare was found a definite increase in heat which 
bore the proper nimxerical relationship to the amount 
of energy. 

For many years, however, it has been recognized 
that heat is merely a descriptive term for the kinetic 
energy of molecular bodies. Today we conceive of 
en^^ as associated with all electrons and protons, 
with their configurations and their motions; and the 
first law becomes our statement of belief in the con- 
servation or indestructibility of the entity energy. 

The second law, which followed the work of Sadi 
Camot about 1824, has also outgrown its earlier 
narrower application to heat engines and become a 
general law of energy. At various times it has re- 
ceived many expressions, of which the most servioe- 
able are formulated in symbols and involve a con- 
cept known as entropy. To this we shall return in 
a moment. 

In so far as the second law is a matter of experi- 
ence it records the impression that there are certain 


natural processes. Water flows down hill; electric- 
ity moves from points of higher to points of lower 
potential; by radiation^ and by actual molecular im- 
pacts if possible^ a net amount of energy is trans- 
ferred from a hot to a cold body; impacts of molar 
bodies and all phenomena of friction result in 
transfers of energy to molecules. In fact, all natural 
processes, directly or ultimately, result in greater 
kinetic energy on the part of molecules. All me- 
chanical operations involve friction and hence all 
contribute to increase the kinetic energy of molecular 
and submolecular systems. Similarly, the con- 
duction of electricity and many ^ chemical reactions 
result in greater activity on the part of the tiny 
grains of our physical universe. 

Sometimes the second law is stated by saying that 
although work (the expenditure of energy in con- 
nection with molar bodies) may always be converted 
into a definite equivalent of heat the reverse transr 
formation is always incomplete. This was the earli- 
est expression of the law and it was reached by a con- 
sideration of heat engines. Even if there were no 
friction whatever, a heat engine could never be 100 
per cent efficient unless its lowest temperature was 
zero on the absolute scale of temperatiu-e. The prop- 
osition was originally proved by Camot, who dealt 
theoretically with an ideal engine and found that tiie 
efficiency depended upon the ratio of the lowest tem- 
perature, say that of the atmosphere, to the highest 
temperature, say that of the boiler. The efficiency 

^When we consider the surroundings as well as l^e reacting 
substances all reactions result in increases of entropy. 


is always less than 100 per cent by the number of per 
cent represented by this ratio. Since temperatures 
are measured from the absolute zero it is evident that 
all actual conversions of heat into work are remark- 
ably inefficient. Of the mechanical energy derived 
from heat energy there is always a certain amount 
which is expended in friction, so that the actual effi- 
ciency is even less than the "thermodynamic effi- 
ciency" which has just been explained. 

Energy once converted into heat and embodied in 
molecular motions can never be completely recov- 
ered. Strictly speaking, therefore, all natural proc- 
esses are irreversible because things can never be as 
they were. The fundamental cause of this so-called 
"thermodjmamic irreversibility" is to be found in the 
characteristics of molecular systems. 

Any material systems which we may use in experi- 
mental investigations involve billions and billions of 
molecules.. With these we can only deal statistically 
treating of average effects. Because of their large 
number, however, the desired average effects may be 
studied by the laws and methods of probability, the 
mathematical science of chance. 

In this field Maxwell made one of his many con- 
tributions to science. He determined the distribu- 
tion of velocities, among the molecules of a gas, 
which would satisfy the experimentally observed 
condition that the pressure on the walls of a retain- 
ing vessel is constant when the temperature is con- 
stant. He found that no matter how collisions oc- 
curred there would be a definite average velocity 
(perpendiciilar to the surface of the container) and 


that the proportion of the total numb^ of moleeules 
which had any particular velocity, eith^ greater or 
lef9N3 than the average^ was definite and calculable. 
If a plot is made, showing the percentage of mole- 
cules striking the contains and their corresponding 
velocities, the result is the form of probability curve 
shown in Fig. 36. 

We have already met one application of the theory 
of probability in the development of an expression 
for the average energy of a large number of oscil- 
lators, each restricted according to the quantmn hy- 


Fig. 36 

Diagrammatic representation of Maxwell's distribution of moliec- 

ular velocities. 

We shall now sketch briefly an application of the 
method of probabilities by which Boltzmann arrived 
at a concept of entropy, the characteristic magnitude 
in terms of which the second law is most satisfac- 
torily expressed. Imagine looking across two paral- 
lel tennis courts. The players are warming up for 
two sets of doubles and each member of a team is 
volleying with an opponent so that four balls are 
constantly in the air. We shall distinguish between 
the balls by the letters a, b, c, and d. 

The distribution of the balls with reference to the 
line of the nets changes from instant to instant. At 
one moment all four may be on the east side, and a 


moment later three on that side and one on the west. 
There are obviously five possible distributions, 
namely: all east, all west, three east and one west, or 
vice versa, and two on each side of the net. 

For any distribution there is one or more "com- 
plexions," as they are called. Thus the distribution 
of three east and one west might be the result aad 
would correspond to aoy one of four complexions, 
for there are four different ways in which we may 
have three balls on one side and one on the other. 
If we tabulate the various possible complexions we 
have the result given below : 

Distribution Gomplexion 

•East West East West 

4 abed 

3 I abc d 

abd c 

acd b 

bed a 






















• ••# •••••#99* *•#< 



o 4 


The distribution of two balls on either side of the 
net is the most probable distribution. Out of six- 


teen pcMSsible complexions this distribution oontains 
six, and that with the next largest niunber oontains 
four. For purposes of later analogy we also note 
that this distribution of two and two r^resents a 
sort of an equilibrium condition. We might also 
note that from the standpoint of an attendant, who 
is accustomed to seeing balls neatly packed in dozens, 
the distribution is not that of ord^. 

Now forget the players^ letting the balls represent 
molecules of a gas and let their niunber be enormous- 
ly increased. There will still be a distribution which 
will contain the maximum numba* of complexions 
and this will be the most probable distribution. It 
will also be the most probable state for the gas, the 
final "equilibriiun state" toward which systems of 
gas molecules inevitably tend. It wiU be the state 
with the largest number of complexions and the 
greatest number of ways in which the gas molecules 
may be associated, the state of greatest disorder. 

As Boltzmann defined it, "thermodynamic prob- 
ability" is a numbOT which expresses how much more 
probable a given state is than some "standard" or 
perfectly ordered state in which the substance occu- 
pies the same volume and has the same energy. 
For example, from the preceding table we see that 
the probability of the most "mixed-up" state is six 
times that of the state where all the balls are on one 
side of the net. The mixed-up state is most prob- 
able. There is always a natural trend toward the 
greatest disorder, toward the state of final equilib- 

When four balls are on one side of the net there is 


greater energy associated with this side than with the 
other. Hence, if we were dealing with molecules ^e 
would expect to obtain some of this energy by allow- 
ing them to pursue their natural haphazard motions 
and by their impacts to drive before them a molar 
body like the piston of an engine. Haphazard mo- 
tions wiU carry the balls across the net and they can 
do mechanical work, as, for example, upon a racquet 
held in their way. In the equilibrium state, how- 
ever, no mechanical work can be recovered, for on the 
average a racquet held over the net would receive as 
many and as hard impacts from one side as from the 
other. We now see that we cannot utilize or obtain 
from a gas, in the state analogous to fom* balls on 
one side, all the energy which its molecules appear to 
be able to expend, since the natural process upon 
which we rely proceeds only to a final equilibrium 
state corresponding to that of two balls on either side 
of the net. 

Unfortunately for the purposes of easy exposition, 
thermodjoiamic probability and entropy are not 
sjoionymous. There is, however, a definite relation 
between them. If one increases the other also in- 
creases but not in direct proportion. With this 
understanding we may proceed to use the term en- 
tropy in place of thermodynamic probability. 

All systems tend to a final state of maximum en- 
tropy, that is a condition of greatest molecular dis- 
order from which no mechanical work may be de- 
rived. N6t only no mechanical work but also no 
chemical or electrical changes can be brought about 
by such a system of itself in such a manner as to per- 


mit energy to be derived from these dxanges. The 
equilibrium condition is a ^'run-down condition'' 
which offers no hope to himian beings who would 
control nature's store of eaetgy. Althou^ energy is 
still associated with the intern its availability has 

Human beings need never be concerned with the 
cons^vation of energy since that is apparently in- 
herent in the entity itself. Their concern is with its 
availability. When en^gy transformations occur 
naturally, and in final analysis all transformations so 
occur, there is a reduction in availability, or as the 
scientist says, an increase in entropy. There is no 
known or anticipated scientific process^ despite all 
the discoveries of radioactive substances, whai^y 
this inevitable and natural increase in aitax)py may 
be avoided. It does seem unnecessary, however, 
that man should accelerate the irrev^!Bible trans- 
formati(His of nature. This he does whenever he 
fails to take from a natural process, as, for example^ 
from the combustion of coal, the fuU amount of use- 
ful energy which is his equity in accordance with the 
second law of thermodynamics. 

The final end of any conservative system, one 
which does not have energy communications with its 
neighbors, is not stagnation but disorder. Orderly 
(systems may have no more energy than disorderly 
systems but their energy is partly available. In- 
evitably any orderly system tends to a state of mazi- 
miun disorder. In the process of attaining this state 
its own entropy is increased. Only a certain amount 
of its energy is available and the expenditure of this 


margin is man's conc^n. It may be expended with 
foresight, as when a waterfall is utilized to make 
chemical compounds in which available energy is 
stored for later release, for example, in nitrogenous 
fertilizers. It may be expended without foresight in 
the innumerable ways which history records. Every 
fire or explosion, every inefficient process, represents 
an increase in the world's entropy — the sum total of 
its disorder. 



To a considerable extent the exposition of the 
previous text has been unrelated to our daily experi- 
ences. It has dealt with minute protons and elec- 
trons, with quanta of energy, and with granular 
structures so fine that they are only to be inferred 
and never to be seen. In this Appendix it is now 
proposed to assemble some numerical expressions 
whereby the tiny magnitudes involved in the modem 
science of electrons and quanta may be related to the 
grosser magnitudes with which we are famiUar. 

In terms of the fundamental scientific units, 
namely, the centimeter (1 cm. =0.394 inch), the 
gram (1 g.=0.0353 ounce), and the second, the sizes 

and masses of the electrical elements are extremely 
small and their number in any sensible volume ex- 
tremely large. Where extremes are to be met, 
numerical expression is most conveniently accom- 
plished by a slight modification of our common 
decimal system. 

Consider firat the expression of numbers greater 
than ten. Ten is one times ten; a hundred is one 
times ten times ten; and one thousand is one times 
the successive product of three tens; and so on as in 



the table bebw. The number of succeesive products 
of ten are represented by exponents of the proper 
value as shown. 

lo = I X lo = 

loo = I X lo X lo == 

1000= I X 10 X 10 X 10 = 

10000=1 X 10 X 10 X 10 X 10 = 

one million = = 

one billion = = 

one million million => = 

one billion billion = = 









On the same basis, any number like 606 is 6.06 
times a hundred or as illustrated below : 

606 = 6.06 X 10* 

6060 = 6.06 X 10* 

60600 = 6.06 X 10* 


When later we find that the number of molecules 
in two grams of hydrogen gas is 6.06X10 ** we shall 
be able to convert this expression into 606 thousand 
billion billion, and thus, perhaps, get some apprecia- 
tion of an enormous number. 

For numb^^ smaller than unity the system is 
equally simple. We write 1/10 as 10"^ ; and 1/100 
as 1/10^ and then as 1X10"^ as in the following 

0.1 = I X i/io = I X 10-^ 
0.01 = I X i/ioo = I X 10-* 
0.001 = I X i/io' = I X 10^ 

one millionth = = I X lor* 

one billionth = = i X lOr* 

one billionth of a billionth = = I X lO"** 


The use of these negative powers of ten is illustrated 


0.264 = 2.64 X 1/10 = 2.64 X 10*^ 
0.0254 = 2.64 X 10» 
0.00264 = 2.64 X lO* 

0.000,002,64 = 2.64 X lO** 

In addition to the convenience and brevity whidi 
this i^yBtem offers it serves to indicate most quickly 
the order of magnitude of a number and its signifi- 
cant figures. Consider for example the value of Avo- 
gadro's constant, that is the nimiber of molecules in 
one "mole" of any substance. ^ 

The most exact value for this constant is 6.062 X 
10^*, SB found by Millikan. 

From the second portion of this expression we 
recognize at once that the constant is of the order of 
hundreds of thousands of a billion billions. The 
first portion of the number contains the significant 
figures. If Millikan's determination had been less 
precise he might have found 6.06X10^', or with still 
less accuracy 6.0 X 10^*. In the latter case he would 
not have written the number as 6.000X10^ for that 
would have implied the same precision as does his 
actual value, that is a precision to the fourth signifi- 
cant figure. 

By the number of significant figures an experi- 
menter indicates the correctness of his results so far 
as concerns the precision with which he has made his 
measurements. He does not, of course, mean that 

*A mole is a number of grams equal to the molecular weight 
of the substance; thus in the case of hydrogen, Hs, a mole is two 
grams, but in that of oxygen, Oi, it is 32 grams. Without re^pEird 
to substance all moles will contain the same number of molecules. 


there may not be present in his determination 
fiouroes of error, inherent in the expmmental con- 
ditions, which may have rendered his results wrong 
even in order of magnitude. By proper attention to 
significant figures throughout any necessary calcula- 
tions he arrives at a final result each figure of which 
is really significant and not merely a result of an 
arithmetical process. 

Tali:ing a simple example, suppose he wishes to 
compute the circumference of a circle the diameter 
of which he has measured as 10.0 cm. He multiplies 
this diameter by Jt, but he uses for it, 3.14 and 
not 3.14156 or some stiU more accurate value. By 
his expression of the diameter as 10.0 cm. he means 
in substance that he has measured it with a centi- 
meter scale whidi is divided into tenths of a centi- 
meter, and that he does not know its value closer 
than a tenth of a centimeter. To write the circum- 
ference as 31.4156 cm. would imply a greater accur- 
acy than he has either right or desire to imply. 

When, therefore, we consider Millikan's value for 
Avogadro's constant we interpret it to mean that he 
has determined the number of molecules in a mole 
to the fourth significant figure. His value, then is 
in doubt by approximately 0.001X10^* or a mere 
matter of a hundred or so billion billion molecules. 
He is right, however, to within about one-hundredth 
of one per cent. A more exact knowledge than this 
would probably avail us but little since there are few 
physical conditions where we may detect a percent- 
age difference as small as this, and few physical con- 


stants which are expressible by more than four sig- 
nificant figures. 

We are now in a position to express numerically 
some important physical magnitudes. We shall 
not, however, go into any detail as to how they have 
been determined. Further, we shall allow the 
numerical values to create their own impressions 
instead of adopting conventional expedients to 
heighten them. For example, one might count the 
average number of letters on a page of the encyclo- 
paedia, divide this number into Avogadro's constant 
and find the number of pages which would be re- 
quired to cont^ a number of letters equivalent to 
this number of molecules, and then calculate the 
number of billions of complete sets ^ and so convey 
an impression. With more tediousness he could take 
the volume of atmospheric gas inspirated by an av- 
erage man in a single breath and by using Avogadro's 
constant express the number of molecules for this 
familiar case in terms of volumes of the encyclo- 
paedia. Arithmetical dexterity and interest will 
produce strange results by such a method, and the 
arithmetic is facilitated by the use of powers of ten. 

Sizes: Known distances in the physical universe 
extend from 10^* cm., representing the distance from 
the earth to the further nebulae, to 10'^^, representing 
the order of magnitude of the diametej of an elec- 
tron. With the microscope one can observe dis- 
tances in ordinary light of the order of 10*^ cm., and 
can detect illuminated specks of somewhat smaller 

* The advertisements say 4.4 x 10' words per set. Hence, allow- 
ing six letters to the word, almost a billion billion sets. 


dimenaiona The diamet^ of a molecule of oxygien 
is 2.99 X 10'^ cm. For hydrogen the diameter is lees, 
being 2.17X10'^ cm. The best indications of the 
diameter of an' electron give 2X10'^' cm. 

M 08968 : The mass of a hydrogm molecule is 3.33 
XlO*** g., and the mass of any oth^ molecule is 

larger in proportion to its molecular wei^t^ thus 
that of the oxygen molecule is 52.8X10'^^ g. The 
mass of the atom of hydrogen is half that of its mole- 
cule and this is also the mass of the proton. The 
mass of an electron is only about 1/1845 of the pro- 
ton and is thus 9.01X10-28 g. 

Velocities: The greatest velocity in the physical 
universe is that of li^t or of other forms of radiant 
energy. Light quanta apparently travel 2.999 X 
10^^ cm. per second. Beta particles have been 
measured witii velocities as hi^ as 9/10 of this. 
Alpha particles, with their greater mass, are ejected 
with smaller velocities in the ord^ of 1/10 the 
velocity of li^t. 

In a voliune of gas imder practically atmospheric 
conditions of pressure and temperature (so-called 
standard conditions) molecules travel wiUi velocities 
which are dependent upon their masses. Hydrogen 
molecules travel fastest, about a mile a ^second or 
1.69X10' cm. per second. Oxygen molecules with 
sixteen times the mass travel one-quarter as fast as 
hydrogen molecules, that is 4.2X10* cm. per second. 

Free Path of Gas Molecvles: Under these stand- 
ard conditions the atoms of a volume of hydrogen 
would travel on the average about 1.76X10*^ cm. be- 
tween successive collisions. On the average, there- 


fore, a hydrogen atom would make ten billion col- 
lisions per second. If the gas is less dense, for ex- 
ample, if the container has been exhausted until the 
pressure is 2.64X10'^^ of the normal atmospheric 
pressure, the number of molecules per c.c. has been 
similarly reduced and the mean free path is increased 
by 3.8X10® times. For oxygen, for example, the 
mean free path under atmospheric conditions is 9.4 
X 10"* cm. and imder the above conditions of rare- 
faction 3.54X10* cm. 

The velocity has not been altered by the reduction 
in pressiire for the temperature has been assumed 
undianged, and hence the kinetic energy is not al- 
tered. The molecule will now make only about one 
collision a second. Such extreme conditions of rare- 
faction are producible today by vacuum pumps 
which employ molecules to bombard other molecules 
and thus drive them from the desired enclosure. 
When the bombarding molecules have done their 
wcMrk they are removed by condensing them into 
drops of liquid. 

Av^adro^s Constcmt: A mole of any gas occu- 
pies a volume of 2.241X10* c.c, that is, about 22 
liters (about 0.79 cubic foot) under standard con- 
ditions of temperature and pressure. In this mole 
there are, as has been said, 6.062X10^^ molecules. 
Per cubic centimeter, therefore, there are about 2.705 
XlO^® molecules. Under the conditions of rare- 
faction which were mentioned above as attainable by 
the modem mercury vapor vacuum pump the num- 
ber per c.c. is reduced to about 7X10*, so that the 
nearest we can come to a perfect vacumn is a mere 


mattar of sevaid billicm molecules in eadi cubic 

Energy Units : The unit of en^gy is the erg. It 
represents twice the kinetic energy which is asso- 
ciated with a mass of one gram whidi is moving at 
the rate of one centimeter a second. It represents 
roughly one-thousandth of the work required to raise 
a gram vertically one centimeter. It is too small a 
unit for convenience in practical mechanics. For 
example, in lifting an ounce vertically a distance of 
l-inch one does 7.07 X 10^ a^ of work. The familiar 
unit of energy, known as the foot-pound, is equiva- 
lent to 1.35X10^ CTga The joule which is used in 
electrical engineering is 10^ ergs. The calorie which 
is the convenient irnit for measuring energy which 
appears as heat is equivalent to 4.19X10'^ ergs. 

Qtumta: Although the erg is too small for many 
practical purposes it is large compared to many of 
the amounts of energy with which the scientist is 
concerned. This is particularly so in the case of 
quanta. Planck's constant is 6.56X10"*^ and the 
number of ergs representing a quantum at any given 
frequency is the product of this constant, h, and the 
frequency n. For example, abput the highest fre- 
quency of visible light is 7.5X10^* vibrations per 
second, so that the corresponding quantmn is 5.0 X 
10"^^ erg. The frequency at which a heated body 
radiates the maximum amount of energy is about 
1.5X 10^*, which is in the infra-red r^on. The cor- 
responding quantum is only 9.9X10"^' erg. 

Gamma rays have the highest known frequencies, 
about 10^ vibrations per second. In this case the 


quantum has its maximum known value of about 6 
X 10-^ erg. 

Kinetic Energy of a Gas Molecule: The kinetic 
energy which, on the average, is associated with each 
molecule of a gas under standard conditions of pres- 
sure and temperature (O'^C.) is 5.62X10'^* erg, and 

for every degree increase in temperature the kinetic 
energy of translation is increased by 2.06X10'^® erg. 

Electrical Units: For measuring electrical phe- 
nomena three systems of units are used, but we shall 
restrict ourselves to the so-called practical units 
known to electricians and the consumers of electrical 

The Electron : The practical unit of quantity of 
electricity is the coulomb. It represents the amount 
of electricity which would be transferred in a silver- 
plating solution of silver nitrate every time that 
0.001118 gram of silver is deposited on the cath- 
ode. If a coulomb is passed through an electrolyte 
under conditions where hydrogen is liberated the 
mass of hydrogen gas is 1.038 X 10"*^ gram. To liber- 
ate a gram of hydrogen requires the passage of 96,- 
500 coulombs* In terms of the coulomb the charge 
of an electron (or of a proton) is 1.591 XlO"^* coul- 

Current: When there is a transfer of electricity 
through any conductor at the rate of one coulomb 
per second a current of one ampere is said to be flow- 
ing. It is thus evident that a current of one ampere 
represents a flow across each and every cross-section 
of the conductor of 6.3X10^® electrons each second. 

Electrical Potential: When a coulomb of elec- 


tridty is transferred betwe^i two points by an ex- 
penditure of one joule of ^lergy (10^ ei^) the points 
are said to dififa* in electrical potential by one volt. 
The lifting circuit of a house or office usually oper- 
ates at a voltage of 115. 

Power: By multipl3dng the voltage across and 
the current through any piece of electrical apparatus 
we find the numba: of joules per second whidi are 
being expended in the apparatus. For joules per 
second, however, there is used a single word, namely, 
watts. When energy is being expaided at the rate 
of one joule per second the power in the circuit is 
one watt. An ordinary house li^t, rated as. 40 
watts, takes a current of 40/115 ampere or a litUe 
more than a third of an amp^ie, and repres^its a 
flow of electrons at the rate of about 2.XlO^* a 

Ionization Potential: The kinetic energy whidi 
an electron acquires in free passage between two 
points differing in potential by one volt is about 1.59 
XlO'^^ erg. Jonization pot^itials are of the order 
of 10 volts so that it requires about 1.6X10"*® &rg to 
knock an electron free from an atomic structure. 
The ionization potential differs with the type of 
atom and some atoms require two or three times as 
much energy in the impact as do others. To ionize 
by removing two electrons requires more energy but 
the amount is still absurdly small compared to any 
of the energy expenditures of our daily lives. 

X rays : In an X-ray tube Uie electrons freed at 
the heated cathode are pulled across the intarv^iing 


space to the target under voltages of the order of 
150,000. As a result each electron delivers to the 
target an energy of about 2.4X10"^ erg. Thia is 
aJx)ut the highest value of energy which physicists 
Ixave yet been able to impart to an electron. 

The Inconstancy of Mass: Ma£» or inertia^ aa 
defined on page 40, depends upon energy and speed. 
[Neglect for the moment the conventional units used 
in this Appendix and return to the simple imits of 
the previous text. An electron moving with imit 
speed (1 cm. per sec.) has imit energy and under 
these conditions the electron has unit inertia. If it 
moves with twice the speed it has four times the en- 
ergy ; with three units of speed, nme units of energy; 
and so on, the energy of the moving electron being 
equal to the square of its speed as long as this speed 
is small as compared to the velocity of light (3X10^^ 
am. per second). Under these conditions the inertia 
or mass of the electron is constant and is measured 
by the ratio of the number of units of energy to the 
square of the number of units of speed. 

Actual comparisons have been made of the ener- 
gies of electrons at different speeds and it has been 
f oimd that as hi^er speeds were attained the energy 
was increasing enormously faster than was the 
square of the velocity, that is, that the iaertia of an 
electron is not constant but always greater for 
greater ^eeds, although the differences are imper- 
ceptible at speeds small as compared to light. For 
this reason the mass may be said to be inconstant. 
The same relation holds for molar bodies as well as 


electronic if we accept, as we must, the so-called 
''special relativity theory." This subject, however, 
demands a whole book to itself, and it has received 
many such in recent days. 


Absolute Zebo 

A temperature of 271.3° below zero on the Centigrade 

seale, equivalent to 456.3*^ below zero Fahrenheit. 
Absorption Spectrum 

A spectrum showing by their absence what radiations 

a given substance fails to transmit. 

Electrolytes for which one product of dissociation is 

a hydrogen ion. 
Alpha Particles 

The combination of four protons and two electrons 

which is expelled from the nucleus of a radioactive 

atom. An alpha particle is identical with the nucleus 

of a helium atom. 
Alpha Rays 

A stream of alpha particles. 

A unit of electrical current. See Appendix. 

A term applied to chemical elements which react either 

as electropositive or electronegative depending on the 

other reactants. 

The plate or other terminal in a conducting gas or 

liquid at which electrons or negative ions are collected. 

The positive electrode. 

The anode or target in an X-ray tube. 

An atomic system which is uncharged having equal 

numbers of protons and electrons. 
Atomic Number 

A number equal to the number of positive charges 



(protons) of a nucleus in excess of the number of nega- 
tive charges (electrons). 

Atomic System 
A nucleus and associated planetary electrons. It may 
be either a normal aUHn or an i(»L 

Atomic Weight 
The number representing, on a scale which assigns 16 
to oxygen, the average mass of the atom of any chemi- 
cal substance. 

A theoretical configuration of the electrons in an atom 
which would account for its properties. 

Electrolytes for which one dissociation product is a 
negative ion formed by an oxygen and a hydrog^ 

Beta Pabticle 
An electron which is ejected by the nucleus of a radio- 
active atom. 

Beta Rays 
A stream of beta particles. 

A unit of energy used in discussing heat. c/. p. 178. 

A chemical compotmd of a particular type which con- 
tains carbon, hydrogen and oxygen. Of this type the 
sugars are examples. 

A plate or other terminal in a conducting gas (or 
liquid) at which positive ions are collected or electrons 
are emitted. The negative electrode. 

Cathode Rays 
A stream of electrons proceeding outward from the 
cathode of a tube (of gas) which is conducting elec- 

Approximately 0.394 inch. 


The excess of positive or negative electricity in a 


Chemical Element 

A substance all of whose atomic systems have the same 
atomic niunber. 

Contact Electbomotivb Fobcb 

The potential difference which is set up by. the contact 
of two dissimilar substances, i. e., substances with dif- 
ferent electronic structure. 


A spectrum which includes all possible frequencies. 


A unit of charge, c/. Appendix. 


A disruption of a molecular system which may or not, 
as the case may be, result in neutral systems. Elec- 
trolytes dissociate into charged systems, the ions. 

A disruption of the nucleus of an atomic systenL 

Disintegration Product 
The atomic system which results when alpha or beta 
particles are expelled from a nucleus. 

Electrical Elements 
The electron and the proton. 


The metal plate which terminates the solid portion 
of an electrically conducting path, the other portion of 
which either is gaseous or liquid or is a vacuum. 

A solution for which the solute partially dissociates 
into ions. 

A piece of magnetic material about which is wound 
a current-carrying loop of wire. 

Electromagnetic Theory 
The generally accepted theory of electricity and mag- 
netism which was formulated by Maxwell. 

An instrument for measuring an electrical charge. 

The elementary corpuscule of negative electricity. It 
is complementary to the proton. 


A term applied to chemical elements whose atoms have 
a negative valence. 


The opposite of electronegative. 

An instrument for detecting an electrical charge. 

A term applied to an electrical charge which is fixed 
in position. 

The name applied to the product formed by the ex- 
pulsion of alpha particles from the nucleus of radiimi or 
thorium atoms. In this book radium emanation is 
called "niton." 

Emission Spectrum 
The spectrum of the radiation from a body. 

The name applied to the motive power in the physical 
universe. One of the two fundamental entities of 
modem physics; the other is electricity. 

A numerical expression which increases as energy loses 
its availability. 

A unit of energy, c/. Appendix. 

Giving rise to radiations of other frequencies than 
those which it absorbs. 

Number of oscillations per second: 

Gamma Rays 
A radiation, similar in type to X-rays, which proceeds 
outward from some radioactive atoms when the sub- 
stance is emitting beta rays. 

A unit of mass approximately equal to 0.0353 ounce. 

A series of equally spaced reflecting surfaces which 
serve to analyse radiations into their component fre- 


A characteristic unwillingness to change in state of 
motion which all bodies display. 

Of lower frequency than the visible radiation. 

An instrument for measuring distances very accurately 
in terms of wave lengths of visible light. Used by 
Michelson to measure the international meter. 

An atomic or molecular system which is electrically 
charged by virtue of an inequality in the number of 
its protons and its electrons. 

A disruption of an atom or molecule into ions or into 
ions and electrons. 

Ionization Potential 
The amount of potential energy which must be con- 
verted into kinetic in order that an impact of the body 
with which the energy is associated shall ionize an 
atom or molecule. 

A substance which occupies with another substance 
the same place in the periodic table of chemical ele- 
ments. The two substances then have the same atomic 
number but different atomic masses. 

A unit of energy, c/. Appendix. 

Kinetic Enebgy 
Energy associated with electricity in motion. 

Line Spectrum 
A discontinuous spectrum formed by radiation of only 
certain definite frequencies. 

The amount of matter in a body; more strictly, a 
measure of its ability to acquire kinetic energy. 

A number of grams of a given substance equal to the 
sum of the atomic weights of all the atoms in a molecule 
of the substance. 


Molecular Heat 
The heat required per molecule (strictly per mole) to 
raise the temperature of a substance 1^ centigrade. 


A union formed by two or more atomic systons. It 
may be either a normal molecule or an ion. 

A molecular system which is uncharged, having equal 
numbers of protons and electrons. 

Radium emanation. An inert gas of atomic number 86. 

One or more protons associated with electrons in a com- 
pact group central to an atomic system. 


An atomic or electronic system the parts of which 

vibrate or oscillate. 

Move apart except as restrained. 
Periodic Table 

The arrangement of the chemical elements, in asc^id- 

ing order of atomic numbers, in which elements of 

somewhat similar electronic structure, ^nd hence 

chemical properties, appear periodically. 

Emitting radiation as a result of radiation which is 

absorbed but after absorption has ceased. 

Pertaining to the emission of electrons which occurs 

under the action of light. 
Planck's Constant 

The factor of proportionality by which the frequency 

of an electronic oscillator must be multiplied in order 

to express a quantum in ergs. 
Planetary Electrons 

The electrons in an atom which are external to the 


The formation of aggregates of molecules which move 

about (in solution) as if they were single molecules. 


A stream of positive ions from a tube of conducting 


A measure of the potential energy which is available 
between two points. 


The measure of the potential energy which is associated 
with a unit quantity of electricity. 

Potential Enebgy 
Energy which it is assumed, upon the basis of the 
conservation of energy, is associated with the con- 
figuration of electrical systems. 

Potential Gradient 
The rate at which the potential difference between two 
points changes as the position of one is varied. 

The elementary corpuscule of positive electricity. It 
is ccmiplementary to the electron. 

A variable amoimt of energy, directly proportional to 
the frequency of the radiation which is emitted by an 
electronic oscillator. 

Energy, unassociated with matter, which is being trans- 
ferred through space. 

A term applied to substances the nuclei of whose atoms 
spontaneously disintegrate. 

The most famous radioactive substance, discovered 
by the Ciuies in 1897. 

Radiation emitted by a body which is absorbing radia*- 
tion from a distant source. 

RisisTANCE (Electrical) 
The unwillingness of a body to transmit electricity, 
which is measured by the ratio of an electrical potential 
(the cause) to a current (the effect). 

RisoNANCB Potential 
The amount of potential energy which must be con- 


verted into kinetic in order that an impact shall excite 
the characteristic radiation from an at(»n. 

Electrolytes which are neither acids nor bases. 

A discrete speck of light produced in a screen by the 
impact of a high speed ion, usually of an alpha particle. 


A tubular winding of wire formed by spiralling a wire 

as in Fig. 4. 
Specific Hbat 

Energy required to raise the temperature of unit mass 

of a substance one degree. 

An instrument for the quantitative analysis of radia- 
tion into its component frequencies. 

An instrument for the qualitative investigation of the 

component frequencies of a given radiation. 

A broad band of radiation in which the several com- 
ponent radiations are arranged side by side in the 

order of their frequencies. 
Temperature Enclobttre 

A region surrounded by walls which are maintained at 

a constant temperature. 
Temperature Equilibrium 

The condition of a system the parts of which undergo 

no relative changes in temperature. 
Temperature Radiation 

Radiation emitted as the result of the thermal agitaticm 

in a body. 

An electron emitted from a body as a result of thermal 

Thermodynamic Efficiency 

c/. p. 186. 
Thermodynamic Probability 

c/. p. 190. 
Thermodynamic Scale of Temperature 

A temperature scale starting from the absolute zero.