Unravelling the Mystery of the Atomic Nucleus || A Nucleus at the Heart of the Atom

A Nucleus at the Heart of the Atom

Les atomes, petits dieux. Le monde n’est pasune facade, une apparence. Il est: ils sont. Ilssont, les innombrables petits dieux, ils rayonnent.Mouvement infini, infiniment prolonge.

Henri Michaux, Difficultes, Plume.

Atoms, little gods. The world is not a facade, anappearance. It is: they are. They are innumerablelittle gods, they radiate. An infinite motion, in-finitely extended.

Prehistory of the Atom

The concept of atoms has existed for centuries, ever since thespeculations of Epicurus, until the hesitations of the abbotNollet. The first experimental manifestations and the conjecturesof Dalton, Avogadro and Prout. The atom, a modest point-likeobject at first, becomes adorned with spectral lines and claimsthe right to possess an internal structure.

We owe the idea that matter should be composed of small indivisible parts, atoms,to the Greek philosophers of the fourth and fifth centuries before Christ, namelyLeucippus, Democritus, and Epicurus. Their writings have been lost for the mostpart. But their ideas are expressed by the Latin poet Lucretius in his De RerumNatura [1]. He lays down several general principles:

B. Fernandez and G. Ripka, Unravelling the Mystery of the Atomic Nucleus:A Sixty Year Journey 1896 — 1956, DOI 10.1007/978-1-4614-4181-6 2,© Springer Science+Business Media New York 2013

47

48 A Nucleus at the Heart of the Atom

We start then from her first great principle

That nothing ever by divine power comes from nothing

[. . . ]

The next great principle is this: that nature

Resolves all things back into their elements

And never reduces anything to nothing.

These principles lead Lucretius to consider that matter is composed of primordiarerum, primeval bodies, in terms of which all others are constructed. When a bodyis destroyed, the original bodies are dispersed and used to form other bodies.The original bodies must therefore be indestructible and eternal. Many centurieslater, the chemical elements of Lavoisier express the same idea. The question ofdivisibility is raised. Can it be repeated forever? Lucretius claims that not:

To proceed with the argument: in every body

There is a point so small that eyes cannot see it.

This point is without parts, and is the smallest

Thing that can possibly exist.

[. . . ]

Besides, unless there is some smallest thing,

The tiniest body will consist of infinite parts

Since these can be halved, and their halves halved again,

Forever, with no end to the division.

So then what difference will there be between

The sum of all things and the least of things?

There will be none at all [. . . ] [1].

The existence of a lower limit of size, of indivisible original elements, atoms,appears to be a question of common sense: to imagine that matter could beindefinitely divisible leads to what Lucretius considers to be an absurdity.

Eighteenth Century: The Abbot Nollet

Debates concerning the existence of atoms lasted for centuries. In the middle ofthe eighteenth century, the abbot Nollet is a known physicist, a member of theRoyal Academy of Science, of the Royal Society of London and a professor ofexperimental physics in the college of Navarre. In 1743, he uses his last lecturesto write a Traite de physique experimentale1 for which he becomes famous [2]. Heasks whether matter is indefinitely divisible, and he concludes:

Although I am more inclined to admit the existence of atoms

or indivisible small bodies, than to suppose that matter can be

1A treatise of experimental physics.

Prehistory of the Atom 49

indefinitely divided, I cannot hide the fact that the argument which I

presented, specious as it might seem, is not strong enough to decide

upon the matter and that we do not have a valid answer.

The conclusion of the abbot Nollet is that of a modern physicist: lackingexperimental evidence, he does not conclude.

Beginning of the Nineteenth Century: John Dalton, William Prout,Gay-Lussac, Avogadro, and Ampere

Until the eighteenth century, the concept of the atom remained the same. Somebelieved in atoms, others did not, and it was impossible to decide who was right orwrong. A major development occurred at the end of the century. Antoine Laurent deLavoisier formulated what was to become the basis of modern chemistry, based onthe conservation of elements and of mass during chemical reactions. He proved thisby a systematic use of scales to measure weights. In 1792, the German chemistJeremias Benjamin Richter showed that, when a salt was formed, the acid andthe base always combined in a definite and constant proportion [3]. In 1794, theFrench chemist Joseph Louis Proust showed that substances always combine inconstant and definite proportions [4, 5]. It is this constancy of proportions whichled a British meteorologist and chemical theorist, John Dalton, to formulate atheory, exposed in his book New System of Chemical Philosophy [6] published in1810 and 1812 and which he completed in 1827. According to Dalton, the law ofconstant proportions can naturally be explained if simple elements are composed ofinvariable atoms which combine to make composite bodies. All matter is composedof indestructible particles, which are identical in a given element. Assuming whattoday we call a chemical formula, which specifies the respective proportions of thesimple substances which combine to make composite substances, he was able tocalculate the relative masses of atoms. For example, he assumed that an atom ofwater (today we would call it a molecule) is composed of an atom of oxygen and anatom of hydrogen. This allowed him to conclude that the oxygen atom is eight timesheavier than the hydrogen atom.1 In 1808, Joseph Louis Gay-Lussac made anotherdiscovery: in a chemical reaction, the volumes of the gases involved are in a simpleratio. For example, 1 liter of oxygen combines with exactly 2 liters of hydrogen inorder to produce water and, if the latter is in form of vapor, exactly 2 liters of watervapor are formed.

It seemed difficult to reconcile this strange law with the law of Proust, whichstates that the masses of elements involved occur in simple ratios. The puzzlewas resolved by Amedeo Avogadro [7] who expressed in 1811 his famous law:

1Dalton was making the simplest assumption. We know today that the water molecule is composedof one oxygen atom and two hydrogen atoms, which we write as H2O . In this case, the mass of anoxygen atom is 16 times higher than the mass of a hydrogen atom.


equal volumes of gas (at the same temperature and pressure) always containthe same number of molecules, whatever the gas is [8]. Sometime later, Ampereindependently came to the same conclusion [9]. This hypothesis, which was neededin order to understand the experimental results in terms of the atomic hypothesis,was truly astounding. It was not easily accepted, and since it was impossible tocount the number of molecules in a given volume, one might as well forget theatomic theory!

William Prout, a medical doctor who was also a chemist, took a further step.Basing himself on what he called the “volume doctrine” of Gay-Lussac, henoted [10] that the masses of known elements, which either he or other chemistshad measured, were proportional to the masses of a given volume of these elements(which today we call the density) when they are in the gaseous phase. He naturallyconcluded that the mass of each atom of a given element was proportional to hisdensity which he called the specific weight. He thus arrived at the same conclusionas Avogadro, expressed in another form. When he calculated the masses of atomsof 14 elements, ranging from carbon to iodine, he noted that they are multiples ofthe mass of hydrogen: carbon is 12 times heavier than hydrogen, nitrogen 14 timesheavier, oxygen 16 times, etc. This led him to propose a new idea: hydrogen couldbe the basic substance from which all atoms are formed:

If our way of understanding, which we take the risk of proposing,

is correct, we can almost assume that the [basic substance] of the

ancients is accounted for by hydrogen [11].

For the first time, the hypothesis is put forth that even atoms have an internalstructure.

Do Atoms Really Exist?

The reality of atoms was slowly accepted, but chemists took longer than physiciststo do so [12]. In 1853, Adolphe Ganot wrote in his Traite elementaire de Physique,published in Paris [13] and translated into English in 1862:

The properties of substances indicate that they do not consist of a

continuous matter, but of infinitely small elements, so to speak, which

cannot be physically split and which are assembled without touching

[. . . ] These elements are called atoms [14].

This does not imply that there existed a general consensus at the time. In a bookpublished in 1895, the Scottish physicist Peter Guthrie Tait (author, with WilliamThomson [lord Kelvin] of a treatise of physics which remained a reference until thebeginning of the twentieth century) writes, on the atomic theory of matter:

This theory must be regarded as a mere mathematical fiction, very

similar to that which (in the hands of Poisson and Gauss) contributed

so much to the theory of statical Electricity [. . . ]


A much more plausible theory is that matter is continuous ( i.e.

not made up of particles situated at a distance from one another)

and compressible, but intensely heterogeneous; [. . . ] The finite

heterogeneousness of the most homogeneous bodies, such as water,

mercury, or lead, is proved by many quite independent trains of

argument based on experimental facts. If such a constitution of matter

be assumed, it has been shown (W. Thomson, Proc. R.S.E., 1862.)

that gravitation alone would suffice to explain at least the greater

part of the phenomena which (for want of knowledge) we at present

ascribe to the so-called Molecular Forces [15].

It is true that, before the kinetic theory of gases was formulated, the atomichypothesis had no incidence on physics. It was only an hypothesis, an interestingphilosophical speculation, not necessarily true. But in chemistry, chemical formulasdiffered according to whether the atomic notation was used or not and so did thereference masses (“atomic” or “equivalent”). Since no agreement was reached,considerable confusion ensued. It is precisely in order to put an end to this confusionthat the German chemist August Kekule took the initiative to organize the firstinternational chemistry meeting [16]. It was held in Karlsruhe on September 3, 4,and 5, 1860. Although a general agreement was not reached, the Italian chemistStanislao Cannizzaro succeeded in convincing a number of his colleagues thatthe atomic notation had a pedagogical advantage and, from then on, it began todominate. In spite of this, the conjecture of Prout was progressively given upbecause increasingly precise mass measurements of Berzelius showed that themasses are not multiples of the hydrogen mass. For example, the Belgian chemistJean Stas believed in 1860 that the conjecture of Prout was only an illusion [17].

1865: Loschmidt Estimates the Size of Air Molecules

The atomic theory had two handicaps: both the size and the number of atoms ina given quantity of matter were unknown. The Austrian physicist Johann JosephLoschmidt was the first to propose a method to measure the size. In a communicationpresented to the Academy of Sciences in Vienna, Loschmidt used the value of themean free path calculated by Maxwell [18] who deduced it from the viscosity ofair.1 The mean free path is the average distance which a molecule of air travelsbefore colliding with another. Loschmidt showed how the mean free path allowedan estimate of the diameter of a molecule: he found one millionth of a millimeter.He knew that this was only an estimate, but he claimed that the order of magnitude

1The viscosity of a fluid determines the velocity with which it escapes out of a small orifice:hydrogen escapes much faster from a balloon than a heavy gas such as krypton. Gases have amuch lower viscosity than liquids: air has a viscosity a 100 times smaller than water, and water a1,000 times smaller than glycerine.


was correct [19]. Those who opposed the atomic hypothesis found a flaw in hisargument: it was based on the kinetic theory of gases, a theory which was notaccepted by all and which assumed the existence of atoms from the outset.

Spectral Lines: A First Indication of an Internal Structureof Atoms

From 1859 onwards, the German physicists Gustav Kirchhoff and Robert Bunsenshowed that the spectrum of light emitted by a given element, when viewed in aspectroscope, consists of lines with definite wavelengths: each element possesses itsown set of spectral lines, by means of which it can be identified. The existence ofsuch spectra is necessarily caused by the structure of the atoms which radiate them.This was the first experimental indication of an internal structure of the atom.

Jean Perrin Advocates the Reality of Atoms

On February 16, 1901, students and members of the Amis de l’Universite de Parisare gathered to hear a lecture of Jean Perrin on the “molecular hypothesis.” At theage of 30, Jean Perrin [20,21] was the author of a brilliant thesis in which he showed,in 1895, that cathode rays carried a negative electric charge [22]. He had been alecturer at the Sorbonne for 2 years. Perrin explains what he still calls the “molecularhypothesis”:

The hypothesis, which is generally assumed to be the simplest,

consists in assuming that any pure substance, water for example, is in

fact composed of a very large number of distinct material particles, all

completely identical, which mark the point beyond which water can

no longer be divided. Those are the molecules of the body [23].

Jean Perrin goes on to explain how the measurement of the viscosity of a gasgives a first estimate of the size of molecules and, as a consequence, of their number:

The number N of molecules contained in a liter of gas, at normal

temperature and pressure, is, as we might have expected, extraordi-

narily large. One finds that it is equal to 55 billion trillions (1022), a

number which is so large that it surpasses our imagination.

During the following years, Jean Perrin devoted his efforts to the determinationof the number of atoms in matter, to be more exact, to the number N of atoms inone mole} of an element, called one “gram-atom” at the time: it was the number ofatoms in 1 g of hydrogen, the lightest of all elements.

One gram of hydrogen gas contains only half as many molecules because eachmolecule is composed of two atoms of hydrogen. Thus 2 g of hydrogen contain


N molecules, the same number contained in 32 g of oxygen, 28 g of nitrogen,because their atomic mass, chemically determined, are in this ratio. Perrin proposedto call this number N the “Avogadro constant” [24]. Today, we call it the Avogadronumber or Avogadro constant. To measure this number, Perrin makes use ofEinstein’s interpretation of Brownian motion. In a book, Les Atomes,1 publishedin 1913, he compares a dozen methods, which are all independent, the intensity ofthe blue sky, radioactivity, Brownian motion, the Planck constant, and more. Hefinds that they all give consistent results,2 and he concludes:

We can only admire the miracle which yields such a precise agreement,

starting from so different phenomena. First, we obtain the same

order of magnitude, with each of the methods, [. . . ] second, the

numbers which are thus unambiguously defined by so many methods,

coincide; this gives to the reality of molecules a likelihood close to a

certainty [25].

A precise determination of the Avogadro number would reveal the real mass ofatoms. The chemical methods used in the nineteenth century could determine theratios of the masses, so that the masses were only known one relative to another. Ifone single mass could be measured, the others could be deduced. And this wouldreveal the size of molecules, assuming that, in a liquid, the molecules would be incontact with each other. For example, if N molecules were known to be containedin 18 g of water, the volume of which is 18 cm3, one could calculate the averagevolume occupied by each molecule of water and therefore estimate its size. TheAvogadro number was a key to many unknowns!

In 1926, Jean Perrin received the Nobel Prize of physics for his determination ofthe Avogadro number.

1Atoms.2These values ranged from about 6:2 � 1023 to about 6:8 � 1023. The presently adopted value is6:022 141 29 � 1023. See the glossary.

The Electrons Are in the Atom 55

1897: The Electrons Are in the Atom

The discovery of the electron, a universal constituent of matter,leads to a burst of speculations in Cambridge, Paris, Heidelberg,Tokyo. . . J. J. Thomson describes the atom as consisting ofthousands of electrons and proposes a “plum-pudding” model ofthe atom. Barkla succeeds in counting the number of electronsin an atom. Nobody understands what prevents the atom fromradiating.

Electric Discharges in Gases, Cathode Rays and the Electron

The study of cathode rays culminated in 1897 with the measurements of EmilWiechert, Walter Kaufmann, and J. J. Thomson, to whom history attributes thediscovery of the electron. Furthermore, the passage of electricity, caused by eitherX-rays or particles emitted by radioactive substances passing through a gas, wasinterpreted as an ionization of the atoms in the gas. The transformation of atomsinto ions was a phenomenon familiar in electrolysis: the atom splits into two ions,one positively and the other negatively charged. The positively charged ions hada mass comparable to the mass of the original atom, and the so-called “negativeions” had a much smaller mass: they displayed an uncanny resemblance to cathoderays. J. J. Thomson measured their mass and electric charge: they were electrons.Thus atoms, the existence of which was not yet universally acknowledged, were notindivisible and eternal objects, because they were able to emit these tiny electrons!The presence of electrons in the atom was further confirmed when Lorentz explainedthe Zeeman} effect. The existence of an inner structure of the atom thus becameconvincing, and the structure involved electrons. In addition, it was known that theˇ-rays emitted by radioactive substances were high-velocity electrons. By 1903, itbecame obvious that the atom contained electrons.

“Dynamids”: The Atoms of Philipp Lenard

In 1903, Philipp Lenard proposes another model of the atom. Born in Hungary in1862, Philipp Lenard obtained the position of Privatdozent in Bonn and becamethe assistant of Hertz. Hertz suggested that he should send a beam of cathoderays through a thin film of aluminum which was just strong enough to maintainthe vacuum. The famous “Lenard window” was constructed, and it led to a seriesof original experiments. Lenard made several crucial observations concerning the


photoelectric effect, which had been discovered by Hertz, namely, that the numberof electrons emitted by the metal depends only on the intensity of the incidentlight, whereas their energy depends only on its frequency. This will be explained byEinstein 2 years later, in 1905. Lenard’s model relies on the fact that cathode rays,namely electrons, pass through matter very easily. This led Lenard to postulate thatthe atom is an assembly of what he called “dynamids,” which are very small particles(more than 10,000 times smaller than the size of the atom) which are separatedby empty space. According to Lenard, “the space occupied by 1 m3 of platinumis empty, just like the astronomical empty space.” Indeed, it is only filled with“dynamids,” the total volume of which does not exceed 1 ml3. This is why cathoderays pass through matter so easily. He believed that a dynamid was an electricallyneutral particle, consisting of an electron associated to a positive charge. Lenard wasawarded the Nobel Prize in 1905 for his work on cathode rays. After that, he becametruly paranoic and he accused everyone of stealing his ideas and his discoveries. Hecould never forgive Einstein for having explained the photoelectric effect which heconsidered to be “his” effect. An ardent Nazi, he occupied an important position inthe Nazi party, and in 1933, he became one of the “theoreticians” of “Aryan science”as opposed to “Jewish science” which included relativity and quantum mechanics.

Numeric Attempts to Describe Spectral Rays: Balmer and Rydberg

There was one perfectly clear and yet completely enigmatic indication of the internalstructure of atoms: namely, the spectral rays which became both a strange andprecise signature of every element. The permanent structure of rays of differentcolors defied all understanding. Failing a physical explanation, several physicistsattempted to discern a logical pattern of the rays. In the report he delivered inthe International Physics Congress of 1900, the Swedish physicist Johannes RobertRydberg, specialized in spectroscopy, quoted about 40 such numerical patterns [26].Only one entered history, the one of the Swiss mathematician Johann Jacob Balmer.In 1885, he showed that the wavelengths � of the four known hydrogen lines, calledH˛ , Hˇ ,H� , and Hı, obeyed the following simple mathematical formula [27]:

� D hm2

m2 � n2;

where h is a factor which is determined empirically and where m and n are smallintegers, equal to 2, 3, 4, and 5. Rydberg generalized this pattern by stating that thefrequencies of the hydrogen spectral rays are equal to the differences of the inversesquares of small integers, multiplied by a constant which today is still called theRydberg constant. This was an entirely empirical law, and nobody understood themeaning of the integers nor the value of the Rydberg constant.


J. J. Thomson’s First Model: An Atom Consisting Entirelyof Electrons

After having discovered that cathode rays consist of small particles which everybodywill soon call “electrons,” J. J. Thomson attempts to measure their mass m and theirelectric charge e. He first measures the ratio e=m which is determined by theirdeflection in a magnetic field. He then makes a direct measurement of their electriccharge by measuring the velocity of small electrically charged water droplets, fallingin the air and by measuring the change in their velocity when they are exposed to anelectric field [28]. This is a very difficult experiment which the American physicistRobert Millikan repeated later [29] using oil droplets which had the advantage ofnot evaporating in the air, as water droplets do, thereby modifying somewhat theresults of the measurements. J. J. Thomson thought that atoms were composed ofelectrons. He knew that electrons were 2000 times lighter than the lightest atoms,which should therefore contain thousands of electrons. The snag was that electronscarry a negative electrical charge, whereas the atom is electrically neutral. In spiteof this, he believed that it was the most plausible hypothesis:

I regard the atom as containing a large number of smaller bodies

which I will call corpuscles; these corpuscles are equal to each other;

the mass of a corpuscle is the mass of the negative ion1of the gas at

low pressure, i.e. about 3�10�26 of a gramme. In the normal atom, this

assemblage of corpuscles forms a system which is electrically neutral.

Though the negative corpuscles behave as negative ions, yet when

they are assembled in a neutral atom the negative effect is balanced

by something which causes the space through which the corpuscles

are spread to act as if it had a charge of positive electricity equal in

amount to the sum of the negative charges of the corpuscles [30].

J. J. Thomson is visibly embarrassed by the negative charge of the electrons in theatom. He formulates a vague hypothesis according to which “something” wouldmodify space which would behave “as if” it was positively charged. In fact, in 1904,he wrote a letter to Oliver Lodge [31] expressing the hope that he could do withoutthis positive electric charge.

A Speculation of Jean Perrin: The Atom Is Likea Small Scale Solar System

In the talk delivered to the Amis de l’Universite de Paris,2 Jean Perrin stresses animportant point:

1What Thomson refers to here as a negative ion is an electron.2“Friends of the University,” see p. 52.


What is essential to note is that the negative particles appear always

to be absolutely identical, whatever the atoms they are ejected from1.

And he imagines a possible structure of the atom:

For the first time a path leads to the intimate structure of the

atom. We will, for example, make the following hypothesis, which

corroborates the preceding facts. Each atom would consist, on one

hand of one or several positively charged masses—a kind of positive

sun the electric charge of which would greatly exceed that of a

particle—and, on the other hand, by numerous particles acting as

tiny negatively charged planets orbiting under the action of the electric

forces, their negative total charge balancing exactly the total positive

charge, thereby making the atom electrically neutral.

He underlines the fact that this is but one of the models which one can conceive.However, he calculates the velocity with which the electrons rotate around their“sun,” and he notes that the rotations have frequencies similar to the frequencies ofthe observed spectroscopic rays. This planetary model of the atom has however aserious drawback which Perrin fails to mention: according to the laws of classicalelectrodynamics, the rotating electrons should radiate electromagnetic waves. Theenergy which they would spend radiating would have to originate from their motion,and they should therefore eventually fall onto what Perrin calls their “positive sun.”One could calculate that it would take hydrogen atom only one ten-millionth of asecond to disappear! Jean Perrin will not make a deeper study of his speculationnor will he publish anything on the subject. His talk is published in the RevueScientifique (Revue Rose), which maintains a good standard but which is not aspecialized scientific journal [23].

The “Saturn” Model of Hantaro Nagaoka

A few years later, the Japanese physicist Hantaro Nagaoka, professor in the ImperialUniversity of Tokyo, proposes a somewhat similar model. He explains that he is notthe only one to seek an explanation of spectral rays:

Since the discovery of the regularity of spectral lines, the kinetics

of a material system giving rise to spectral vibrations has been a

favorite subject of discussion among physicists. The method of enquiry

has been generally to find a system which will give rise to vibrations

conformable to the formulæ given by Balmer, by Kayser and Runge,

and by Rydberg [32].

He then explains his model in which the electrons form rings similar to the ringsof Saturn:

1The emphasis on “absolutely identical” is by Jean Perrin.


I propose to discuss a system whose small oscillations agree qualita-

tively with the regularities observed [. . . ] The system consists of large

number of particles of equal mass arranged in a circle at equal angular

intervals and repelling each other with forces inversely proportional to

the square of the distance; at the centre of the circle, place a particle

of large mass attracting the other particles according to the same law

of force.

He is perfectly conscious of the objection which one could have already raisedto the model of Jean Perrin:

The objection to such a system of electrons is that the system must

ultimately come to rest, in consequence of the exhaustion of energy

by radiation, if the loss be not properly compensated.

Without replying to this objection, Nagaoka pursues and writes down theequations which determine the stability of the system. His calculations remainhowever formal, and he makes no numerical evaluation. He simply states that thecentral charge must be “very large” compared to that of the electron. He studies theform of the vibrational modes. Unfortunately, a simple calculation suffices to showthat the rings becomes unstable as soon as an electron moves out of the plane of therings. This instability should be added to the one caused by the radiation.

The “Plum-Pudding” Atom of J. J. Thomson

Two months earlier, Joseph John Thomson, following an idea which had been putforth by Lord Kelvin [33], published a paper in the Philosophical Magazine, inwhich he proposed another model, consisting of electrons embedded in a positivelycharged sphere [34]. The electrons are subject to two opposing forces: the repulsiveforces which attempt to separate the negatively charged electrons and the attractionwhich is exerted on them by the positively charged sphere, as soon as they attemptto escape from it. The positively charged sphere has the size of the atom. Themain problem addressed by Thomson is the stability of such a system. Does thesystem have an equilibrium shape such that, if it is perturbed, it returns to itsequilibrium shape, or does the atom fall apart? To answer this question, Thomsonis inspired by the experiments of Alfred Mayer, a physicist who became known fordesigning some simple, pedagogical, and yet spectacular experimental setups. In his“floating magnet” experiment [35], Mayer stuck a few magnetic needles verticallyinto a floating material and let them float freely on water, their north pole pointingvertically upwards. Left as such, the magnetic needles would repel each other witha force which decreases as the square of the distance separating them. However,Mayer then placed a strong negative magnetic pole above the water. The floatingneedles are all attracted to this pole by a force which decreases as the inverse ofthe distance to the negative pole. The magnetic needles, which are forced to moveon the water surface, are subject to two opposing forces, similar to the electrons on


the “plum-pudding” model of J. J. Thomson. Mayer noticed a curious phenomenon:the magnetic needles had a tendency to form concentric rings on the water surface.This observation led Thomson to formulate a model in which the electrons rotatein concentric rings. He shows that this is a stable configuration provided that theelectrons rotate fast enough. The atom is akin to a merry-go-round!

However, as in the other models, the electrons should radiate and the atomtherefore cannot remain stable. In a previous publication, Thomson showed thatthe energy radiated by a large number of electrons, rotating and equally spaced on acircle, decreases as the number of electrons increases. For example, two electrons,rotating at a speed equal to 1/100 of the speed of light, radiate 1000

�103

�times less

energy than a single electron; six electrons would radiate 1017 times less energy.And because Thomson believes that the atom contains thousands of electrons, hisargument carries some weight, even if his atom still suffers from some instabilities.Thomson is quite aware of the fact that his model assumes that the electrons allmove in a plane, as planets almost do in the solar system, but what forces theelectrons to do so in a real atom? He admits to not having a mathematical solutionto this problem. However, he attempts to imagine a solution by extrapolating whathe considered to be natural:

When the corpuscles are not constrained to one plane, but can move

about in all directions, they will arrange themselves in a series of

concentric shells; for we can easily see that, as in the case of the ring,

a number of corpuscles distributed over the surface of a shell will not

be in stable equilibrium if the number of corpuscles is large, unless

there are other corpuscles inside the shell, while the equilibrium can

be made stable by introducing within the shell an appropriate number

of other corpuscles.

This is his plum-pudding model of the atom, named after the very BritishChristmas pudding. It becomes a new version of the electronic theory of matter.It will remain a reference until the work of Rutherford,1 in 1911.

Charles Barkla Measures the Number of Electrons in an Atom

J. J. Thomson thought that the mass of the atom was the sum of the masses of itsconstituent electrons. This is why he assumed that the atom contained thousands ofelectrons. A crucial step consisted therefore in measuring the number of electrons.

As soon as they were discovered in 1895, X-rays fascinated physicists. Asearly as 1897, Jean Perrin noticed that, in addition to ionizing the gas theypassed through, X-rays caused a particular phenomenon when they impinged ona metal [22, 36]. The French physicist Georges Sagnac then showed that the gas,

1See p. 74.


through which X-rays had passed, became the source of a secondary emission,which he called a proliferation and which he thought was due either to a scatteringprocess or to luminescence [37]. He was particularly interested on the effect of X-rays impinging on metals [38]. In a series of experiments which he performed withPierre Curie [39,40], he showed that the secondary emission carried negative electriccharge: it consisted of electrons. The other emitted rays were X-rays probablyscattered by the atoms, just as light is scattered by particles of smoke.

In 1902, a 25-year-old physicist begins to study the secondary X-rays producedby gases and he will continue to do so all his life. Charles Barkla studied inthe University of Liverpool, after which he worked at the Cavendish under thesupervision of J. J. Thomson. It is at King’s College that he tackles the problem.He observes the secondary X-rays emitted by various gases (air, hydrogen, sulfurichydrogen, carbon dioxide, sulfur dioxide) exposed to a primary X-ray beam. He hasan electrometer with which he measures the intensity of the secondary rays and itsprogressive attenuation as it passes through matter. The rate at which the secondaryradiation is absorbed allows him to estimate, roughly at least, its energy. With thiselectrometer, together with a few absorptive sheets, Barkla obtains an importantresult: all gases subject to X-rays, emit secondary X-rays which are identical to theprimary X-rays. The secondary radiation is more intense when the gas is composedof heavy atoms [41]. Barkla makes a careful measurement of the rate at which theX-rays are absorbed by air. He finds that their intensity is reduced by 0.024 % percm of air they pass through [42]. This attenuation had in fact been calculated byJ. J. Thomson with his electronic theory of matter [43]. Thomson assumed thatthe X-rays were scattered (or disseminated, as Sagnac would say) by the electronscontained in the atoms of the gas. He could relate the attenuation of X-rays to thenumber of electrons contained in a given volume of gas. Barkla uses the formulagiven by Thomson, and he concludes that the number of electrons contained in1 cm3 of gas is equal to 0:6 � 1022. This corresponds to about a 100 electrons peratom of nitrogen. He concludes that the X-rays are indeed reemitted by the electronsand not by the molecules of the gas, which would need to be a hundred billion timesmore numerous to produce the observed effect. J. J. Thomson then uses the results ofBarkla to measure the number of electrons per atom. He invents two further methodsto measure this number, which are completely independent of the method used byBarkla: the index of refraction of the gas (in other words its capacity to deflectlight) and the attenuation of ˇ-rays passing through the gas. The three methods givecompatible results:

The evidence at present available seems sufficient [. . . ] to establish

the conclusion that the number of corpuscles is not greatly different

from the atomic weight [44].

The atom does not therefore contain thousands of electrons as Thomson himselfhad suggested. Thomson does not mention this nor does he discuss the problemof the stability of the atom, in spite of the fact that with so few electrons, hisatom cannot be stable. Nonetheless, as noted by Abraham Pais [45], the paper ofJ. J. Thomson is a decisive step forward because it gives a tangible information


about the structure of the atom, namely, its number of electrons. For several years,Barkla continues to study X-rays. In 1911, he discusses his 1904 measurements inthe light of more precise values available for the mass and the electric charge ofelectrons. He estimates that:

The theory of scattering as given by Sir J. J. Thomson leads to the

conclusion that the number of scattering electrons par atom is about

half the atomic weight in the case of light atoms [46].

He adds the footnote:

This applies to atomic weights not greater than 32, with the possible

exception of hydrogen.

The picture becomes clearer: carbon, for example, with atomic mass 12, wouldhave six electrons; oxygen, with atomic mass 16, would have eight electrons, andhydrogen, a single electron.

The Scattering of ˛ Particles 63

The Scattering of ˛ Particles Makes It Possible to “See”a Nucleus in the Atom

The genius in Manchester, namely Ernest Rutherford, observesdeviations of the trajectories of ˛-rays, which were believednever to deviate. He actually sees them rebound from a collisionwith an incredibly small nucleus. The stability of the atomremains a mystery.

An Observation of Marie Curie

In 1900, Marie Curie studied the penetration power of ˛-particles which she stillconsidered to be rays which could not be deviated [47]. She used a radioactivesource consisting of polonium, which was known to radiate only ˛-particles. Shewas surprised to discover that the ˛-rays, which could not be deviated, would losetheir ionization power after traveling a distance of only 4 cm in the air. Furthermore:

The rate of absorption of the non-deviable rays increases as they pass

through increasing thickness of matter. This singular absorption law

is opposite to the one known for other radiation; it suggests rather

the behavior of a projectile which looses part of its kinetic energy by

passing through obstacles [47].

In their report to the 1900 International Congress of Physics, Pierre and MarieCurie emphasize the curious absorption law of the rays which could not bedeviated [48].

William Henry Bragg: The Slowing Down of ˛-Particles in Matter

A few years later, in 1904, a physics professor in the University of Adelaide, SouthAustralia, happens to read the paper of Marie Curie. William Bragg was born,July 2, 1862, in Westward, Cumberland, a county in North-East England. Afterbrilliant studies in mathematics in Cambridge, he studied physics at the CavendishLaboratory, under the supervision of J. J. Thomson. But that same year, he accepteda professor’s chair at the University of Adelaide, in Australia. His first 20 yearsthere were devoted to teaching. But the paper he reads changes everything:


It was known that when the radium atom broke up into two parts, one

large and one small, the latter, which was really an atom of helium, was

driven into the surrounding air, and these particles constituted what

was called the ‘alpha’ radiation. Mme Curie described experiments

which implied that all the alpha particles thus expelled travelled about

the same distance.

This interested me greatly. All ordinary radiations fade away

gradually with distance; the alpha particles seemed to behave like

bullets fired into a block of wood. But, if this were so, the particle must

travel in a straight line through the air, as the bullet does through the

block. Now some hundreds of thousands of air atoms would necessarily

be met with on its journey. How did it get past? [. . . ]

There was only one answer to the problem. The particle must go

through the air atoms that it met [49].

Together with his assistant Richard Kleeman, he studies ˛-particles emitted byvarious radioactive substances. Bragg speculates: the ˛-particle must pass throughatoms without being deviated from its straight-line trajectory. He assumes that theonly difference between ˛- and ˇ-rays is that ˇ-particles are deflected by collisions,whereas ˛-particles are not. We are in 1904, and Bragg believes in the model ofJ. J. Thomson, according to which the ˛-particle consists of thousands of electrons,which explains its behavior:

The ˛ ray is a very effective ionizer, and rapidly spends its energy on

the process. It is of course far more likely than the ˇ ray to ionize an

atom through which it is passing, because it contains some thousands

of electrons and the ionizing collision is so much more probable. But

a collision between an electron of the flying atom of the ˛ ray and

an electron of the atom traversed, can have very little effect on the

motion of the ˛ atom as a whole [50].

In the experiments which he performs with Kleeman, he shows that the ionizationis roughly constant throughout its trajectory and suddenly stops at the end. He usesa very thin radium source because he does not have access to a polonium source, asMarie Curie did. He observes a complex curve which suggests the existence of threeor four groups of ˛-particles with different velocities. He proposes the followinginterpretation:

The atom passes through several changes, and it is supposed that at

four of these an ˛ atom is expelled. Probably the ˛ particles due to one

change are all projected with the same speed. We ought therefore to

expect four different streams of ˛ particles, differing from each other

only in initial energy.

The fact, that all the ˛-particles emitted by a given radioactive substance havethe same energy, will play an important role later. The paper ends by a detailedstudy performed with Kleeman and dated September 8, 1904. As Marie Curie hadobserved 4 years earlier, they note that:


The alpha particle is a more efficient ionizer towards the extreme end

of its course [51].

They attempt to explain this phenomenon:

The disturbing influence of the ˛ particle in its transit through an atom

must become greater as the speed diminishes. The diminution is not

likely to be great except at the end. [. . . ] Theoretical considerations

based on a somewhat insufficient hypothesis show that the effect

should be inversely proportional to the energy of the moving particle

[. . . ]. It is possible that it is only at the end, when the change of

velocity is very great in proportion of what remains, that the influence

of this cause is perceptible. It is also conceivable that the particle, as

its speed approaches the critical value below which it looses the power

of penetration, may leave its rectilinear path and be buffeted about,

causing a considerable amount of ionization without getting much

further away from its source.

They present a last paper on the subject to the Royal Society of South Australia. Itis published in September 1905 in the Philosophical Magazine. Bragg and Kleemanrepeat their previous conclusions, and they add more precise data on the trajectoriesof the ˛-particles emitted by radium and of the emanation of radium A and C, whichthey determine to, within half a millimeter [52]. The slowing down of ˛-particlespassing through matter is the subject of a series of subsequent experiments in otherlaboratories [53–55]. They confirm the results of Bragg, namely, that:

• ˛-particles emitted by a given radioactive substance all have the same velocity.• The slowing down of ˛-particles is roughly constant (slightly increasing in fact)

along its observed trajectory, and it suddenly increases considerably towards theend of its trajectory, and drops to zero soon after.

The “Scattering” of ˛-Particles

By that time, Rutherford, then at the University of McGill, is determined to ascertainthe nature of the ˛-particle. He believes that it is an ionized helium atom, buthe has no decisive proof of this. He makes precise measurements of the chargeto mass ratio e=m of ˛-particles and makes sure that it does not depend on theirvelocity. In a talk delivered to the Royal Society of Canada, he praises the resultsof Bragg and Kleeman and he calls range the distance to which the ˛-particlespenetrate into matter [56]. The word is used by the military to designate the “range”of firearms. We return to the concept of a projectile, suggested by Marie Curie.According to Rutherford, the ˛-particle emitted by a radioactive substance is aprojectile of “exceptional violence.” Rutherford begins to measure the velocity of˛-particles which pass through successive thin aluminum strips, by deviating themwith a magnetic field. He finds that the range measured by Bragg is also the distancebeyond which the ˛-particles fail to leave a trace on a photographic plate or to cause


phosphorescence on a zinc sulfide screen. Beyond this range, the ˛-particles can nolonger be detected; they disappear. In a paper dated November 15, 1905, Rutherfordreports for the first time that the spot formed by ˛-particles, after passing through agiven thickness of matter, becomes broader and loses some of its definition:

The greater width and lack of definition of the ˛-lines have been

noticed in all other experiments and show evidence of an undoubted

scattering of the rays, in their passage through air [57].

It follows that ˛-particles may well be deviated when they pass through matter.On February 27, 1906, Rutherford sends a letter to the Philosophical Magazine inwhich he reports on his most recent observations of the slowing down of ˛-particles.The slowest observed ˛-particles had 43 % of their initial velocity, and he confirmedthat they retained their mass and charge, no matter what their velocity was [58]. Ina complete paper, dated June 14, 1906, he describes this “scattering”:

There is [. . . ] an undoubted slight scattering or deflection of the path

of the ˛ particle in passing through matter [. . . ]

From measurements of the width of the band due to the scattered

˛ rays, it is easy to show that some of the ˛ rays in passing through the

mica have been deflected from their course through an angle of about

2ı. It is possible that some were deflected through a considerably

greater angle; but, if so, their photographic action was too weak to

detect on the plate [. . . ]

It can easily be calculated that the change of direction of 2ı in the

direction of the motion of some of the ˛ particles in passing through

the thickness of mica (0,003 cm) would require over that distance

an average transverse electric field of about 100 million volts per cm.

Such a result brings out clearly the fact that the atoms of matter must

be the seat of very intense electrical forces—a deduction in harmony

with the electronic theory of matter [59].

Rutherford considered this to be an important result which was thereafter studiedin various laboratories [60–62]. In 1907, when he became professor of physics atthe University of Manchester, Rutherford marked on his notebook a list of “possibleresearches” [63]. It consisted of ideas for experiments, among which were the“scattering of ˛-rays” and the “number of ˛-rays from radium,” experiments whicheventually completely modified the physics of the atom.

The Nature of the ˛-Particle: An Unresolved Question

Rutherford still does not consider that the nature of the ˛-particle is firmlyestablished; its electric charge, for example, is not measured. On January 31, 1908,he delivers a talk at the Royal Institution:


We may regard the ˛-particle as a projectile traveling so swiftly that it

plunges through every molecule in its path, producing positively and

negatively charged ions in the process. On an average, an ˛ particle

before its career of violence is stopped breaks up about 100,000

molecules. So great is the kinetic energy of the ˛-particle that its

collisions with matter do not sensibly deflect it, and in this respect

it differs markedly from the ˇ-particle, which is apparently easily

deflected by its passage through matter. At the same time, there

is undoubted evidence that the direction of motion of some of the

˛-particles is slightly changed by their passage through matter [64].

Although its charge to mass ration e=m is known, the mass of the ˛-particle isunknown. The observed deviations produced by a magnetic field suggest that itsmass is similar to that of a light atom. It could have two units of charge and fourunits of mass (i.e., a mass equal to four times the mass of hydrogen), in which caseit could be a helium atom which has lost two electrons. But it could equally wellhave a single unit of charge and two units of mass. To decide, it was necessaryto devise an instrument able to count the ˛-particles one by one. With such aninstrument, Rutherford would be able to count the number of particles emitted by agiven quantity of radium, measure their total electric charge, and deduce the electriccharge of a single ˛-particle.

The First Geiger Counter

On his first visit to the laboratory in Manchester, Rutherford was guided by a youngphysicist, Hans Geiger, who showed him the available equipment and described theongoing experiments. Geiger was finishing a one-year postdoc position and wasabout to return to Erlangen, in Germany.

Hans Geiger was born on September 30, 1882, in Neustadt, in the Palatinate,which was then part of the kingdom of Bavaria [65, 66]. He studied in Erlangenwhere his father was professor of ancient languages. In 1906, he defended his Ph.D.thesis on the discharge of gases. His thesis advisor was Gustav Wiedemann [67].He then spent one year in Manchester. He must have pleased Rutherford, whosuggested that he should stay longer and work with him. Geiger must have beenimpressed by the reputation and the personality of Rutherford, and he gave up theidea of returning to Erlangen.

Geiger was an exceptionally gifted and rigorous experimentalist with an insa-tiable desire to work [68]. He acquired both prestige and popularity in the lab.In a speech delivered in 1950, the chemist Alexander Russel spoke of him in thefollowing terms:

Geiger was too much of an Olympian for me to know him well. Gentle,

without being docile, and aloof, he seemed in laboratory hours to live

entirely for the work. He was a beautiful experimenter of the Sir James


Dewar type, splendid with his hands. Like many Germans, he loved

good music and good dinners [69].

Rutherford still intends to count the ˛-particles, one by one, but the amountof electricity induced by one particle is far too small to induce a signal in anelectrometer. He calculates that the ionization caused by an ˛-particle producesabout 20,000 pairs of ions, which could produce a potential of 6 �V with theavailable electric fields and capacities. That was too small to be observed.

John Townsend, who was professor in Oxford and whom Rutherford hadmet before in the Cavendish, discovered and studied a potentially interestingphenomenon [70–73]. It was well understood (and Rutherford had contributed tothis) that the electric current, which passes through a gas exposed, for example, toX-rays, is due to the ionization of the molecules of the gas which liberate electronsand positive ions. The observed current is due to the motion of the electrons. Whenthe applied electric field} is progressively increased, the current increases at firstand then it reaches a constant value. It is said to “saturate.” Indeed, when theapplied electric field is weak, the velocity of the electrons is small and some of themcan recombine with positive ions and form neutral atoms. This has the unfortunateconsequence that the induced electric current is not a measure of the initial numberof liberated electrons and therefore of the intensity of the X-rays. When the appliedelectric field is increased, the electrons move faster and eventually none of themrecombine. This is why the induced electric current attains a constant “saturation”value. However, Townsend, who was studying gases maintained at a low pressure,showed that, when the applied electric current is further increased above a certainvalue, the induced current increases again, because the electrons then acquire avelocity large to enough to ionize other atoms which in turn emit electrons. In otherwords, the number of electrons proliferates, just as a falling snowball can grow intoan avalanche. More charge is then collected than had originally been liberated bythe X-rays. There is an amplification of the signal.

This phenomenon became known as the “Townsend avalanche,” and it attractedthe attention of Rutherford. It might provide a way to detect a single ˛-particle.Rutherford probably knew about the experiment performed by P. J. Kirkby, astudent of Townsend, who constructed an apparatus which consisted of an aluminumcylinder, which played the role of a cathode, and of a wire running along itsaxis which was the anode [74]. Rutherford suggests that Geiger should attemptto use this phenomenon in order to detect individual ˛-particles. A year later, in1908, Rutherford and Geiger succeed in making the first counter work. After ashort communication sent to the Manchester Literary and Philosophical Society onFebruary 11, they send a detailed report [75, 76] to the Royal Society on June 18. Itis a decisive step towards the detection of radiation.

This first counter is the ancestor of “Geiger counters.” It is a metallic tube, 25 cmlong and 17 mm in diameter. A metal wire runs through the center. A potential of1,200–1,300V is established between the wire which is connected to the positivepole of an electric battery (or rather to a rack of hundreds of batteries connected inseries), while the external cylinder is connected to the negative pole. The cylinder


contains a gas (air or carbon dioxide) maintained at a low pressure, a few percent ofnormal atmospheric pressure. When an ˛-particle passes through the tube, electron-ion pairs are created along its trajectory. The electrons are attracted to the positivecentral wire, while the ions travel towards the external cylinder. The electrons,being much lighter, acquire a considerable velocity. Furthermore, the cylindricalshape causes the electric field}, which drives the electrons towards the centralwire, to increase as they approach the wire. They acquire sufficient velocity toionize the molecules they collide with, and new pairs of electrons are thus created.This is the avalanche phenomenon described above. In the first counter constructedby Rutherford and Geiger, one electron could produce a 1,000 electrons, therebyamplifying considerably the electric signal on the wire. The goal was attained: asingle ˛-particle, passing through the counter produced an observable effect on theelectrometer. Rutherford finally succeeded in counting individual ˛-particles. Thisancestor of Geiger counters, which are still used today, was not so easy to use.Between 10 and 20 s were required for the “avalanche” to die out before anotherparticle could be detected. However, Rutherford set out immediately to count thenumber of ˛-particles emitted by a sample of radium-C.

The Nature of the ˛-Particle

That same day, Rutherford and Geiger send another communication to the RoyalSociety, concerning “the electric charge and the nature of the ˛-particle.” From theoutset, they state:

In a previous paper, we have determined the number of ˛-particles

expelled per second per gramme of radium by a direct counting

method. Knowing this number, the charge carried by each particle

can be determined by measuring the total charge carried by the ˛-

particles expelled per second from a known quantity of radium [77].

After a detailed description of their experiment and of their results, they quotethe result they worked so hard to achieve:

Considering the data as a whole, we may conclude with some certainty

that the ˛-particle carries a charge 2e, and that the value of e is not

very different from 4 � 65 � 10�10 E.S. unit.

They add a footnote:

It is of interest to note that Planck deduced a value of

e D 4 � 69 � 10�10 E.S. unit from a general optical theory of the natural

temperature-radiation.

The agreement cannot be fortuitous. Rutherford finally reaches his goal:


We may conclude that an ˛-particle is a helium atom, or, to be more

precise, the ˛-particle, after it has lost its positive charge, is a helium

atom.

But that is not all. Once the electric charge of the ˛-particle is known, it becomespossible to calculate other fundamental quantities. Thus, the radioactive half-life ofradium is estimated to be 1760 years (today, the value of 1600 years is retained).They also determine the famous Avogadro number, by a completely independentmethod. The value they find agrees with the other determinations. They stand onsure ground.

Another Way to Count ˛-Particles: Scintillations

There was in fact another way to detect ˛-particles one by one. Fluorescentsubstances, such as zinc sulfide, were known to emit a weak light signal when theywere placed in the proximity of a radioactive source. In 1903, William Crookesobserved the luminous surface of zinc sulfide through a magnifier. He noticedthat the luminosity was not constant but that it was caused by a large number ofpunctual and very short flares. He even constructed a simple device to observethem, which he named the “spinthariscope,” from the Greek word spintharis, spark,scintillation [78]. Elster and Geitel made the same observation [79]. It was quitetempting to attribute these flares to a passing particle, but how could one be surethat it was one and only one particle which caused the substance to scintillate? Inhis lectures on “radioactive transformations” delivered in 1905 in Yale University,Rutherford reviews the ways in which radioactive radiation could be detected andmeasured:

There are three general properties of the rays from radioactive

substances which have been utilized for the purpose of measurements,

depending on (1) the action of the rays on a photographic plate, (2)

the phosphorescence excited in certain crystalline substances, (3) the

ionization produced by the rays in a gas [57].

He is however cautious concerning the counting of flares in a scintillatingsubstance:

The property of the ˛ rays of producing scintillations on a screen

covered with zinc sulphide is especially interesting, and it has been

found possible by this method to detect the ˛ rays emitted by feebly

active substances like uranium, thorium and pitchblende. Screens of

zinc sulphide have been used as an optical method for demonstrating

the presence of the emanations from radium and actinium. Speaking

generally, the phosphorescent method, while interesting as an optical

means for examining the rays, is very limited in its application and is

only roughly quantitative.


But as soon as he could use his counter to evaluate the accuracy of thescintillation method, Rutherford and Geiger compare results obtained by the twomethods. Good news:

The number of scintillations observed on a properly-prepared screen

of zinc sulphide is, within the limit of experimental error, equal

to the number of ˛-particles falling upon it, as counted by the

electrical method. It follows from this that each ˛-particle produces a

scintillation [76].

The two independent methods give the same results. During the following20 years, Rutherford will exclusively use the scintillation method, which was mucheasier to use. The young German physicist Erich Regener, who was trying tomeasure the elementary electric charge}, made a careful study of the method.He perfected an operating procedure to count particles using a scintillating ma-terial [80]. He recommended to work in a weakly illuminated room, and to usea microscope with a medium magnifying power and a large aperture, in order toincrease the luminosity of the flares. The screen was dimly illuminated. Each timea scintillation occurred, the physicist would press an electric contact which causeda deviation of the line on the paper strip of a chronograph. The counting requiredgreat concentration in order not to miss a flare. Eyes would quickly tire, and thismade it necessary to make short observation periods and take frequent breaks.A well-trained observer could register 95 % of the flares, provided that no more thanabout 20 flares would occur per minute. The method had many advantages. First, itallowed to detect only ˛-particles because neither ˇ- nor � -rays would producevisible scintillations. Furthermore, the device was very simple to set up and reliable.For 20 years, it remained the supreme method of counting ˛-rays.

Back to the Scattering of ˛-Particles

While they were perfecting their counter, Rutherford and Geiger noticed a weakscattering of the ˛-particles which had to pass through a 4 m tube before beingdetected. The scattering was caused by the gas remaining in the tube. Rutherfordthen proposed that Geiger should make a systematic study of the scattering of ˛-rays using the scintillation method which had proved to be so accurate. On July17, 1908, Rutherford reports to the Royal Society on the first observations made byGeiger, who placed a source of ˛-rays at the extremity of a tube 114 cm long. Afterpassing through the tube, the ˛-particles pass through a narrow slit before beingdetected on a screen situated 54 cm from the extremity of the tube. The apparatusis maintained in vacuum. No scattering of the ˛-particles is observed. The particlesmove in a straight line. But if a gold or aluminum sheet is placed in front of the slit,the image becomes blurred:

The observations just described give direct evidence that there is

a very marked scattering of the ˛-rays in passing through matter,


whether gaseous or solid. It will be noticed that some of the ˛-particles

after passing through the very thin leaves—the stopping power of one

leaf corresponded to about 1 mm of air—were deflected through quite

an appreciable angle [81].

Hans Geiger makes a systematic study of these deviations. He studies thedeviations of ˛-particles by various metals of different thickness. He uses goldsheets because gold is the metal which produces the largest deviations. Afterobserving the deviation caused by up to 35 gold sheets, he concludes that the mostlikely angle by which an ˛-particle is deviated is proportional to the atomic weightof the atoms of the sheet placed in front of the slit. In the case of gold, the angleis, on the average, about 1/200 of a degree after passing through a single atom [82].The deviation can be considerably larger after passing through a large number ofatoms:

The probable angle through which an ˛-particle is turned in passing

through an atom is proportional to its atomic weight. The actual value

of this angle in the case of gold is about 1/200 of a degree.

Geiger observes deviations as large as 15ı. About 3,000 deviations, all in thesame direction, would be required to attain such a large deviation. This is mostunlikely since successive deviations have random values. These large deviationspuzzle Rutherford.

The Experiments of Geiger and Marsden

In a talk given in Cambridge in 1936,1 Rutherford recalls:

One day Geiger came to me and said, “Don’t you think that young

Marsden, whom I am training in radioactive methods, ought to begin

a small research?” Now I had thought that too, so I said, “Why not

let him see if any ˛-particles can be scattered through a large angle?”

I may tell you in confidence that I did not believe that they would be,

since we knew that the ˛-particle was a very fast massive particle, with

a great deal of energy, and you could show that if the scattering was

due to the accumulated effect of a number of small scatterings the

chance of an ˛-particle being scattered backwards was very small [84].

1The University of Cambridge organized in 1936 a series of lectures on the history of science.Rutherford delivered two lectures entitled “Forty Years of Physics,” the first one on “The Historyof Radioactivity” and the second one on “The Development of the Theory of Atomic Structure.”These lectures were published in a book, Background to Modern Science [83], but Rutherforddied before being able to write them in a form suitable for publication. The text was thereforeprepared by John Ratcliffe, a radiophysicist from Cambridge, on the basis of the verbatim taken bya stenographer.


The young Ernst Marsden was a 20-year-old student. Rutherford continues:

Then I remember two of three days later Geiger coming to me in

great excitement and saying, “We have been able to get some of the

˛-particles coming backwards[. . . ]”. It was quite the most incredible

event that ever happened to me in my life. It was almost as incredible

as if you fired a 15-inch shell at a piece of tissue paper and it came

back and hit you [85].

On June 17, 1909, Rutherford presents to the Royal Society the work of Geigerand Marsden:

When ˇ-particles fall on a plate, a strong radiation emerges from the

same side of the plate as that on which the ˇ-particles fall [. . . ]

For ˛-particles a similar effect has not been previously observed,

and is perhaps not to be expected on account of the relatively

small scattering that ˛-particles suffer in penetrating matter. In the

following experiments, however, conclusive evidence was found of the

existence of a diffuse reflection of the ˛-particles. A small fraction of

the ˛-particles falling upon a metal plate have their directions changed

to such an extent that they emerge again at the side of incidence [86].

Geiger and Marsden used sheets consisting of various metals: aluminum, iron,tin, gold and lead. They noticed that the effect is larger with heavier metals. Theystack a number of plates of various thicknesses and they observe that, to some extent,the effect increases with the thickness of the target, which proves that the effect isnot a reflection on its surface but a phenomenon which occurs inside the sheets.

It seems very surprising that some of the ˛-particles, as the experiment

shows, can be turned within a layer of 6 � 10�5 cm of gold through

an angle of 90ı, and even more [. . . ] Three different determinations

showed that, of the incident ˛-particles, about 1 in 8 000 was reflected,

under the described conditions.

Are the Large Deviations Caused by Multiple Small Deviations?

How could one understand that a particle as massive and rapid as an ˛-particlecould rebound on a surface which was expected to be soft? According to theplum-pudding model of Joseph John Thomson, the ˛-particle would pass througha kind of positively charged jelly (the pudding) where it would collide only withnegatively charged particles which had a 7 000 times smaller mass and which couldtherefore not scatter them backwards. A first possibility would be multiple scatteringduring which the ˛-particle would undergo a large number of small deviations.However, in a different context, Lord Rayleigh (William Strutt) had calculated themean deviation caused by a succession of random deviations [87]. According tohis calculation, the fraction of ˛-particles which would suffer deviations larger than90ıwould be much smaller than the fraction observed by Geiger and Marsden.


Rutherford Invents the Nucleus

Rutherford ponders for a long time. A year later, on December 14, 1910 he writesto his friend Bertram Boltwood:

I have been doing a good deal of calculation on scattering. I think I

can devise an atom much superior to J. J.’s, for the explanation of

and stoppage of ˛ and ˇ particles, and at the same time I think it will

fit extraordinarily well with the experimental numbers. It will account

for the reflected ˛ particles observed by Geiger, and generally, I think,

will make a fine working hypothesis. Altogether I am confident that we

are going to get more information from scattering about the nature

of the atom than from any other method of attack [88].

He is of course referring to the large angle scattering of ˛-particles and “J. J.”is no other than J. J. Thomson. And indeed, a short time later in 1911, as Geigerrecalls:

He entered my office visibly in a good mood and he told me that he

now knew what the atom looked like and how one could understand

the large deviations. That same day, I began research to check the

relation which Rutherford had established between the deviation angle

and the number of particles. The strong variation of this function with

angle made my work relatively easy and it was possible to check rather

quickly at least the approximate validity of his model [89].

Rutherford reached what he believed to be an inescapable conclusion. If the ˛-particle bounces back, it must have undergone a strong thrust from a sufficientlymassive object. And this must have occurred in a single collision, because toofew particles would scatter backwards in the case of multiple collisions. However,with the plum-pudding model of J. J. Thomson, backward scattering would beimpossible because, although the sphere carrying the positive charge may havesufficient mass, it dilutes the positive charge in a too large volume. There remainsone other possibility, the only one Rutherford can think of: the sphere must be muchsmaller. At first he even imagines that the positive charge is concentrated at onepoint. An ˛-particle which gets close enough to the tiny positively charged spherecan scatter backwards and Rutherford calculates the fraction of particles whichscatter at a given angle. The first measurements of Geiger confirm his calculation.What might at first have appeared to be a crazy idea, acquires some substance andin a two-page note read to the Manchester Literary and Philosophical Society, onMarch 7, 1911. Rutherford presents a first description of his model of the atom:

The scattering of the electrified particles is considered for a type of

atom which consists of a central electric charge concentrated at a

point and surrounded by a uniform spherical distribution of opposite

electricity equal in amount [90].


This atom is quite different from the model of J. J. Thomson! In April, Rutherfordwrites a paper which is published in the May issue of the Philosophical Magazine.From the outset, he states:

Since the ˛ and ˇ particles traverse the atom, it should be possible

from a close study of the nature of the deflection to form some idea of

the constitution of the atom to produce the effects observed. In fact,

the scattering of high speed charged particles by the atoms of matter

is one of the most promising methods of attack of this problem. The

development of the scintillation method of counting single ˛ particles

affords unusual advantages of investigation, and the researches of

H. Geiger by this method have already added much to our knowledge

of the scattering of alpha rays by matter [91].

He then presents a detailed account of his model. He describes the trajectoriesof the scattered particles and he estimates the value of the positive electric chargeconcentrated at a point in the center of the atom. He also discusses the possible sizeof the central positive charge:

It is of interest to examine how far the experimental evidence throws

light on the question of the extent of the distribution of the central

charge.

He then shows that one cannot explain the observed results if the ˛-particles passthrough the volume occupied by the positive charge (otherwise they would suffersmaller deviations). The central region is therefore very small. Rutherford estimatesthat for a substance consisting of atoms with a central charge equal to 100 units ofelementary charge, which he believes is the case of gold,1 some of the ˛-particlescome as close as 3 � 10�12 cm to the central charge, which is 30,000 times smallerthan the atom itself! Furthermore not only is the total positive charge concentratedthere, but so is practically all the mass of the atom! This is all which Rutherfordclaims at the time. Such a structure is reminiscent of the model proposed by Perrinor Nagaoka, the latter being simply quoted in the paper. He does not dwell furtheron the question of the stability of atom:

The question of the stability of the atom proposed need not be

considered at this stage, for this will obviously depend upon the minute

structure of the atom, and on the motion of the constituent charged

parts.

Indeed, an atom with such a structure is a priori unstable. According to a theoremproved by Samuel Earnshaw, there is no static equilibrium state for particles whichinteract with forces which are proportional to the inverse square of the distanceseparating them [92]. But if electrons wander around the central positive charge asplanets do around the sun, then they should radiate energy and the system would notbe stable.

1It was measured shortly afterwards to be equal to 79 units of elementary charge.


So far, Rutherford only mentions a “small region” of charge concentrated atone point. In a paper dated August 16, 1912 and published in October, he uses,apparently for the first time, the Latin (and therefore learned!) term nucleus [93].The word was used in biology to designate the nucleus of a cell. The strange andincredibly small object which concentrates all its positive charge and practically allits mass now bears a name: the nucleus of the atom.

As mentioned above, Rutherford did not dwell on the structure of the atom andhe was well aware of the fact that his model was unsatisfactory. He simply statedwhat his experiments suggested. For him, the role of the experimentalist consisted inreading nature. And he read beyond doubt that the atom consisted of a tiny nucleussurrounded by electrons. Why did it not radiate? A young Danish physicist wouldsoon resolve the problem.

Moseley Measures the Charge of the Nucleus 77

A Last Ingredient: Moseley Measures the Chargeof the Nucleus in the Atom

Max von Laue succeeds in diffracting X-rays. Bragg invents theX-ray spectrometer. The young Moseley measures the character-istic radiation of elements. The atomic number of Mendeleev isno longer simply a catalogue number, but is identified, instead, toa fundamental physical constant, namely the number of positiveelectric charges in the nucleus of the atom.

Barkla Creates X-ray Spectroscopy

We described above the fundamental work of Barkla on X-rays, which allowedthe determination of the number of electrons in each kind of atom.1 Now Barklamakes another important observation: part of the secondary X-ray radiation, causedby atoms irradiated by primary X-rays, does not have the same energy as theprimary X-rays. This secondary radiation is not a simple scattering because itsenergy is independent of the energy of the primary radiation. It is characteristicof the irradiated element [46, 94–101]. Barkla lists, element by element, not theenergy (which he could not measure) but the absorption coefficient (a numberwhich measures how quickly the radiation is absorbed as it passes through matter)which depends sensitively on the energy. He notes also that this characteristic X-rayradiation behaves exactly as fluorescence}, and he notices that these “fluorescentRontgen radiations” can be divided into two families, which he first calls A and B

but which he later prefers to call K and L because, he claims, there must certainlybe radiation which is more penetrating that the one he labels K and less penetratingthan the one he labels L. One can only wonder and admire how Barkla managedto obtain such a wealth of data, using simply an X-ray source, an electrometer anda few aluminum sheets. The road is now clear for a precise measurement of thewavelength of the X-rays.

1See p. 60.


The Diffraction of X-rays: Max von Laue, William Henryand William Lawrence Bragg

As soon as X-rays were discovered, physicists attempted to obtain diffraction} orinterference} which would have immediately proved the wave-character of the X-rays. However these early attempts failed. The French physicist Gouy [102] X-rayeda fine grating of wires, with no result and this allowed him to fix an upper limit of50 A on the wavelength of X-rays.1 In 1903, two Dutch physicists form Gronigen,Hermanus Haga and C. H. Wind used a 15 �m (15/1000 of a millimeter) slit as asource and a triangular slit for diffraction, the width of which was 27 �m at oneend and zero at the other. However, their results were not conclusive [103]. In 1909,two physicists from Hamburg, B. Walter and R. Pohl, made a similar attempt. Theycould only give an upper limit to the wavelength of the X-rays, namely somewherebetween one and one tenth of an angstrom [104].

In 1912, the young Paul Ewald was preparing his Ph.D. thesis in Munich, underthe leadership of Arnold Sommerfeld. It is for this work that he sought the adviceof Max von Laue, who was then a Privatdozent (assistant) in Munich, on themathematical analysis he was making of light passing through a crystal. Max vonLaue asked him what would happen in the wavelength of the light was smaller thanthe distance separating the atoms in the crystal, and Ewald replied that his analysiswould still remain valid. Laue then wondered if that would not be a way to diffractX-rays and he suggested to Walter Friedrich, an assistant of Sommerfeld, to dothe experiment. In spite of the skepticism of Sommerfeld, Friedrich performed theexperiment with the help of the student Paul Knipping. The roughly 1-mm wide X-ray beam was focused by a series of slits. It was incident on a crystal. Photographicplates were placed behind and on the side of the crystal. At first, they used a coppersulphide crystal and the image was blurred. Then, with a blende (a zinc sulphidecubic, waxlike and bluish crystal) they obtained a much finer picture consisting ofgeometrically placed spots which clearly showed that the X-rays were diffracted bythe crystal [105]. Von Laue made a mathematical analysis of the diffraction patternwhich showed that the incident beam had a definite wavelength [106]. His analysisenabled him to determine the ratio between the wavelength of the incident X-rays,and the distance between the atoms in the crystal. He found thus that the wavelengthof the X-rays was very small, between 3 % and 14 % of the distance separating theatoms, which is about 1 A.

The next step was taken by William Henry Bragg, whom we mentioned inconnection with his work on the slowing down of ˛-particles,2 and his son WilliamLawrence Bragg. The two succeeded in obtaining the diffraction of X-rays whichwere reflected by the crystal [107]. Their X-ray spectrometer was similar to anoptical spectrometer, except for the fact that the prism was replaced by the crystal,

1One angstrom is equal to one ten-millionth of a millimeter.2See p. 63.


on which the X-rays were reflected before impinging on a photographic plate oran ionization chamber [108], which enabled them to measure also the intensity ofthe reflected beam. Their first results were spectacular: by displacing the detector,they found that the intensity of the beam varied with the reflection angle and that itdisplayed well defined peaks, which indicated monochromatic rays on top of a whitebackground, consisting of a mixture of several wavelengths. They had discovered away to measure the wavelength, which was much simpler than the method usedby von Laue. This new spectrometer gave birth to two new domains of physics:the study of X-rays emitted by various elements and the study of the structure ofcrystals. William Henry, the father, worked mostly on the first, whereas WilliamLawrence, the son, mostly on the second.

Henry Moseley Measures the Charge of Nuclei

As soon as the results of von Laue, Friedrich and Knipping were published, ayoung physicist from Manchester begins an active study of X-rays. Henry GwynJeffreys Moseley [109] was born in 1887. He obtained his Ph.D. in Oxford afterwhich he joins Rutherford in Manchester. He first uses the experimental setup ofFriedrich et Knipping, and then the one of Bragg. He publishes a first paper in1913, with Charles Galton Darwin, a theoretician in Manchester, the grandson ofthe founder of the theory of the evolution of species. Moseley is mainly interested inthe “selective reflection” which had been observed by the two Braggs. He describesthe experimental difficulties [110]:

The ratio of the selective to the general reflection is greatly increased

by limiting the breadth of the slits and so increasing the parallelism of

the primary beam. Unfortunately, a very small rotation of the crystal

will then remove all traces of the selective effect. It therefore proved

necessary to take readings with the crystal set at every 50 of arc

between 10ı and 14ı.

This preliminary work allows him to measure the scope of the problem.Moseley then begins to measure, for each element, the wavelengths of theX-ray radiation, which Barkla called the “characteristic radiation.” He measuresthe wavelength of the radiation of eleven elements: calcium, scandium, titanium,vanadium, chromium, manganese, iron, cobalt, nickel, copper and zinc [111]. Ineach case he finds two high-frequency rays, which he calls ˛ and ˇ, and he noticesthat the wavelengths decrease regularly as the atomic masses increase.

Moseley then makes a big discovery. He draws a table in which he notes, for eachelement, the famous characteristic angles, the wavelengths of the ˛ and ˇ radiation,


the atomic mass (which was called the “atomic weight” at the time), and a quantityQ; which he calculates using the wavelength.1

Until that time, the atomic number was simply an index which denoted theorder of the elements in the Mendeleev table and by which the elements wereordered by increasing mass (with a few exceptions). It is upon ordering the elementsthat Mendeleev noticed some regularities in the chemical properties of variouselements}. In 1913, the atomic number had no physical or chemical meaning. ButMoseley notices something curious:

It is at once evident that Q increases by a constant amount as we pass

from one element to the next, using the chemical order of the elements

in the periodic system. Except in the case of nickel and cobalt, this

is also the order of the atomic weights. While, however, Q increases

uniformly, the atomic weights vary in an apparently arbitrary manner,

so that an exception in their order does not come as a surprise. We

have there a proof that there is in the atom a fundamental quantity,

which increases by regular steps as we pass from one element to the

next. This quantity can only be the charge on the central positive

nucleus, of the existence of which we already have definite proof [. . . ]

We are therefore led by experiment to the view that N is the same

as the number of the place occupied by the element in the periodic

system [111].

Moseley made a major discovery: the atomic number of an element is equal to thenumber of elementary charges in the nucleus of the atom! He can even measureit. He works very hard, assembling and disassembling apparatus to improve it.He constructs a second spectrometer and soon he publishes a second paper [112].He has measured the K-rays of 44 elements, ranging from aluminum to gold andhe determined their atomic number. From then on, the atomic number will beunderstood as the number of charges in the nucleus.

A year after the onset of the First World War, Moseley is drafted into the navyand is killed in the battle of the Dardanelles. In a letter, Rutherford announces thissad news to his friend Boltwood:

You will be very sorry to hear that Moseley was killed in the Dardanelles

on Aug. 10th. You will see my obituary notice of him in Nature. He

was the best of the young people I ever had and his death is a severe

loss to science [113].

Clearly, Rutherford considered Moseley to be one of the best physicists of hisgeneration.

1In fact he used the frequency which he called �, related to Q by the expression Q D q�

34 �0

,

where �0 is a reference frequency related to the Rydberg constant N0 D �0

cD 109:72.


A Paradox

Through the work Rutherford, Barkla and of Moseley, experiment had spoken: theatom appears to consist of a central nucleus, with a known positive charge and mass(almost equal to the mass of the atom). The nucleus is surrounded by electrons,the number of which is equal to the charge of the nucleus, so that the atom iselectrically neutral. But there is a flaw in this model. As discussed above,1 Newton’sand Maxwell’s laws forbid the existence of such a stable and static structure. Theelectrons would always end up collapsing into the nucleus. If electrons describeorbits around the nucleus, as planets do around the sun, then Maxwell’s equationsalso state that this is an unstable state, because a rotating electron would radiate,lose its energy and finally collapse into the nucleus.

There is no solution to this problem, within the framework of the dynamics ofNewton and of Maxwell. Who will have the imagination, the clear-sightedness andthe audacity to solve this puzzle?

1See p. 75.

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