Klassische Atommodelle

Atomphysik

Klassische Atommodelle

  • Welche Vorstellungen hatten die alten Griechen von Atomen?
  • Was versteht man unter dem „Plumpudding-Modell“?
  • Welche Vorhersagen macht das BOHRsche Atommodell?
  • Mit welchen Atommodellen arbeitet die moderne Physik?

Joseph John THOMSON (1856 -1940)

von Not Mentioned (First World War.com) [Public domain], via Wikimedia Commons

Joseph John THOMSON studierte in Cambridge und wurde 1884, also bereits mit 28 Jahren, Professor am berühmten Cavendish-Laboratorium (seine Vorgänger waren MAXWELL und RAYLEIGH).

THOMSON wies 1896/97 die elektrische Leitfähigkeit von Gasen in evakuierten Gefäßen unter Röntgenbestrahlung nach.

Zusammen mit Lord Kelvin entwickelte er 1898 das nach ihm benannte Atommodell, einen Vorläufer des Atommodells von RUTHERFORD.

1899 entdeckte Joseph THOMSON unabhängig von Philipp LENARD, dass auch beim Photo- und beim glühelektrischen Effekt Elektronen emittiert werden.

1906 erhielt er für seine Arbeiten über den Durchgang der Elektrizität durch Gase den Nobelpreis für Physik.

1907 gelang es THOMSON durch Ablenkung von Kanalstrahlen (das sind diejenigen Teilchen, die sich auf die Kathode zu bewegen) im elektrischen Feld Parabeln zu erhalten, von denen jede einer der verschiedenen vorhandenen Atom- und Molekülarten entsprach.

Zusammen mit Francis ASTON wies er 1913 mit dem Massenspektrographen beim Element Neon nach, dass auch nichtradioaktive Elemente Isotope haben.

THOMSON gilt als der Entdecker des Elektrons (er nannte sie zunächst Korpuskel). Das von ihm entwickelte Atommodell war das zu seiner Zeit bedeutendste, welches die elektrischen Eigenschaften der Materie berücksichtigte.

Eine sehr ausführliche und liebevoll gestaltete Biographie mit der Darstellung der wesentlichen Versuche von THOMSON findet man hier .

Die englischsprachige Biographie von THOMSON (mit Link zu dessen Nobelvortrag) finden Sie hier.

Niels BOHR (1885 -1962)

von Unbekannt (http://www.dfi.dk/dfi/pressroom/kbhfortolkningen/) [Public domain], via Wikimedia Commons

Niels BOHR wird am 7. Oktober 1885 in Kopenhagen als Sohn des Physiologieprofessors Christian Bohr und dessen jüdischer Ehefrau Ellen geboren. Er studiert Physik und promoviert 1911 in Kopenhagen über eine Theorie der Metallelektronen. Bohr geht nun zu J.J. Thomson nach Cambridge und im Jahre 1912 zu Ernest Rutherford nach Manchester. Dort erfährt er von den experimentellen Ergebnissen, die zunächst zum rutherfordschen Atommodell führten.

Noch im Jahre 1912 wird Bohr Assistent an der Universität in Kopenhagen. Geprägt von den experimentellen Ergebnissen Rutherfords, aber auch durch die Überlegungen von M. Planck und A. Einstein entwickelt er 1913 das nach ihm benannte Atommodell (er ist einer der ersten, der die plancksche Quantenhypothese, die sich bei der einsteinschen Deutung des Photoeffekts so gut bewährt hat, in die Atomtheorie einführt). In seiner berühmten Arbeit "On the Constitution of Atoms and Molecules" im Philosophical Magazine Vol. 26 (1913) erklärt er die Balmerserie durch die diskreten Energiezustände im Atom. In der gleichen Arbeit zeigt er, dass die Pickering-Serie im Spektrum des Sterns ξ-Pupis auf das ionisierte Helium zurückzuführen ist.

Bohr gelang es mit seinem Korrespondenzprinzip zu zeigen, dass seine revolutionär neuen Ideen für hohe Quantenzahlen mit dem Bewährten der klassischen Physik in Einklang zu bringen waren.

Im Jahre 1916 wird er Professor für theoretische Physik in Kopenhagen.

1922 bekommt Niels Bohr den Nobelpreis für Physik.

In den zwanziger Jahren des 20. Jahrhunderts wird Bohrs Institut zum "Mekka der Atomphysik", wo sich alle namhaften Theoretiker auf diesem Gebiet ein Stelldichein geben.

In den Jahren 1926/27 arbeiten Bohr und Heisenberg die sogenannte "Kopenhagener Interpretation der Quantenphysik" aus. Hierin spielt das von Bohr ausgearbeitete Komplementaritätsprinzip eine wesentliche Rolle.

Das Komplementaritätsprinzip besagt, dass zur vollständigen Beschreibung von Phänomenen der Mikrophysik im Rahmen der klassischen Physik sich ausschließende Begriffe wie z.B. Welle und Teilchen je nach Art der Messanordnung als sich ergänzende "komplementäre" Begriffe für eine widerspruchsfreie Beschreibung notwendig sind.

In den dreißiger Jahren wendet sich Bohr der Kernphysik zu und entwickelt das "Tröpfchenmodell" des Atomkerns.

1943 verlässt Bohr das von deutschen Truppen besetzte Dänemark und gelangt über Cambridge nach Amerika. Dort wird er Koordinator eines Kernenergie-Projekts. Bohr erkennt sehr schnell die Gefahren und den Nutzen der Kernenergie und dringt 1950 in einem Memorandum an die UN auf internationale Regelungen.

Am 18. November 1962 stirbt Bohr in Kopenhagen.

Der bekannte Physiker und Philosoph C. F. von Weizsäcker beschreibt 1955 den Wandel der Grundvorstellungen in der Physik im ersten Viertel des 20. Jahrhunderts. Bei der Charakterisierung der maßgeblichen Persönlichkeiten schreibt er: "Sollte man sich auf genau drei Namen beschränken, so müsste man ohne Zweifel Rutherford, Einstein und Bohr nennen. Einstein leitete mit der Relativitätstheorie eine neue Art theoretisch-physikalischen Denkens ein, Rutherford eröffnete die experimentelle Erforschung der Atome, Bohr ihr theoretisches Verständnis. Ist von den drei genannten Physikern Rutherford vielleicht der kräftigste, Einstein der genialste, so ist Bohr der tiefste".

Die englischsprachige Biographie Bohrs (mit Link zu dessen Nobelvortrag) finden Sie hier.

Ernest RUTHERFORD (1871 - 1937)

von George Grantham Bain Collection (Library of Congress) [Public domain], via Wikimedia Commons

Ernest RUTHERFORD wurde am 30.August 1871 in Spring Grove, Neuseeland geboren und starb am 19.Oktober 1937 in Cambridge.

Rutherford war der Sohn zweier britischer Einwanderer. Er zeichnete sich früh durch außergewöhnliche schulische Leistungen aus, so dass ihn mehrfach gewährte Stipendien in die Lage versetzten, die Universität von Christchurch in Neuseeland und danach das Cavendish-Laboratorium in Cambridge zu besuchen. Unter der Leitung von Joseph John THOMSON führte er zunächst seine schon in Neuseeland begonnenen Arbeiten - seine erste wissenschaftliche Publikation erschien 1894 in den 'Transactions of the New Zealand Institute' - über die magnetisierende Wirkung schnell oszillierender elektromagnetischer Felder fort. Mit einem selbsterfundenen magnetischen Detektor stellte er den damaligen Entfernungsrekord für Radiowellenempfang von 0.5 Meilen auf.

Die Entdeckung der Radioaktivität durch Antoine Henri Becquerel im Februar 1896 gab seiner Forschung eine neue, für seine weitere Laufbahn bestimmende Richtung. Er untersuchte die ionisierende Wirkung radioaktiver Strahlung auf Gase und entdeckte zwei unterschiedlich stark absorbierbare Komponenten, die er Alpha-Strahlen und Beta-Strahlen nannte.

Im Sommer 1898 erhielt er eine Berufung als Professor für Physik an die Mc Gill-Universität in Montreal, Kanada, an der er ein knappes Jahrzehnt (bis 1907) blieb.

Die Alpha-Teilchen waren ein Lieblingsgegenstand seiner Forschungen. 1903 gelang ihm ihre Ablenkung im starken Magnetfeld und der Nachweis, dass sie positiv geladen sind. Dass es sich um zweifach positiv geladene Heliumionen bzw. Helimukerne handelt zeigten 1908 zwei Mitarbeiter Rutherfords, Hans Geiger und Thomas Royds. Das Gesetz des radioaktiven Zerfalls, die herausragende Entdeckung seiner kanadischen Zeit, fand er 1902 zusammen mit Frederick Soddy. Für seine "Untersuchungen über den Zerfall der Elemente und die Chemie der radioaktiven Materie" erhielt er 1908 den Nobelpreis für Chemie.

Rutherford und sein Schüler Geiger vor der
Originalapparatur

1907 kehrte Rutherford als Nachfolger von Arthur Schuster, der zu Rutherfords Gunsten auf den Langworthy-Lehrstuhl in Manchester verzichtet hatte, nach England zurück.

Im Anschluss an die 1906 beobachtete Schmalwinkelstreuung von Alpha-Teilchen beim Durchgang durch dünne Materieschichten suchten im Frühjahr 1909 Ernest Marsden und Hans Geiger in Rutherfords Labor nach einer potentiellen Weitwinkelstreuung. Das Ergebnis war so verblüffend, dass Rutherford später darüber sagte:

"Es war bestimmt das unglaublichste Ergebnis, das mir je in meinem Leben widerfuhr. Es war fast so unglaublich, als wenn einer eine 15-Zoll-Granate auf ein Stück Seidenpapier abgefeuert hätte und diese zurückgekommen wäre und ihn getroffen hätte."

Atommodell von Rutherford

RUTHERFORD war ein hervorragender und sehr kooperativer Wissenschaftler. Er liebte das Leben, ging aus, feierte und konnte sich an allen Dingen erfreuen. Er war aber auch ein hart arbeitender Mann, der die Wissenschaft - allein wegen ihrer Möglichkeit neue Erkenntnisse zu gewinnen - liebte und der unermüdlich in seinem Labor forschte und variierte. Er hatte selten irgendwelche Probleme mit anderen Menschen, manches Mal gelang es ihm sogar, einen potenziellen Widersacher dazu zu gewinnen, dass er ein effektiver Mitarbeiter wurde. Wenn er Leute wie Einstein, Lorentz oder Planck traf, gelang es ihm auf Anhieb, sie in eine fruchtbare und konstruktive Diskussion zu führen. Er hatte eine sehr freundschaftliche Beziehung zu Marie Curie. Beide waren begeisterte Wissenschaftler, die sich von den Experimenten mitreißen ließen, die einzig und allein den Zweck hatten, neue Erkenntnisse zu gewinnen und das Wesen der Dinge zu verstehen.

Für die Deutung der Beobachtung des Streuexperiments von GEIGER und MARSDEN brauchte er fast zwei Jahre; er fand sie kurz vor Weihnachten 1910 und veröffentlichte sie im März/April 1911. Die Lösung des Problems lag in der Annahme, dass das Atom "aus einer zentralen, punktförmig konzentrierten elektrischen Ladung besteht, die von einer gleichförmig sphärischen Ladungsverteilung des entgegengesetzten Vorzeichens und des gleichen Betrages umgeben ist" Damit war der Begriff des Atomkerns, wenn auch noch nicht dessen Name, geboren. Dieser trat erstmals 1912 auf.

Das rutherfordsche Modell des Atoms mit Kern (engl.: nucleus) war die Grundlage der Atomtheorie Niels Bohrs, der im Sommer 1912 bei Rutherford gearbeitet hatte und Mitte 1913 seine neuen Ideen publizierte. Nach jahrelangen Vorarbeiten gelang Rutherford 1919 der Nachweis der ersten künstlich erzielten Kernumwandlung. Im gleichen Jahr wurde Rutherford Nachfolger seines Lehrers Thomson und Leiter des Cavendish-Laboratoriums in Cambridge. Hier entfaltete er seine Qualitäten als Dirigent aktueller Forschung. 1932 krönte sein Schüler James Chadwick diese Phase seines Lebens mit der Entdeckung des von Rutherford schon 1920 vermuteten Neutrons.

Rutherford war einer der erfolgreichsten Experimentatoren der Geschichte (darin Michael Faraday vergleichbar), der zudem eine ganze Anzahl hervorragender Schüler hatte. Außer den bereits genannten gehörten dazu Otto Hahn (Entdecker der Kernspaltung) , Georg von Hevesy, Patrick M.S.Blackett, John Cockcroft und Ernest Walton (Erfinder des elektrostatischen Beschleunigers).

Rutherford wurde 1911 geadelt, 1925 zum Präsidenten der Royal Society gewählt und 1931 baronisiert (Lord Rutherford of Nelson).

Er wurde in Westminster Abbey nahe dem Grabe Isaac Newtons bestattet.

Die englischsprachige Biographie RUTHERFORDs (mit Link zu dessen Nobelvortrag) finden Sie hier.

Philipp LENARD (1862 -1947)

Philipp LENARD (1862-1947)
Bundesarchiv, Bild 146-1978-069-26A / CC-BY-SA [CC-BY-SA-3.0-de], via Wikimedia Commons

Philipp Lenard wird 1862 im österreichisch-ungarischen Preßburg (heute: Bratislava, Slowakei) geboren. Er studierte in Budapest, Wien und Heidelberg, wo er 1886 seine Dissertation anfertigte und anschließend Assistent bei Prof. Quinke wurde.

An der Universität Bonn entwickelt er 1892 bei Heinrich Hertz eine Kathodenstrahlröhre mit einem Fenster (Lenard-Fenster) durch das die Elektronen in Luft oder andere Materie eintreten können. Er studiert die dabei auftretende Fluoreszenz und schließt aus der Tatsache, dass die Elektronen viele Atomschichten ungehindert durchdringen können auf die "löchrige Struktur" der Materie.

1895 wechselt Lenard an die Technische Hochschule Aachen, wo er sich weiter mit Kathodenstrahlen beschäftigt. Die Entdeckung der Röntgenstrahlen durch Wilhelm Conrad Röntgen überrascht Lenard, der ihm bei der Beschaffung geeigneter Entladungsröhren behilflich war. Lenard hatte gehofft, diese Entdeckung selbst zu machen, da seine Experimente ähnlich weit fortgeschritten waren. Er gebrauchte im Folgenden immer den Begriff der "Hochfrequenzstrahlung" anstelle des gebräuchlichen der "Röntgenstrahlen".

Lenard beschäftigt sich auch mit dem Photoeffekt. Mit Hilfe elektrischer und magnetischer Felder kann er nachweisen, dass bei wachsender Lichtintensität zwar die Zahl der ausgelösten Elektronen wächst, aber deren kinetische Energie gleich bleibt. Außerdem kann er zeigen, dass die Elektronengeschwindigkeit und damit deren kinetischen Energie ausschließlich von der Frequenz des eingestrahlten Lichts abhängt, was mit der Wellenvorstellung vom Licht nur schwer vereinbar war.

Lenardrohr mit Fenster auf der linken Seite mit Leuchterscheinung in der Luft; rechts unten: Hochspannungsquelle für das Rohr

Im Jahre 1903 entwickelte Lenard ein Atommodell, welches auf den Ergebnissen seiner Durchstrahlungsversuche der Materie mit Elektronen beruht, das Dynamiden-Modell.

Im Jahre 1905 erhält Lenard für seine Forschungen auf dem Gebiet der Kathodenstrahlen (Elektronen-Strahlen) den Nobelpreis für Physik.

Lenard lebte mit einer Reihe von Forschern (z.B. mit J.J. Thomson) im Streit. 1914, also zu Beginn des 1. Weltkriegs, veröffentlicht er eine Hetzschrift mit dem Titel "England und Deutschland zur Zeit des großen Krieges", in der er seine Kritik an Thomson mit nationalistischen Ausfällen gegen England verbindet.

Auch mit der Relativitätstheorie Einsteins oder mit der Deutung der Quantenmechanik durch Max Born war er nicht einverstanden. Zu den neuen Ansätzen in der Physik findet Lenard als Experimentalphysiker schwer Zugang. Er versucht die experimentelle Physik zu einer "nordischen Wissenschaft" zu stilisieren, die sich von der theoretischen Physik - in seinen Augen "jüdischer Weltbluff" - abhebt. Im Jahr 1936 erscheint Lenards vierbändiges Lehrbuch für Experimentalphysik "Deutsche Physik". Demnach kann wahre Naturkenntnis nur von der "arischen Rasse" gewonnen werden. Die Arbeiten Einsteins bezeichnet Lenard als "Jahrmarktslärm" und "Judenbetrug".

Die englischsprachige Biographie Lenards mit einem Link zu dessen Nobelvortrag findest du bei http://www.nobelprize.org.

Auszüge aus der Originalarbeit von J. J. Thomson

XXIV. On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure

by J.J. Thomson, F.R.S., Cavendish Professor of Experimental Physics, Cambridge
Philosophical Magazine
Series 6, Volume 7, Number 39
March 1904, p. 237-265


The view that the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, suggests, among other interesting mathematical problems, the one discussed in this paper, that of the motion of a ring of n negatively electrified particles placed inside a uniformly electrified sphere. Suppose when in equilibrium the n corpuscles are arranged at equal angular intervals round the circumference of a circle of radius a, each corpuscle carrying a charge e of negative electricity. Let the charge of positive electricity be ne, then if b is the radius of this sphere, the radial attraction on a corpuscle due to positive electrification is equal to e2a/b2; if the corpuscles are at rest this attraction must be balanced by the repulsion exerted by the other corpuscles. Now, the repulsion along OA, O being the centre of the sphere, exerted on a corpuscle at A by one at B is equal to (e2 / AB2) cos OAB and, if OA = OB, this is equal to e2 / (4 OA2 sin 1/2 AOB) : hence, if we have n corpuscles arranged at equal angular intervals 2p / n round the circumference of a circle, the radial repulsion on one corpuscle due to the other (n - 1) . . . . . .

Application of the preceding Results to the Theory of the
Structure of the Atom

We suppose that the atom consists of a number of corpuscles moving about in a sphere of uniform positive electrification: the problems we have to solve are (1) what would be the structure of such an atom, i.e. how would the corpuscles arrange themselves in the sphere; and (2) what properties would this structure confer upon the atom. The solution of (1) when the corpuscles are constrained to move in one plane is indicated by the results we have just obtained -- the corpuscles will arrange themselves in a series of concentric rings. This arrangement is necessitated by the fact that a large number of corpuscles cannot be in stable equilibrium when arranged as a single ring, while this ring can be made stable by placing inside it an appropriate number of corpuscles. 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.

The analytical and geometrical difficulties of the problem of the distribution of the corpuscles when they are arranged in shells are much greater than when they are arranged in rings, and I have not as yet succeeded in getting a general solution. We can see, however, that the same kinds of properties will be associated with the shells as with the rings; and as our solution of the latter case enables us to give definite results, I shall confine myself to this case, and endeavour to show that the properties conferred on the atom by this ring structure are analogous in many respects to those possessed by the atoms of the chemical elements, and that in particular the properties of the atom will depend upon its atomic weight in a way very analogous to that expressed by the periodic law.

Let us suppose, then, that we have N corpuscles each carrying a charge e of negative electricity, placed in a sphere of positive electrification, the whole charge in the sphere being equal to Ne; let us find the distribution of the corpuscles when they are arranged in what we may consider to be the simplest way, i.e. when the number of rings is a minimum, so that in each ring there are as nearly as possible as many corpuscles as it is possible for the corpuscles inside to hold in equilibrium. Let us suppose that the number of internal corpuscles required to make the equilibrium of a ring of n corpuscles stable is f(n). The values of f(n) for a series of valyes of n is given in the table on p. 254; in that table f(n) is denoted by p. The number of corpuscles in the outer ring n1 will then be determined by the condition at N - n1, the number of corpuscles inside, must be just sufficient to keep the ring of n1 corpuscles in equilibrium, i.e., n1 will be determined by the equation

N - n1 = f(n1)

If the value of n1 got from this equation is not an integer we must take the integral part of the value. . . . . . .


Originalarbeit von RUTHERFORD

Für historisch und in der Theorie interessierte Lehrer und Schüler bieten wir die Originalarbeit von Rutherford zum lesen an. Dabei sollen Sie einen Eindruck bekommen, wie eine solche Originalarbeit, die 1911 in einer entsprechenden naturwissenschaftlichen Zeitschrift abgedruckt wurde, abgefasst ist.

Auch wenn mancher theoretische Schritt in der Arbeit für Sie nicht nachvollziehbar ist, können Sie an geeigneten Textstellen diejenigen Aussagen finden, die heute noch in den Schulbüchern (in einfacherer Form) wieder zu finden sind.

The Scattering of α and β Particles by Matter and the Structure of the Atom

E. Rutherford, F.R.S.*
Philosophical Magazine
Series 6, vol. 21
May 1911, p. 669-688

 

669

§ 1. It is well known that the α and the β particles suffer deflexions from their rectilinear paths by encounters with atoms of matter. This scattering is far more marked for the β than for the α particle on account of the much smaller momentum and energy of the former particle. There seems to be no doubt that such swiftly moving particles pass through the atoms in their path, and that the deflexions observed are due to the strong electric field traversed within the atomic system. It has generally been supposed that the scattering of a pencil of α or β rays in passing through a thin plate of matter is the result of a multitude of small scatterings by the atoms of matter traversed. The observations, however, of Geiger and Marsden** on the scattering of α rays indicate that some of the α particles, about 1 in 20,000 were turned through an average angle of 90 degrees in passing though a layer of gold-foil about 0.00004 cm. thick, which was equivalent in stopping-power of the α particle to 1.6 millimetres of air. Geiger*** showed later that the most probable angle of deflexion for a pencil of α particles being deflected through 90 degrees is vanishingly small. In addition, it will be seen later that the distribution of the α particles for various angles of large deflexion does not follow the probability law to be expected if such large deflexion are made up of a large number of small deviations. It seems reasonable to suppose that the deflexion through a large angle is due to a single atomic encounter, for the chance of a second encounter of a kind to produce a large deflexion must in most cases be exceedingly small. A simple calculation shows that the atom must be a seat of an intense electric field in order to produce such a large deflexion at a single encounter.










 

* Communicated by the Author. A brief account of this paper was communicated to the Manchester Literary and Philosophical Society in February, 1911.
** Proc. Roy. Soc. lxxxii, p. 495 (1909)
*** Proc. Roy. Soc. lxxxiii, p. 492 (1910)
**** Camb. Lit. & Phil Soc. xv pt. 5 (1910)

 

670

Recently Sir J. J. Thomson**** has put forward a theory to explain the scattering of electrified particles in passing through small thicknesses of matter. The atom is supposed to consist of a number N of negatively charged corpuscles, accompanied by an equal quantity of positive electricity uniformly distributed throughout a sphere. The deflexion of a negatively electrified particle in passing through the atom is ascribed to two causes -- (1) the repulsion of the corpuscles distributed through the atom, and (2) the attraction of the positive electricity in the atom. The deflexion of the particle in passing through the atom is supposed to be small, while the average deflexion after a large number m of encounters was taken as [the square root of] m · θ, where θ is the average deflexion due to a single atom. It was shown that the number N of the electrons within the atom could be deduced from observations of the scattering was examined experimentally by Crowther* in a later paper. His results apparently confirmed the main conclusions of the theory, and he deduced, on the assumption that the positive electricity was continuous, that the number of electrons in an atom was about three times its atomic weight.
The theory of Sir J. J. Thomson is based on the assumption that the scattering due to a single atomic encounter is small, and the particular structure assumed for the atom does not admit of a very large deflexion of diameter of the sphere of positive electricity is minute compared with the diameter of the sphere of influence of the atom.
Since the α and β particles traverse the atom, it should be possible from a close study of the nature of the deflexion 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 α 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 α rays by matter.





 

* Crowther, Proc. Roy. Soc. lxxxiv. p. 226 (1910)
** The deviation of a particle throughout a considerable angle from an encounter with a single atom will in this paper be called 'single' scattering. The deviation of a particle resulting from a multitude of small deviations will be termed 'compound' scattering.

 

 

671

§ 2. We shall first examine theoretically the single encounters** with an atom of simple structure, which is able to produce large deflections of an α particle, and then compare the deductions from the theory with the experimental data available.

Consider an atom which contains a charge ± Ne at its centre surrounded by a sphere of electrification containing a charge ± Ne [N.B. in the original publication, the second plus/minus sign is inverted to be a minus/plus sign] supposed uniformly distributed throughout a sphere of radius R. e is the fundamental unit of charge, which in this paper is taken as 4·65· 10¯10 E.S. unit. We shall suppose that for distances less than 10¯12 cm. the central charge and also the charge on the alpha particle may be supposed to be concentrated at a point. It will be shown that the main deductions from the theory are independent of whether the central charge is supposed to be positive or negative. For convenience, the sign will be assumed to be positive. 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.

In order to form some idea of the forces required to deflect an alpha particle through a large angle, consider an atom containing a positive charge Ne at its centre, and surrounded by a distribution of negative electricity Ne uniformly distributed within a sphere of radius R. The electric force X and the potential V at a distance r from the centre of an atom for a point inside the atom, are given by

\[\begin{array}{l}X = Ne\left( {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right)\\V = Ne\left( {\frac{1}{r} - \frac{3}{{2R}} - \frac{{{r^2}}}{{2{R^3}}}} \right)\end{array}\]

Suppose an α particle of mass m and velocity u and charge E shot directly towards the centre of the atom. It will be brought to rest at a distance b from the centre given by

\[{\textstyle{1 \over 2}}m{u^2} = NeE\left( {\frac{1}{b} - \frac{3}{{2R}} + \frac{{{b^2}}}{{2{R^3}}}} \right)\]

It will be seen that b is an important quantity in later calculations. Assuming that the central charge is 100 e, it can be calculated that the value of b for an α particle of velocity 2,09·109 cms. per second is about 3,4·10¯12 cm. In this calculation b is supposed to be very small compared with R. Since R is supposed to be of the order of the radius of the atom, viz. 10¯8 cm., it is obvious that the α particle before being turned back penetrates so close to

 

672

the central charge, that the field due to the uniform distribution of negative electricity may be neglected. In general, a simple calculation shows that for all deflexions greater than a degree, we may without sensible error suppose the deflexion due to the field of the central charge alone. Possible single deviations due to the negative electricity, if distributed in the form of corpuscles, are not taken into account at this stage of the theory. It will be shown later that its effect is in general small compared with that due to the central field.

 

Consider the passage of a positive electrified particle close to the centre of an atom. Supposing that the velocity of the particle is not appreciably changed by its passage through the atom, the path of the particle under the influence of a repulsive force varying inversely as the square of the distance will be an hyperbola with the centre of the atom S as the external focus. Suppose the particle to enter the atom in the direction PO (fig. 1), and that the direction of motion on escaping the atom is OP'.

 

OP and OP' make equal angles with the line SA, where A is the apse of the hyperbola. p = SN = perpendicular distance from centre on direction of initial motion of particle.

     

673

Let angle POA = θ.

Let V = velocity of particle on entering the atom, v its velocity at A, then from consideration of angular momentum

pV = SA·v.

From conservation of energy

\[\begin{array}{l}{\textstyle{1 \over 2}}m{V^2} = {\textstyle{1 \over 2}}m{v^2} - \frac{{NeE}}{{SA}},\\{v^2} = {V^2}\left( {1 - \frac{b}{{SA}}} \right)\end{array}\]

 

Since the eccentricity is sec q,

SA = SO + OA = p cosecθ·(1 + cosθ)

= p cotθ/2

p2 = SA(SA - b) = p cot θ/2(p cot θ/2 - b),

therefore b = 2·p·cot θ.

The angle of deviation \(\phi \)of the particles is π - 2θ and

cot\(\phi \)/2 = (2p/b) * . . . . (1)

This gives the angle of deviation of the particle in terms of b, and the perpendicular distance of the direction of projection from the centre of the atom.

For illustration, the angle of deviation \(\phi \) for different values of p/b are shown in the following table: --

p / b . . . . . 10 5 2 1 0.5 0.25 0.125
\(\phi \) . . . . . . . 5°.7 11°.4 28° 53° 90° 127° 152°

 

§ 3. Probability of single deflexion through any angle

Suppose a pencil of electrified particles to fall normally on a thin screen of matter of thickness t. With the exception of the few particles which are scattered through a large angle, the particles are supposed to pass nearly normally through the plate with only a small change of velocity. Let n = number of atoms in unit volume of material. Then the number of collisions of the particle with the atom of radius R is π·R2·n·t in the thickness t.

* A simple consideration shows that the deflexion is unaltered if the forces are attractive instead of repulsive.

 

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The probability m of entering an atom within a distance p of its center is given by

m = π·p2·n·t.

Chance dm of striking within radii p and p + dp is given by

dm = 2π·p·n·t . dp = (π/ 4)·n·t·b2 cot \(\phi \)/2 cosec2 \(\phi \)/2 d\(\phi \) . . . . (2)

since

cot \(\phi \)/2 = 2p/b

The value of dm gives the fraction of the total number of particles which are deviated between the angles \(\phi \) and \(\phi \) + d\(\phi \).

The fraction ρ of the total number of particles which are deflected through an angle greater than\(\phi \) is given by

ρ = (π/ 4)·n·t·b2·cot2 \(\phi \)/2 . . . . . . (3)

The fraction ρ which is deflected between the angles \(\phi \)1 and \(\phi \)2 is given by

ρ = (π/ 4)·n·t·b2 ·(cot2 \(\phi \)1/2 - cot2 \(\phi \)2/2) . . . . . . . . . . . . . (4)

It is convenient to express the equation (2) in another form for comparison with experiment. In the case of the α rays, the number of scintillations appearing on the constant area of the zinc sulphide screen are counted for different angles with the direction of incidence of the particles. Let r = distance from point of incidence of a rays on scattering material, then if Q be the total number of particles falling on the scattering material, the number y of α particles falling on unit area which are deflected through an angle\(\phi \) is given by

\[y = \frac{{Qdm}}{{2\pi {r^2}\sin \phi  \cdot d\phi }} = \frac{{nt{b^2} \cdot Q\cos e{c^4}\phi /2}}{{16{r^2}}}.\,\quad .\quad .\quad (5)\]

Since \(b = \frac{{2 \cdot N \cdot e \cdot E}}{{m \cdot {u^2}}}\), we see from this equation that the number of α particles (scintillations) per unit area of zinc sulphide screen at a given distance r from the point of

 

 

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Incidence of the rays is proportional to

(1) cosec4 \(\phi \)/2 or 1/\(\phi \)4 if \(\phi \) be small;
(2) thickness of scattering material t provided this is small;
(3) magnitude of central charge Ne;
(4) and is inversely proportional to (mu2)2, or to the fourth power of the velocity if m be constant.

In these calculations, it is assumed that the α particles scattered through a large angle suffer only one large deflexion. For this to hold, it is essential that the thickness of the scattering material should be so small that the chance of a second encounter involving another large deflexion is very small. If, for example, the probability of a single deflexion\(\phi \) in passing through a thickness t is 1/1000, the probability of two successive deflexions each of value \(\phi \) is 1/106 , and is negligibly small.

The angular distribution of the α particles scattered from a thin metal sheet affords one of the simplest methods of testing the general correctness of this theory of single scattering. This has been done recently for α rays by Dr. Geiger,* who found that the distribution for particles deflected between 30° and 150° from a thin gold-foil was in substantial agreement with the theory. A more detailed account of these and other experiments to test the validity of the theory will be published later.

§ 4. Alteration of velocity in an atomic encounter

It has so far been assumed that an α or ß particle does not suffer an appreciable change of velocity as the result of a single atomic encounter resulting in a large deflexion of the particle. The effect of such an encounter in altering the velocity of the particle can be calculated on certain assumptions. It is supposed that only two systems are involved, viz., the swiftly moving particle and the atom which it traverses supposed initially at rest. It is supposed that the principle of conservation of momentum and of energy applies, and that there is no appreciable loss of energy or momentum by radiation.

* Manch. Lit. & Phil. Soc. 1910.

 

 

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Let m be mass of the particle,

v1 = velocity of approach,
v2 = velocity of recession,
M= mass of atom,
V = velocity communicated to atom as result of encounter.

Let OA (fig. 2) represent in magnitude and direction the momentum mv1 of the entering particle, and OB the momentum of the receding particle which has been turned through an angle AOB =\(\phi \). Then BA represents in magnitude and direction the momentum MV of the recoiling atom.

(MV)2 = (mv1)2 + (mv2)2 - 2m2v1v2 cos f . . . (1)

By conservation of energy

MV2 = mv12 - mv22 . . . . .(2)

Suppose M/m = K and v2 = ρv1, where ρ < 1.
From (1) and (2),

\[\left( {K + 1} \right) \cdot {\rho ^2} - 2 \cdot \rho  \cdot \cos \phi  = K - 1\]

\[\rho  = \frac{{\cos \phi }}{{K + 1}} + \frac{1}{{K + 1}}\sqrt {{K^2} - {{\sin }^2}\phi } \]

Consider the case of an α particle of atomic weight 4, deflected through an angle of 90° by an encounter with an atom of gold of atomic weight 197.

Since K= 49 nearly,

\[\rho  = \sqrt {\frac{{K - 1}}{{K + 1}}}  = 0,979\]

or the velocity of the particle is reduced only about 2 per cent. by the encounter.

In the case of aluminium K=27/4 and for \(\phi \) = 90° ρ = 0.86.

It is seen that the reduction of velocity of the α particle becomes marked on this theory for encounters with the lighter atoms. Since the range of an α particle in air or other matter is approximately proportional to the cube of the velocity, it follows that an α particle of range 7 cms. has its range reduced to 4.5 cms. after incurring a single

 

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deviation of 90° in traversing an aluminium atom. This is of a magnitude to be easily detected experimentally. Since the value of K is very large for an encounter of a β particle with an atom, the reduction of velocity on this formula is very small.

Some very interesting cases of the theory arise in considering the changes of velocity and the distribution of scattered particles when the α particle encounters a light atom, for example a hydrogen or helium atom. A discussion of these and similar cases is reserved until the question has been examined experimentally.

§ 5. Comparison of single and compound scattering

Before comparing the results of theory with experiment, it is desirable to consider the relative importance of single and compound scattering in determining the distribution of the scattered particles. Since the atom is supposed to consist of a central charge surrounded by a uniform distribution of the opposite sign through a sphere of radius R, the chance of encounters with the atom involving small deflexions is very great compared with the change of a single large deflexion.

This question of compound scattering has been examined by Sir J. J. Thomson in the paper previously discussed (§1). In the notation of this paper, the average deflexion \(\phi \)1 due to the field of the sphere of positive electricity of radius R and quantity Ne was found by him to be

\[{\phi _1} = \frac{\pi }{4} \cdot \frac{{NeE}}{{m{u^2}}}\frac{1}{R}\]

The average deflexion \(\phi \)2 due to the N negative corpuscles supposed distributed uniformly throughout the sphere was found to be

\[{\phi _2} = \frac{{16}}{5}\frac{{eE}}{{m{u^2}}}\frac{1}{R}\sqrt {\frac{{3N}}{2}} \]

The mean deflexion due to both positive and negative electricity was taken as

(\(\phi \)12 + \(\phi \)22)1/2

In a similar way, it is not difficult to calculate the average deflexion due to the atom with a central charge discussed in this paper.

Since the radial electric field X at any distance r from the

 

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centre is given by

\[X = Ne\left( {\frac{1}{{{r^2}}} - \frac{r}{{{R^3}}}} \right)\]

it is not difficult to show that the deflexion (supposed small) of an electrified particle due to this field is given by

\[\theta  = \frac{b}{p} \cdot {\left( {1 - \frac{{{p^2}}}{{{R^2}}}} \right)^{3/2}}\]

Where p is the perpendicular from the center on the path of the particles and b has the same value as before. It is seen that the value of θ increases with diminution of p and becomes great for small value of \(\phi \).

Since we have already seen that the deflexions become very large for a particle passing near the center of the atom, it is obviously not correct to find the average value by assuming θ is small.

Taking R of the order 10-8 cm., the value of p for a large deflexions is for α and ß particles of the order 10-11 cm. Since the chance of an encounter involving a large deflexion is small compared with the chance of small deflexions, a simple consideration shows that the average small deflexion is practically unaltered if the large deflexions are omitted. This is equivalent to integrating over that part of the cross section of the atom where the deflexions are small and neglecting the small central area. It can in this way be simply shown that the average small deflexion is given by

\[{\phi _1} = \frac{{3\pi }}{8} \cdot \frac{b}{R}\]

This value of \(\phi \)1 for the atom with a concentrated central charge is three times the magnitude of the average deflexion for the same value of Ne in the type of atom examined by Sir J. J. Thomson. Combining the deflexions due to the electric field and to the corpuscles, the average deflexion is

\[{\left( {\phi _1^2 + \phi _2^2} \right)^2}\quad or\quad \frac{b}{{2R}}{\left( {5 \cdot 54 + \frac{{15 \cdot 4}}{N}} \right)^{1/2}}\]

It will be seen later that the value of N is nearly proportional to the atomic weight, and is about 100 for gold. The effect due to scattering of the individual corpuscles expressed by the second term of the equation is consequently small for heavy atoms compared with that due to the distributed electric field.

 

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Neglecting the second term, the average deflexion per atom is \(\frac{{3 \cdot \pi  \cdot b}}{{8 \cdot R}}\). We are now in a position to consider the relative effects on the distribution of particles due to single and to compound scattering. Following J. J. Thomson's argument, the average deflexion θt after passing through a thickness t of matter is proportional to the square root of the number of encounters and is given by

\[{\Theta _t} = \frac{{3\pi b}}{{8R}}\sqrt {\pi {R^2}.n.t}  = \frac{{3\pi b}}{8}\sqrt {\pi nt} \]

where n as before is equal to the number of atoms per unit volume.

The probability p1 for compound scattering that the deflexion of the particle is greater than \(\phi \) is equal to \({e^{ - {\phi ^2}/\Theta _t^2}}\).

Consequently

\[{\phi ^2} =  - \frac{{9{\pi ^3}}}{{64}}{b^2} \cdot n \cdot t \cdot \log {p_1}\]

Next suppose that single scattering alone is operative. We have seen (§3) that the probability p2 of a deflexion greater than\(\phi \) is given by

\[{p_2} = \frac{\pi }{4} \cdot {b^2} \cdot n \cdot t \cdot {\cot ^2}\phi /2\]

By comparing these two equations

p2 log p1= - 0.181\(\phi \)2 cot2 \(\phi \)/2 ,

\(\phi \) is sufficiently small that

tan \(\phi \)/2 = \(\phi \)/2,

p2 log p1= -0.72

If we suppose that

p2 = 0.5, then p1 = 0.24

If

p2 = 0.1, then p1 = 0.0004

It is evident from this comparison, that the probability for any given deflexion is always greater for single than for compound scattering. The difference is especially marked when only a small fraction of the particles are scattered through any given angle. It follows from this result that the distribution of particles due to encounters with the atoms is for small thicknesses mainly governed by single scattering. No doubt compound scattering produces some effect in equalizing the distribution of the scattered particles; but its effect becomes relatively smaller, the smaller the fraction of the particles scattered through a given angle.

 

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§6. Comparison of Theory with Experiments

On the present theory, the value of the central charge Ne is an important constant, and it is desirable to determine its value for different atoms. This can be most simply done by determining the small fraction of α or β particles of known velocity falling on a thin metal screen, which are scattered between \(\phi \) and \(\phi \) + d\(\phi \) where \(\phi \) is the angle of deflexion, The influence of compound scattering should be small when this fraction is small.

Experiments in these directions are in progress, but it is desirable at this stage to discuss in the light of the present theory the data already published on scattering of α and ß particles,

The following points will be discussed: --

(a) The 'diffuse reflexion' of a particles, i.e. the scattering of α particles through large angles (Geiger and Marsden.)
(b) The variation of diffuse reflexion with atomic weight of the radiator (Geiger and Marsden.)
(c) The average scattering of a pencil of α rays transmitted through a thin metal plate (Geiger.)
(d) The experiments of Crowther on the scattering of ß rays of different velocities by various metals.

(a) In the paper of Geiger and Marsden (loc.cit.) on the diffuse reflexion of α particles falling on various substances it was shown that about 1/8000 of the α particles from radium C falling on a thick plate of platinum are scattered back in the direction of the incidence. This fraction is deduced on the assumption that the α particles are uniformly scattered in all directions , the observation being made for a deflexion of about 90°. The form of experiment is not very suited for accurate calculation, but from the data available it can be shown that the scattering observed is about that to be expected on the theory if the atom of platinum has a central charge of about 100 e.

(b) In their experiments on this subject, Geiger and Marsden gave the relative number of α particles diffusely reflected from thick layers of different metals, under similar conditions . The numbers obtained by them are given in the table below, where z represents the relative number of scattered particles, measured by the of scintillations per minute on a zinc sulphide screen.

 

 

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Metal Atomic weight
z
z / A3/2
Lead
207
62
208
Gold
197
67
242
Platinum
195
63
232
Tin
119
34
226
Silver
108
27
241
Copper
64
14.5
225
Iron
56
10.2
250
Aluminium
27
3.4
243
      Average 233

On the theory of single scattering, the fraction of the total number of α particles scattered through any given angle in passing through a thickness t is proportional to n . A2t , assuming that the central charge is proportional to the atomic weight A. In the present case, the thickness of matter from which the scattered α particles are able to emerge and affect the zinc sulphide screen depends on the metal. Since Bragg has shown that the stopping power of an atom for an α particle is proportional to the square root of its atomic weight, the value of nt for different elements is proportional to \(1/\sqrt A \) . In this case t represents the greatest depth from which the scattered α particles emerge. The number z of α particles scattered back from a thick layer is consequently proportional to A3/2 or z / A3/2 should be a constant.

To compare this deduction with experiment, the relative values of the latter quotient are given in the last column . Considering the difficulty of the experiments, the agreement between theory and experiment is reasonably good.*

The single large scattering of α particles will obviously affect to some extent the shape of the Bragg ionization curve for a pencil of α rays. This effect of large scattering should be marked when the a rays have traversed screens of metals of high atomic weight, but should be small for atoms of light atomic weight.

(c) Geiger made a careful determination of the scattering of α particles passing through thin metal foils, by the scintillation method, and deduced the most probable angle

* The effect of change of velocity in an atomic encounter is neglected in this calculation.

 

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through which the α particles are deflected in passing through known thickness of different kinds of matter.

A narrow pencil of homogeneous α rays was used as a source. After passing through the scattering foil , the total number of α particles are deflected through different angles was directly measured. The angle for which the number of scattered particles was a maximum was taken as the most probable angle. The variation of the most probable angle with thickness of matter was determined, but calculation from these data is somewhat complicated by the variation of velocity of the α particles in their passage through the scattering material. A consideration of the curve of distribution of the α particles given in the paper (loc.cit. p. 498) shows that the angle through which half the particles are scattered is about 20 per cent greater than the most probable angle.

We have already seen that compound scattering may become important when about half the particles are scattered through a given angle, and it is difficult to disentangle in such cases the relative effects due to the two kinds of scattering. An approximate estimate can be made in the following ways: -- From (§5) the relation between the probabilities p1 and p2 for compound and single scattering respectively is given by

p2 log p1= -0.721.

The probability q of the combined effects may as a first approximation be taken as

q = (p12 +p22)1/2.

If q = 0.5, it follows that

p1 = 0.2 and p2 = 0.46

We have seen that the probability p2 of a single deflexion greater than\(\phi \)is given by

p2 = (p / 4)n . t . b2 (cot2 \(\phi \)/2) .

Since in the experiments considered f is comparatively small

\[\frac{{\phi \sqrt {{p_2}} }}{{\sqrt {\pi nt} }} = b = \frac{{NeE}}{{m{u^2}}}\]

 

Geiger found that the most probable angle of scattering of the α rays in passing through a thickness of gold equivalent in stopping power to about 0.76 cm. of air was 1° 40'. The angle \(\phi \) through which half the a particles are tuned thus corresponds to 2° nearly.

t = 0.00017 cm.; n = 6.07 x 1022;

u (average value) = 1.8 x 109.

E/m = 1.5 x 1014 E.S. units; e = 4.65 x 10-10,

 

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Taking the probability of single scattering = 0.46 and substituting the above value in the formula, the value of N for gold comes out to be 97.

For a thickness of gold equivalent in stopping power to 2.12 cms, of air, Geiger found the most probable angle to be 3° 40'. In this case, t = 0.00047, \(\phi \) = 4°.4, and average u =1.7 x 109, and N comes out to be 114.

Geiger showed that the most probable angle of deflexion for an atom was nearly proportional to its atomic weight. It consequently follows that the value for N for different atoms should be nearly proportional to their atomic weights, at any rate for atomic weights between gold and aluminum.

Since the atomic weight of platinum is nearly equal to that of gold, it follows from these considerations that the magnitude of the diffuse reflexion of α particles through more than 90° from gold and the magnitude of the average small angle scattering of a pencil of rays in passing through gold-foil are both explained on the hypothesis of single scattering by supposing the atom of gold has a central charge of about 100 e.

(d) Experiments of a Crowther on scattering of ß rays. --
We shall now consider how far the experimental results of Crowther on scattering of β particles of different velocities by various materials can be explained on the general theory of single scattering. On this theory, the fraction of β particles p turned through an angel greater than
\(\phi \) is given by

p = (p / 4)n . t . b2 (cot2 \(\phi \)/2) .

In most of Crowther's experiments f is sufficiently small that tan f/2 may be put equal to f/2 without much error. Consequently

\(\phi \)2 = 2πn . t . b2   if   p =1/2

On the theory of compound scattering, we have already seen that the chance p1 that the deflexion of the particles is greater than \(\phi \) is given by

\[{\phi ^2}/\log {p_1} =  - \frac{{9{\pi ^3}}}{{64}}n.t.{b^2}\]

Since in the experiments of Crowther the thickness t of matter was determined for which p1 = 1/2,

\(\phi \)2 = 0.96π n t b2.

For the probability of 1/2, the theories of single and compound

 

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scattering are thus identical in general form, but differ by a numerical constant. It is thus clear that the main relations on the theory of compound scattering of Sir J. J. Thomson, which were verified experimentally by Crowther, hold equally well on the theory of single scattering.

For example, it tm be the thickness for which half the particles are scattered through an angle f, Crowther showed that \(\phi /\sqrt {{t_m}} \) and also \(\frac{{m \cdot {u^2}}}{E} \cdot \sqrt {{t_m}} \) were constants for a given material when \(\phi \) was fixed. These relations hold also on the theory of single scattering. Notwithstanding this apparent similarity in form, the two theories are fundamentally different. In one case, the effects observed are due to cumulative effects of small deflexion, while in the other the large deflexions are supposed to result from a single encounter. The distribution of scattered particles is entirely different on the two theories when the probability of deflexion greater than \(\phi \) is small.

We have already seen that the distribution of scattered α particles at various angles has been found by Geiger to be in substantial agreement with the theory of single scattering, but can not be explained on the theory of compound scattering alone. Since there is every reason to believe that the laws of scattering of α and β particles are very similar, the law of distribution of scattered β particles should be the same as for α particles for small thicknesses of matter. Since the value of mu2 / E for β particles is in most cases much smaller than the corresponding value for the α particles, the chance of large single deflexions for β particles in passing through a given thickness of matter is much greater than for α particles. Since on the theory of single scattering the fraction of the number of particles which are undeflected through this angle is proportional to kt, where t is the thickness supposed small and k a constant, the number of particles which are undeflected through this angle is proportional to 1 - kt. From considerations based on the theory of compound scattering, Sir J.J. Thomson deduced that the probability of deflexion less than \(\phi \) is proportional to 1 - eμ / t where m is a constant for any given value of \(\phi \).

The correctness of this latter formula was tested by Crowther by measuring electrically the fraction I / Io of the scattered ß particles which passed through a circular opening subtending an angle of 36° with the scattering material. If

\[I/{I_0} = 1 - {e^{ - \mu /t}}\]

the value of I should decrease very slowly at first with

 

 

685

increase of t. Crowther, using aluminium as scattering material, states that the variation of I/Io was in good accord with this theory for small values of t. On the other hand, if single scattering be present, as it undoubtedly is for α rays, the curve showing the relation between I/Io and t should be nearly linear in the initial stages. The experiments of Marsden* on scattering of β rays, although not made with quite so small a thickness of aluminium as that used by Crowther, certainly support such a conclusion. Considering the importance of the point at issue, further experiments on this question are desirable.

From the table given by Crowther of the value \(\phi /\sqrt {{t_m}} \) for different elements for ß rays of velocity 2.68 x 10-10 cms. per second, the value of the central charge Ne can be calculated on the theory of single scattering. It is supposed, as in the case of the α rays, that for given value of \(\phi /\sqrt {{t_m}} \) the fraction of the ß particles deflected by single scattering through an angle greater than \(\phi \) is 0.46 instead of 0.5

The value of N calculated from Crowther's data are given below.

Element
Atomic weight
\(\phi /\sqrt {{t_m}} \)
N
Aluminium
27
4.25
22
Copper
63.2
10.0
42
Silver
108
29
138
Platnium
194
29
138

It will be remembered that the values of N for gold deduced from scattering of the α rays were in two calculations 97 and 114. These numbers are somewhat smaller than the values given above for platinum (viz. 138), whose atomic weight is not very different from gold. Taking into account the uncertainties involved in the calculation from the experimental data, the agreement is sufficiently close to indicate that the same general laws of scattering hold for the α and ß particles, notwithstanding the wide differences in the relative velocity and mass of these particles.

As in case of the α rays, the value of N should be most simply determined for any given element by measuring

* Phil. Mag. xviii. p. 909 (1909)

 

686

the small fraction of the incident β particles scattered through a large angle. In this way, possible errors due to small scattering will be avoided.

The scattering data for the β rays, as well as for the α rays indicate that the central charge in an atom is approximately proportional to its atomic weight. This falls in with the experimental deductions of Schmidt.* In his theory of absorption of β rays, he supposed that in traversing a thin sheet of matter, a small fraction α of the particles are stopped, and a small fraction b are reflected or scattered back in the direction of incidence. From comparison of the absorption curves of different elements, he deduced that the value of the constant β for different elements is proportional to nA2 where n is the number of atoms per unit volume and A the atomic weight of the element. This is exactly the relation to be expected on the theory of single scattering if the central charge on an atom is proportional to its atomic weight.

§7. General Considerations

In comparing the theory outlined in this paper with the experimental results, it has been supposed that the atom consists of a central charge supposed concentrated at a point, and that the large single deflexions of the α and ß particles are mainly due to their passage through the strong central field. The effect of the equal and opposite compensation charge supposed distributed uniformly throughout a sphere has been neglected. Some of the evidence in support of these assumptions will now be briefly considered. For concreteness, consider the passage of a high speed α particle through an atom having a positive central charge Ne, and surrounded by a compensating charge of N electrons. Remembering that the mass, momentum, and kinetic energy of the a particle are very large compared with the corresponding values of an electron in rapid motion, it does not seem possible from dynamic considerations that an α particle can be deflected through a large angle by a close approach to an electron, even if the latter be in rapid motion and constrained by strong electrical forces. It seems reasonable to suppose that the chance of single deflexions through a large angle due to this cause, if not zero, must be exceedingly small compared with that due to the central charge.

It is of interest to examine how far the experimental evidence throws light on the question of extent of the

Annal. d. Phys. iv. 23. p. 671 (1907)

 

 

687

distribution of central charge. Suppose, for example, the central charge to be composed of N unit charges distributed over such a volume that the large single deflexions are mainly due to the constituent charges and not to the external field produced by the distribution. It has been shown (§3) that the fraction of the α particles scattered through a large angle is proportional to (NeE)2, where Ne is the central charge concentrated at a point and E the charge on the deflected particles, If, however, this charge is distributed in single units, the fraction of the α particles scattered through a given angle is proportional of Ne2 instead of N2e2. In this calculation, the influence of mass of the constituent particle has been neglected, and account has only been taken of its electric field. Since it has been shown that the value of the central point charge for gold must be about 100, the value of the distributed charge required to produce the same proportion of single deflexions through a large angle should be at least 10,000. Under these conditions the mass of the constituent particle would be small compared with that of the α particle, and the difficulty arises of the production of large single deflexions at all. In addition, with such a large distributed charge, the effect of compound scattering is relatively more important than that of single scattering. For example, the probable small angle of deflexion of pencil of α particles passing through a thin gold foil would be much greater than that experimentally observed by Geiger (§ b-c). The large and small angle scattering could not then be explained by the assumption of a central charge of the same value. Considering the evidence as a whole, it seems simplest to suppose that the atom contains a central charge distributed through a very small volume, and that the large single deflexions are due to the central charge as a whole, and not to its constituents. At the same time, the experimental evidence is not precise enough to negative the possibility that a small fraction of the positive charge may be carried by satellites extending some distance from the centre. Evidence on this point could be obtained by examining whether the same central charge is required to explain the large single deflexions of α and ß particles; for the α particle must approach much closer to the center of the atom than the ß particle of average speed to suffer the same large deflexion.

The general data available indicate that the value of this central charge for different atoms is approximately proportional to their atomic weights, at any rate of atoms heavier than aluminium. It will be of great interest to examine

 

688

experimentally whether such a simple relation holds also for the lighter atoms. In cases where the mass of the deflecting atom (for example, hydrogen, helium, lithium) is not very different from that of the α particle, the general theory of single scattering will require modification, for it is necessary to take into account the movements of the atom itself (see § 4).

It is of interest to note that Nagaoka* has mathematically considered the properties of the Saturnian atom which he supposed to consist of a central attracting mass surrounded by rings of rotating electrons. He showed that such a system was stable if the attracting force was large. From the point of view considered in his paper, the chance of large deflexion would practically be unaltered, whether the atom is considered to be disk or a sphere. It may be remarked that the approximate value found for the central charge of the atom of gold (100 e) is about that to be expected if the atom of gold consisted of 49 atoms of helium, each carrying a charge of 2 e. This may be only a coincidence, but it is certainly suggestive in view of the expulsion of helium atoms carrying two unit charges from radioactive matter.

The deductions from the theory so far considered are independent of the sign of the central charge, and it has not so far been found possible to obtain definite evidence to determine whether it be positive or negative. It may be possible to settle the question of sign by consideration of the difference of the laws of absorption of the ß particles to be expected on the two hypothesis, for the effect of radiation in reducing the velocity of the ß particle should be far more marked with a positive than with a negative center. If the central charge be positive, it is easily seen that a positively charged mass if released from the center of a heavy atom, would acquire a great velocity in moving through the electric field. It may be possible in this way to account for the high velocity of expulsion of α particles without supposing that they are initially in rapid motion within the atom.

Further consideration of the application of this theory to these and other questions will be reserved for a later paper, when the main deductions of the theory have been tested experimentally. Experiments in this direction are already in progress by Geiger and Marsden.

University of Manchester
April 1911

Nagaoka, Phil. Mag. vii. p. 445 (1904).

Historische Entwicklung der Untersuchungen

I. January 1906
Rutherford announced the discovery of alpha particle scattering by air in Jan. 1906. He took a wire coated with radioactive material and passed the alpha rays through a narrow slit. This resulted in a narrow, rectangular beam rather than a narrow, circular pencil-shaped beam.

In vacuum, the narrow slit showed perfectly sharp edges on a photographic plate the alpha rays hit. However, when the beam was passes through air, the edges of the slit became diffuse and widened. Rutherford wrote ". . . the greater width and lack of definition of the air lines show evidence of an undoubted scattering of the rays in their passage through air."

II. January to June 1906
Rutherford did not work in a vacuum (although most of the experiments were!), but rather discussed his results with colleagues, including William H. Bragg (who, together with his son William L. Bragg, would win the 1915 Nobel Prize in Physics). Bragg was not happy with Rutherford's conclusion and suggested an alternative explanation. Rutherford's response was to perform a more definitive experiment, publishing the results in June 1906.

III. June 1906: Scattering by Mica
Rutherford used his wire coated with the alpha-emitting radioactive element, but he modified the slit the alpha rays traveled through. Half the slit was left open and half was covered by a thin (0.003 cm) mica plate. The experiment was done in the vacuum; the mica taking the place of the air. The open side of the resulting photographic image was sharp and the mica side was diffuse.

He also subjected the alpha beam to a magnetic field. This was in response to Bragg's alternative explanation which involved electrons (the exact details are not necessary). Since electrons bend the opposite way from alpha particles, any electrons produced by the mica as the beam went through it would be swept away. The result? The image was the same as when there was no magnetic field. The vacuum side was sharp and the mica side was diffuse.

Rutherford had proved conclusively the alpha particles could be scattered.

IV. More Results from the Mica Experiment
Careful measuring of the images allowed Rutherford to deduce that some alpha particles had been scattered by 2° from a straight-line path. In light of future events, he makes the interesting statement that other particles may have been deflected "through a considerably greater angle."

He also calculates that a field strength of 100 million volts per cm is required to bend the alpha particles through 2°. In another very interesting statement given future events, he says this 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." By this he meant the Thomson model of the atom.

Keep in mind that the Thomson model (announced in early 1904, but speculated on in print by Thomson as early as 1899) is still the only model of the atom acceptable to the British. The "Saturnian model," announced by Nagaoka in May 1904, had been totally discredited by Thomson and his allies. Or so they thought!! Also, remember that Rutherford had been Thomson's student and the two were very close. (J.J.'s son George has many memories, from his childhood, of Rutherford and his wife over for dinner.) So it is quite natural for Rutherford to believe that J.J.'s model is correct.

V. Moving to Manchester
All this time, Rutherford had been in Canada (since 1898) at McGill University in Montreal. In 1907, a position came open at the University of Manchester and Rutherford applied it and was selected. Now he was back in England and, more importantly for our story, he hooked up with Hans Geiger.

VI. Manchester, 1908
One of the central goals of Rutherford's work was to determine the nature of the alpha particle. Was it a singly-charged hydrogen molecule or a doubly-charged helium atom? The e / m ratio was consistent with either. Although in 1907 he was confident it was the latter, he sought additional confirmation. To this end, while in Canada he had tried an experiment which needed to count the number of alpha particles. It was a failure. However, with Geiger now involved, a satisfactory counting device was designed and built.

However, the scattering of the alpha particle was wreaking havoc on their results. The counter worked fine, but as Rutherford put it in a letter to a friend, "the scattering is the devil." It was evident to both Rutherford and Geiger that an accurate picture of alpha particle scattering was required. Geiger started on this work even before the counting experiment was done, and in June 1908 he announced some preliminary results.

Above is Geiger's 1908 apparatus. R is the source, S is the thin metal foil which scatters the particles, Z is the zinc sulfide screen that flashed when struck (it was called the scintillation method), and M is a microscope to view the flashes with. It almost goes without saying, this work was done in a very dark room.

As this work proceeded, Geiger began to notice what he termed a "notable" scattering; in other words he was seeing scattering by greater angles than he had expected. In addition to this, he found that gold foil scattered through a greater angle than aluminum. As Geiger put it, "quite an appreciable angle." He proposed to continue with as many metals as possible "in the hope of establishing some connection between the scattering and stopping powers of these materials." In other words, what was first a problem now bcame the subject of study.

VII. Marsden Enters the Scene
To assist in these experiments, twenty-year-old Ernest Marsden joined Geiger. The tube was improved and lengthened, but experimental difficulties persisted. They could gain only a rough estimate of the most probable angle of deflection for a given metal. They (by the early spring of 1909) decided the trouble was somehow related to scattering by the tube walls and a series of washers installed in the tube solved the problem. According to Marsden (many years later), neither of them thought the alpha particles were being directly REFLECTED from the walls or the metal foil.

As Geiger himself says, some thirty years later:

"In the electric counting of alpha-particles it was seen that the small residuum of gas in the four-metre long tube . . . influenced the result. We attributed this to a slight scattering of the alpha-particles. Later on, I examined scattering quantitatively in several experiments. The most important observation was the appearance of isolated instances of extremely large angles of deflection, which were far outside the normal variations. At first we could not understand this at all."

VIII. Rutherford makes the Critical Suggestion
Hans Geiger was a scientist in his own right. He held a Ph.D., was a teacher on staff, and did research with Rutherford's direction and collaboration. It was at this time that he said (according to Rutherford), "Don't you think that young Marsden whom I am training in radioactive methods ought to begin a small research?" Rutherford agreed and, as Marsden remembers it 50 years later, he came into the lab one day, turned to Marsden and said "See if you can get some effect from alpha particles directly reflected from a metal surface." Marsden goes on to say about his own thoughts:

"I did not think he expected any such result, but it was one of those hunches that perhaps some effect might be observed . . . ."

The year before he died, Rutherford himself recalled what then happened:

"Two or three days later Geiger came to me in great excitement and said: "We have been able to get some of the alpha particles coming backwards."

For Ernest Rutherford, winner of the 1908 Nobel Prize in Chemistry, his greatest scientific achievement still lay two years into the future. Sometime in late 1910/early 1911, he switched roles with Geiger, who remembers it from 27 years later:

"One day Rutherford, obviously in the best of spirits, came into my room and told me that he now knew what the atom looked like."

IX. The Experiment of 1909
Marsden first used the following set-up in his search for reflected alpha particles:

The alpha emitter was placed at A on top of a lead plate which prevented direct access of the particles to the counter located at S. With nothing placed at position R the counter did not record any hits. However, when one thin gold foil was placed at R, the counter came to life.

It was from this experimental set-up that Geiger reported two or thre days later that some alpha particles had been reflected back.

This is the opening paragraph of Geiger and Marsden's paper of May 1909:

When b-particles fall on a plate, a strong radiation emerges from the same side of the plate as that on which the b-particles fall. This radiation is regarded by many observers as a secondary radiation, but more recent experiments seem to show that it consists mainly of primary b-particles, which have been scattered inside the material to such an extent that they emerge again at the same side of the plate. For a-particles a similar effect has not previously been observed, and is perhaps not to be expected on account of the relatively small scattering which a-particles suffer in penetrating matter.

This is the data they reported in that same paper:

1.
Metal
2.
Atomic weight, A
3.
Number of scintillations
per minute, Z.
4.
A/Z.
Lead
207
62
30
Gold
197
67
34
Platinum
195
63
33
Tin
119
34
28
Silver
108
27
25
Copper
64
14·5
23
Iron
56
10·2
18·5
Aluminium.
27
3·4
12·5

For platinum, Geiger and Marsden reported:

"Three different determinations showed that of the incident a-particles about 1 in 8000 was reflected, under the described conditions."

X. 1909 Fades into 1910 and then 1911
Now, Ernest Rutherford was confronted with the challenge of explaining the results. His answer, to be published in May 1911, was the nuclear atom and it made Rutherford unique among all other Nobel Prize winners. You see, almost all historians of science call the discovery of the nucleus Rutherford's greatest scientific work. He is the only one to do his greatest work after receiving the Nobel Prize.

Here is what he says in a lecture at Clark University in September, 1909; just 6 months after the discovery of large-angle scattering:

"Geiger and Marsden observed the suprising fact that about one in eight thousand a particles incident on a heavy metal like gold is so deflected by its encounters with the molecules that it emerges again on the side of the incidence. Such a result brings to mind the enormous intensity of the electric field surrounding or within the atom."

Notice the word "encounters;" it's plural. Rutherford is thinking about multiple scattering. In other words, the alpha particle encounters one gold atom after another and each encounter deflects the alpha a bit more, so that the sum of all the deflections is to make the alpha particle come flying out 90° or more from the direction it went in.

In 1910, two events important to our story happen.

1) On Feb, 17, 1910, Geiger reads a paper in which he determines the most likely angle of deflection for any one alpha particle to be about 1°. However, in the same paper, he says, "It does not appear profitable at present to discuss the assumption that might be made to account for [it]." It seems safe to say that 10 months after the discovery of large-angle scattering, Geiger (and Rutherford) do not have a clue as to its explanation.

2) J.D. Crowther (a student of J.J. Thomson) publishes a theory of beta-particle scattering in March 1910. He follows up with more data in June and then December. He uses the 'multiple scattering' idea; that is, many small deflecions which add up to one large angle. Each deflecion is caused by the particle encountering an atom. Over time, Rutherford (in discussion with his friend W.H. Bragg) will become convinced that this is the incorrect explanation for large angle scattering.

It is not possible to put a precise date on when Rutherford hit on single scattering as the answer. The papers which bear his calculations are undated. However a series of letters he wrote at this time allow a glimse into when he started to put everything together. The very first mention of the atom occurs in a letter dated Dec. 14, 1910 (to B.B. Boltwood, an American chemist) in which Rutherford says he has been doing "a good deal of calculation on scattering." Scattering and the atom figure in nine letters between then and Feb. 19, 1911. To keep these dates in perspective, remember that Rutherford's published paper appeared in Philosophical Magazine for May 1911.

Just to review, 'single scattering' refers to one encounter of the alpha particle with an atom. One single incident is sufficient to deflect the alpha more than 90°. It does seem a bit fantastic that only one encounter with an atom was sufficient, but Rutherford was having serious problems making multiple scattering fit.

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