4142:"...the magnitude of this negative charge is about 6 Γ 10 electrostatic units, and is equal to the positive charge carried by the hydrogen atom in the electrolysis of solutions. In gases at low pressures these units of negative electric charge are always associated with carriers of a definite mass. This mass is exceedingly small, being only about 1.4 Γ 10 of that of the hydrogen ion, the smallest mass hitherto recognized as capable of a separate existence. The production of negative electrification thus involves the splitting up of an atom, as from a collection of atoms something is detached whose mass is less than that of a single atom."
3641:. The positive charge in the Thomson model is too diffuse to produce an electric field of sufficient strength to cause such scattering and the electrons are too light to alter the course of the alpha particle. Rutherford deduced that the positive charge of the atom, along with most of the atom's mass, was concentrated in a tiny nucleus at the center of the atom. Only such an intense concentration of charge and mass, could have scattered the alpha particle beam so dramatically. Rutherford paper showed that this model explained both the results of Thomson and Crowther and the new large angle scattering results of Geiger and Marsden.
414:
scattering, beta ray absorption, or optical properties of gases, to estimate that "number of corpuscles is not greatly different from the atomic weight". This reduced the number of electrons to tens or at most a couple of hundred and it required that the positive sphere in
Thomson's atom model contain most of the mass of the atom. This in turn meant that Thomson's mechanical stability work from 1904 and the comparison to the periodic table were no longer valid. Moreover, the alpha particle, so important to the next advance in atomic theory by Rutherford, would no longer be viewed as an atom containing thousands of electrons.
3686:
2480:
2311:
3660:
The scattering model predictions were not considered definitive evidence against
Thomson's plum pudding model. Thomson and Rutherford had pioneered scattering as a technique to probe atoms, its reliability and value were unproven. Before Rutherford's paper the alpha particle was considered an atom, not a compact mass. It was not clear why it should be a good probe. Moreover, Rutherford's paper did not discuss the atomic electrons vital to practical problems like chemistry or atomic spectroscopy. Rutherford's nuclear model would only become widely accepted after the work of
364:
1143:
20:
3793:"With regard to positive electrification I have been in the habit of using the crude analogy of a liquid with a certain amount of cohesion, enough to keep it from flying to bits under its own repulsion. I have however always tried to keep the physical conception of the positive electricity in the background because I have always had hopes (not yet realised) of being able to do without positive electrification as a separate entity and to replace it by some property of the corpuscles."
433:, giving a result in better agreement with other approaches to the problem. Experiments by other scientists in this field had shown that atoms contain far fewer electrons than Thomson previously thought. Thomson now believed the number of electrons in an atom was a small multiple of its atomic weight: "the number of corpuscles in an atom of any element is proportional to the atomic weight of the element β it is a multiple, and not a large one, of the atomic weight of the element."
5236:
5246:
1390:
3732:, p. 103 "In default of exact knowledge of the nature of the way in which positive electricity occurs in the atom, we shall consider a case in which the positive electricity is distributed in the way most amenable to mathematical calculation, i.e., when it occurs as a sphere of uniform density, throughout which the corpuscles are distributed."
56:
positive charge, Thomson tentatively proposed that it was everywhere in the atom, the atom being in the shape of a sphere for the sake of mathematical simplicity. Following from this, Thomson imagined that the balance of electrostatic forces in the atom would distribute the electrons more or less evenly throughout this hypothetical sphere.
3342:
656:
94:. Neither Thomson nor his colleagues ever used this analogy. It seems to have been conceived by popular science writers to make the model accessible to the layman. The analogy is perhaps misleading because Thomson likened the sphere to a liquid rather than a solid, since he thought the electrons moved around in it.
1123:
model and furthermore claimed to show that Helium would contain 12 electrons (vs 2 in modern theories) and an alpha particle about 10 electrons (vs zero in modern theories). Importantly, Crowther measurements were confined to small angles and used an indirect technique less reliable than the one adopted by Geiger.
376:
296:) has the same mass-to-charge ratio as cathode rays; then he applied his previous method for determining the charge on ions to the negative electric particles created by ultraviolet light. By this combination he estimated that the electron's mass was 0.0014 times that of the hydrogen ion (as a fraction:
192:, had the same charge/mass ratio as cathode rays. These beta particles were believed to be electrons traveling at much high speeds. These beta particles would be used by Thomson to probe atoms to find evidence for his atomic theory. The other form of radiation critical to this era of atomic models was
3636:
While in
Thomson's "plum pudding" model it is mathematically possible that an alpha particle could be deflected by more than 90Β° after 10,000 collisions, the probability of such an event is so low as to be undetectable. This extremely small number shows that Thomson's model of 1906 cannot explain the
396:
in 1878. The demonstration involved magnetized pins pushed into cork disks and set afloat in a basin of water. The magnetized pins were oriented such that they repelled each other. Above the center of the basin was suspended an electromagnet that attracted the pins towards the center. The equilibrium
203:
published near the end of the 19th century. Part of the attraction of the vortex model was its possible role in describing the spectral data as vibrational responses to electromagnetic radiation. Neither
Thomson's model nor its successor, Rutherford's model, made progress towards understanding atomic
3659:
Rutherford's 1911 paper on alpha particle scattering showed that
Thomson's scattering model could not explain the large angle scattering and it showed that multiple scattering was not necessary to explain the data. However, in the years immediately following its publication few scientists took note.
913:
338:
Primarily focused on the corpuscles, Thomson adopted the positive sphere from Kelvin's atom model proposed a year earlier. He then gives a detailed mechanical analysis of such a system, distributing the corpuscles uniformly around a ring. The attraction of the positive electrification is balanced
316:
I regard the atom as containing a large number of smaller bodies which I shall call corpuscles; these corpuscles are equal to each other; the mass of a corpuscle is the mass of the negative ion in a gas at low pressure, i.e. about 3 Γ 10 of a gramme. In the normal atom, this assemblage of corpuscles
1122:
Also in 1910, Crowther published a series of experiments on scattering of beta particles through aluminum and platinum foils. These experiments used beta particles of approximately one energy rather than the natural energy spread of beta emission. Crowther's analysis confirmed
Thomson's theoretical
452:
to experiment with beta scattering through thin foils and, in 1910, Thomson produced a new theory of beta scattering. The two innovations in this paper was the introduction of scattering from the positive sphere of the atom and analysis that multiple or compound scattering was critical to the final
3709:
While the negative electricity is concentrated on the extremely small corpuscle, the positive electricity is distributed throughout a considerable volume. An atom would thus consist of minute specks, the negative corpuscles, swimming about in a sphere of positive electrification, like raisins in a
413:
Before 1906 Thomson considered the atomic weight to be due to the mass of the electrons (which he continued to call "corpuscles"). Based on his own estimates of the electron mass, an atom would need tens of thousands electrons to account for the mass. In 1906 he used three different methods, X-ray
400:
For instance, he observed that while five pins would arrange themselves in a stable pentagon around the center, six pins could not form a stable hexagon. Instead, one pin would move to the center and the other five would form a pentagon around the center pin, and this arrangement was stable. As he
55:
in 1911. The model tried to account for two properties of atoms then known: that there are electrons and that atoms have no net electric charge. Logically there had to be an equal amount of positive charge to balance out the negative charge of the electrons. As he had no idea of the source of this
3465:
This should not have been possible according to the
Thomson model: the scattering into large angles should have been negligible. In a 1911 paper, Rutherford developed similar equations for alpha particle scattering and showed that they did not agree with experimental results of Geiger and Marsden
1019:
On average the positive sphere and the electrons alike provide very little deflection in a single collision. Thomson's model combined many single-scattering events from the atom's electrons and a positive sphere. Each collision may increase or decrease the total scattering angle. Only very rarely
221:
models for the atom. His first versions were qualitative culminating in his 1906 paper and follow on summaries. Thomson's model changed over the course of its initial publication, finally becoming a model with much more mobility containing electrons revolving in the dense field of positive charge
4487:, p. 162: "Since the mass of a corpuscle is only about one-seventeen-hundredth part of that of an atom of hydrogen, it follows that if there are only a few corpuscles in the hydrogen atom the mass of the atom must in the main be due to its other constituent β the positive electricity."
265:
who in 1815 noted that the atomic weights of various elements were multiples of hydrogen's atomic weight and hypothesized that all atoms were hydrogen atoms fused together. While Prout's hypothesis was dismissed by chemists when it was found by the 1830s that some elements seemed to have a
2432:
is the mass of the alpha particle. No correction for recoil is needed here because the gold atom is nearly 20 times as heavy as the alpha particle. The equation shows that the largest possible deflection caused by the positive sphere will be very small. But what of the average deflection
118:
could be formed by additions of single electrons. His concentric rings of electrons introduced an idea that later became "core" and "valence" electrons. And his model was based on a model of mechanical stability. Being based on experimentally studied subatomic "corpuscles", now known as
1679:
154:(later Lord Kelvin) in 1867. By 1890, J.J. Thomson had his own version called the "nebular atom" hypothesis, in which atoms were composed of immaterial vortices and suggested similarities between the arrangement of vortices and periodic regularity found among the chemical elements.
3146:
513:
3022:
317:
forms a system which is electrically neutral. 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 on the corpuscles.
3466:
when applied to
Thomson's atom model. The critical issue was large angle scattering. A gold foil like the one Geiger and Marsden experimented with would be around 10,000 atoms thick. The probability that an alpha particle will be deflected by a total of more than 90Β° after
114:. Among these models, Thomson's can be considered the first modern model. Thomson's model is distinguished by being the first with internal structure; it was the best available model between 1904 and 1910. Thomson's model introduced the idea that successive elements in the
2735:
424:
In
Chapter 6, he further elaborates his experiment using magnetized pins in water, providing an expanded table. For instance, if 59 pins were placed in the pool, they would arrange themselves in concentric rings of the order 20-16-13-8-2 (from outermost to innermost).
1015:
1838:
2425:
5020:"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"
798:
1939:
246:. He observed that cathode rays can be deflected by electric and magnetic fields, which does not happen with light rays. In a few paragraphs near the end of this long paper Thomson discusses the possibility that atoms were made of these
354:
Thomson believed that all the mass of the atom was carried by the electrons. This would mean that even a small atom would have to contain thousands of electrons, and the positive electrification the encapsulated them was without mass.
351:. This concept, that a model based subatomic particles could account for chemical trends, encouraged interest in Thomson's model and influenced future work even if the details Thomson's electron assignments turned out to be incorrect.
2054:
1371:
2850:
1550:
216:
Thomson's model was the first to assign a specific inner structure to an atom, though his earliest descriptions did not include mathematical formulas. From 1897 through 1913, Thomson proposed a series of increasingly detailed
2156:
404:
From this, Thomson believed the electrons arranged themselves in concentric shells, and the electrons could move about within these shells but did not move out of them unless electrons were added or subtracted from the atom.
3033:
is the average horizontal momentum, which is first reduced then restored as horizontal force switches direction as the alpha particle goes across the sphere. Since we already know the deflection is very small, we can treat
145:
Throughout the 19th century evidence from chemistry and statistical mechanics accumulated that matter was composed of atoms. The structure of the atom was discussed, and by the end of the century the leading model was the
342:
After discussing his many formulae for stability he turned to analyzing patterns in the number of electrons in various concentric rings of stable configurations. These regular patterns
Thomson argued are analogous to the
289:. While Thomson did not adopt the terminology, the connection convinced other scientists that cathode rays were particles, an important step in their eventual acceptance of an atomic model based on sub-atomic particles.
2886:
3549:(β2.71828...). Assuming an average deflection per collision of 0.008Β°, and therefore an average deflection of 0.8Β° after 10,000 collisions, the probability of an alpha particle being deflected by more than 90Β° will be
2578:
428:
In Chapter 7, Thomson summarized his 1906 results on the number of electrons in an atom. He included one important correction: he replaced the beta-particle analysis with one based on the cathode ray experiments of
3423:
2587:
3632:
922:
1115:
1254:
3676:
in mathematics seeks the optimal distribution of equal point charges on the surface of a sphere; it is a generalization of the plum pudding model in the absence of its uniform positive background charge.
1519:
3462:
was their preferred material because gold is very malleable and can therefore be made into an especially thin foil. They found that the gold foil could scatter alpha particles by more than 90 degrees.
1724:
2325:
3337:{\displaystyle {\bar {\theta }}_{2}={\frac {1}{\pi R^{2}}}\int _{0}^{R}{\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {2{\sqrt {R^{2}-b^{2}}}}{v}}\cdot {\frac {1}{mv}}\cdot 2\pi b\cdot \mathrm {d} b}
651:{\displaystyle {\bar {\theta }}_{1}={\frac {16}{5}}\cdot {\frac {kq_{a}q_{e}}{mv^{2}}}\cdot {\frac {1}{R}}\cdot {\sqrt {\frac {3N}{2}}}\approx 0.00007{\text{ radians or }}0.004{\text{ degrees}}}
440:). Thomson still did not know what substance constituted the positive electrification, though he noted that no scientist had yet found a positively-charged particle smaller than a hydrogen ion.
3537:
2261:
4225:: "We suppose that the mass of an atom is the sum of the masses of the corpuscles it contains, so that the atomic weight of an element is measured by the number of corpuscles in its atom."
1844:
1450:
2160:
This then-standard application of hyperbolic orbits for trajectories in a central potential was also used in Rutherford's more famous 1911 paper (a full explanation is available in
3131:
2467:
1717:
436:
This would mean that almost all of the atom's mass was carried by the positive sphere. In this book he now estimates that a hydrogen atom is 1,700 times heavier than an electron (
3458:
collaborated on a series of experiments in which they bombarded metal foils with a beam of alpha particles and measured the intensity versus scattering angle of the particles.
1960:
1263:
3065:
1051:
464:
The average deflection caused by the atom's electrons was calculated by matching a hyperbolic orbit to the collision geometry and then multiplied by a factor proportional to
3714:
The analogy was never used by Thomson nor his colleagues. It seems to have been a conceit of popular science writers to make the model easier to understand for the layman.
461:
In his 1910 paper Thomson presented equations that modeled how beta particles scatter in a collision with an atom. This section adapts those equations to alpha particles.
2751:
3092:
2879:
1543:
486:
258:, thereby generating cathode rays. Thomson thus showed evidence that atoms were in fact divisible, though he did not attempt to describe their structure at this point.
2187:
2299:
equal to that of a gold atom, just close enough to graze its edge, will experience the sphere's electric field at its strongest. This occurs for an impact parameter
3638:
2066:
339:
by the mutual repulsion of the corpuscles. His analysis focuses on stability, looking for cases where small changes in position are countered by restoring forces.
453:
results. This theory and Crowther's experimental results would be confronted by Rutherford's theory and Geiger and Mardsen new experiments with alpha particles.
2494:
506:
908:{\displaystyle {\bar {\theta }}_{2}={\frac {\pi }{4}}\cdot {\frac {kq_{a}q_{g}}{mv^{2}}}\cdot {\frac {1}{R}}\approx 0.00013{\text{ radians or 0.007 degrees}}}
3348:
3554:
2161:
292:
In 1899, reiterated his atomic model in a paper that showed that negative electricity created by ultraviolet light landing on a metal (known now as the
281:
suggested that the corpuscle identified by Thomson from cathode rays and proposed as parts of an atom was a "free electron", as described by physicist
1062:
3806:
Kragh, H. (2012). Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913-1925. United Kingdom: OUP Oxford.
90:
Thomson's model is popularly referred to as the "plum pudding model" with the notion that the electrons are distributed uniformly, like raisins in a
1180:
334:... the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, ...
3965:
2489:
Inside a sphere of uniformly distributed positive charge the force exerted on the alpha particle at any point along its path through the sphere is
270:
has an atomic weight of about 35.45βthe concept continued to have influence. Eventually the discrepancies would be explained with the discovery of
5064:
4688:
4917:
Although Thomson's model has been outdated for a long time by quantum mechanics, his problem of placing charges on a sphere is still noteworthy.
3817:
2277:
are the masses of the two colliding particles, enters the model when the two-body coordinates are written as the equivalent one-body problem.
123:, Thomson's model was the first model to be subject to direct experimental tests. By 1909 these tests began to reveal new ideas, and in 1911
3907:
1674:{\displaystyle {\frac {1}{\pi R^{2}}}\int _{0}^{R}{\sqrt {2{\sqrt {R^{2}-b^{2}}}}}\cdot 2\pi b\cdot \mathrm {d} b={\frac {4}{5}}{\sqrt {2R}}}
254:. Thomson believed that the intense electric field around the cathode caused the surrounding gas molecules to split up into their component
1955:
In Thomson's model of scattering, the average angle by which an alpha particle should be deflected by the positive sphere of the atom is
3710:
parsimonious plum-pudding, units of negative electricity being attracted toward the centre, while at the same time repelling each other.
3475:
1119:
The electron and positive sphere deflections combine to 0.008Β°. Thus, assuming 10,000 collisions, the average deflection would be 0.8Β°.
369:
A 1905 diagram by J. J. Thomson illustrating his hypothetical arrangements of electrons in an atom, ranging from one to eight electrons.
2061:
In 1906, Thomson provided an equation which models how a beta particle should be deflected by an atomic electron in a close encounter:
3017:{\displaystyle \tan \theta _{2}={\frac {\Delta p_{y}}{p_{x}}}={\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {L}{v}}\cdot {\frac {1}{mv}}}
4974:
793:
The average angle by which an alpha particle should be deflected by the positive sphere of the atom was simply given by Thomson as:
1020:
would a series of collisions all line up in the same direction. The result is similar to the standard statistical problem called a
397:
arrangement the pins took informed Thomson on what arrangements the electrons in an atom might take and he provided a brief table.
196:. Heavier and slower than beta particles, these would be the key tool used by Rutherford to find evidence against Thomson's model.
1463:
5131:
2472:
Consider an alpha particle passing through the positive sphere of a gold atom, with its initial trajectory at a lateral distance
5041:
3701:, a British dessert with whole raisins, was an anonymous reporter who wrote an article for the British pharmaceutical magazine
2730:{\displaystyle F_{y}={\frac {kq_{a}q_{g}}{r^{2}}}\cdot {\frac {r^{3}}{R^{3}}}\cdot \cos \varphi ={\frac {bkq_{a}q_{g}}{R^{3}}}}
5294:
5274:
4793:
4671:
4020:
3885:
59:
Thomson attempted without success to develop a complete model that could predict other known properties of the atom, such as
199:
In addition to the emerging atomic theory, the electron, and radiation, the last element of history was the many studies of
4089:
1010:{\displaystyle {\bar {\theta }}={\sqrt {{\bar {\theta }}_{1}^{2}+{\bar {\theta }}_{2}^{2}}}\approx 0.008{\text{ degrees}}}
2196:
4176:
3947:
392:
in 1905, Thomson reviewed his 1904 paper and demonstrated some of its concepts with a practical experiment invented by
389:
222:
rather than a static structure. Thomson attempted unsuccessfully to reshape his model to account for some of the major
4557:
Thomson, Joseph J. "On the scattering of rapidly moving electrified particles". Cambridge Philosophical Society, 1910.
4963:
3441:
68:
261:
Thomson notes that he was not the first scientist to propose that atoms are actually divisible, making reference to
1258:
The net deflection caused by all the electrons within this cylinder of effect around the alpha particle's path is
1833:{\displaystyle {\bar {\theta }}_{1}={\frac {32}{5}}\cdot {\frac {kq_{a}q_{e}}{mv^{2}}}\cdot {\sqrt {N_{0}\pi R}}}
4598:
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
4515:
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
4044:. RePoSS: Research Publications on Science Studies 10. Aarhus: Centre for Science Studies, University of Aarhus.
4058:
2058:
Neither Thomson nor Rutherford explained how this equation was developed, but here an educated guess is made.
1402:
5176:
5094:
4571:
2420:{\displaystyle \theta _{2}=2\arctan \left({\frac {kq_{a}q_{g}}{mv^{2}b}}\right)\approx 0.02{\text{ degrees}}}
437:
23:
A hypothetical atom with seven electrons, arranged in a pentagonal dipyramid, as imagined by Thomson in 1905.
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448:
Thomson's difficulty with beta scattering in 1906 lead him to renewed interest in the topic. He encouraged
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3100:
2436:
1686:
177:
5124:
4737:
3939:
4873:"Description of a highly symmetric polytope observed in Thomson's problem of charges on a hypersphere"
4722:
Goldstein, Herbert. Classical Mechanics. United States, Addison-Wesley, 1950.
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1027:
5162:
278:
147:
1139:. The effect of the positive sphere is ignored so as to isolate the effect of the atomic electrons.
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140:
4818:
Levin, Y.; Arenzon, J. J. (2003). "Why charges go to the Surface: A generalized Thomson Problem".
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5289:
4355:
4316:
3070:
2857:
1934:{\displaystyle ={\frac {16}{5}}\cdot {\frac {kq_{a}q_{e}}{mv^{2}R}}\cdot {\sqrt {\frac {3N}{2}}}}
1524:
467:
166:
4593:
4317:"A. M. Mayer's experiments with floating magnets and their use in the atomic theories of matter"
3963:
O'Hara, J. G. (March 1975). "George Johnstone Stoney, F.R.S., and the Concept of the Electron".
3685:
5117:
5072:
5024:
4929:
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1024:. If the average deflection angle of the alpha particle in a single collision with an atom is
5053:
3750:
449:
2479:
2310:
5002:
4884:
4837:
4773:
4522:
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421:
which reviewed his ideas on the atom's structure and proposed further avenues of research.
293:
32:
4090:"Corpuscles, Electrons and Cathode Rays: J.J. Thomson and the 'Discovery of the Electron'"
2049:{\displaystyle {\bar {\theta }}_{2}={\frac {\pi }{4}}\cdot {\frac {kq_{a}q_{g}}{mv^{2}R}}}
1366:{\displaystyle \theta _{1}={\frac {4kq_{a}q_{e}}{mv^{2}g}}\cdot {\sqrt {N_{0}\pi g^{2}L}}}
8:
64:
4888:
4841:
4777:
4526:
4262:
3833:
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5220:
5155:
4853:
4827:
4443:
4248:
3990:
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491:
4872:
4767:
4236:
401:
added more pins, they would arrange themselves in concentric rings around the center.
381:
Thomson's diagram of Mayer's practical experiment for exploring electron arrangements.
173:" in 1891. However even late in 1899, few scientists believed in subatomic particles.
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5245:
4959:
4908:
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4857:
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3546:
3447:
2845:{\displaystyle \Delta p_{y}=F_{y}t={\frac {bkq_{a}q_{g}}{R^{3}}}\cdot {\frac {L}{v}}}
2285:
717:
363:
176:
Another emerging scientific theme of the 19th century was the discovery and study of
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124:
72:
48:
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773:
128:
76:
60:
4594:"On the scattering of Homogeneous Ξ²-Rays and the number of Electrons in the Atom"
4511:"On the scattering of Homogeneous Ξ²-Rays and the number of Electrons in the Atom"
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3673:
393:
286:
193:
185:
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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
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200:
115:
111:
52:
19:
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4993:
4785:
4709:
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4209:
4105:
3920:
326:
Thomson provided his first detailed description of the atom in his 1904 paper
5268:
5065:"The Scattering of Ξ± and Ξ² Particles by Matter and the Structure of the Atom"
4904:
4689:"The Scattering of Ξ± and Ξ² Particles by Matter and the Structure of the Atom"
4663:
4619:
4544:
4439:
4379:
4340:
4278:
4113:
3849:
2151:{\displaystyle \tan {\frac {\theta _{e}}{2}}={\frac {kq_{e}q_{e}}{m'v^{2}b}}}
430:
282:
262:
223:
40:
3751:"J. J. Thomson's plum-pudding atomic model: The making of a scientific myth"
5169:
4912:
4772:. Undergraduate Texts in Physics. Cham: Springer International Publishing.
4610:
4535:
4510:
3978:
3774:
3698:
2190:
344:
239:
181:
103:
91:
2573:{\displaystyle F={\frac {kq_{a}q_{g}}{r^{2}}}\cdot {\frac {r^{3}}{R^{3}}}}
188:
determined that the highly penetrating radiation from uranium, now called
4832:
3787:
Letter from J. J. Thomson to Oliver Lodge dated 11 April 1904, quoted in
3451:
1021:
151:
107:
4447:
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5196:
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242:
are not light but made of negatively charged particles which he called
205:
189:
80:
3986:
3841:
3418:{\displaystyle ={\frac {\pi }{4}}\cdot {\frac {kq_{a}q_{g}}{mv^{2}R}}}
3627:{\displaystyle e^{-(90/0.8)^{2}}\approx e^{-12656}\approx 10^{-5946}}
375:
5019:
3902:
106:
ranging from the philosophical models of the ancient Greeks through
4655:
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
4650:
For example overview of classical mechanics was published in 1904:
2320:
Using Thomson's equation from above to model this collision gives:
1389:
271:
267:
162:
158:
120:
44:
4253:
3936:
Quantum Generations: A History of Physics in the Twentieth Century
5109:
1110:{\displaystyle {\bar {\theta }}_{n}={\bar {\theta }}{\sqrt {n}}}
2295:
An alpha particle passing by the positive sphere with a radius
102:
Thomson's plum-pudding model of the atom is one of a series of
79:
featuring a compact nuclear center. This model was taken up by
4237:"Early atomic models β from mechanical to quantum (1904β1913)"
1249:{\displaystyle {\frac {2kq_{a}q_{e}}{mv^{2}{\tfrac {1}{2}}g}}}
1131:
Consider an alpha particle passing through an atom of radius
161:
in 1897 changed his views. Thomson called them "corpuscles" (
1514:{\displaystyle {\sqrt {L}}={\sqrt {2{\sqrt {R^{2}-b^{2}}}}}}
1386:
is the distance the alpha particle passes through the atom.
165:), but they were more commonly called "electrons", the name
5095:"On the Scattering of rapidly moving Electrified Particles"
4572:"On the Scattering of rapidly moving Electrified Particles"
4416:"The Scattering of Ξ± and Ξ² Particles and Rutherford's Atom"
3459:
84:
36:
1156:
of the alpha particle's path, their mean distance will be
4490:
4194:"The first subatomic explanations of the periodic system"
1175:. Therefore, the average deflection per electron will be
4565:
4563:
3878:
Inward bound: of matter and forces in the physical world
917:
The net deflection per atom combines the two equations:
3697:
The first known writer to compare Thomson's model to a
3693:, not Thomson's preferred analogy for his atomic model.
330:. Thomson starts with a short description of his model
4150:
4148:
3749:
Hon, Giora; Goldstein, Bernard R. (6 September 2013).
2201:
1229:
110:'s chemistry-based atom to the modern quantum atom of
47:
in 1897, but it was subsequently rendered obsolete by
5003:"On the Masses of the Ions in Gases at Low Pressures"
4732:
4730:
4728:
4560:
4129:"On the Masses of the Ions in Gases at Low Pressures"
4013:
A history of the theories of aether & electricity
3557:
3478:
3351:
3149:
3103:
3073:
3040:
2889:
2860:
2754:
2590:
2497:
2439:
2328:
2199:
2170:
2069:
1963:
1847:
1727:
1689:
1553:
1527:
1466:
1405:
1266:
1183:
1065:
1030:
925:
801:
516:
494:
470:
408:
4652:
Whittaker, E. T.; McCrae, Sir William (1988-12-15).
2162:
the article on the Rutherford scattering experiments
1950:
321:
4454:
4145:
4069:
4042:
Before Bohr: Theories of atomic structure 1850-1913
3430:
5099:Proceedings of the Cambridge Philosophical Society
4725:
4576:Proceedings of the Cambridge Philosophical Society
3809:
3744:
3742:
3740:
3738:
3626:
3532:{\displaystyle e^{-(90/{\bar {\theta }}_{n})^{2}}}
3531:
3427:This matches Thomson's formula in his 1910 paper.
3417:
3336:
3125:
3086:
3059:
3016:
2873:
2844:
2729:
2572:
2461:
2419:
2256:{\displaystyle {\tfrac {m_{1}m_{2}}{m_{1}+m_{2}}}}
2255:
2181:
2150:
2048:
1933:
1832:
1711:
1673:
1537:
1513:
1444:
1365:
1248:
1109:
1045:
1009:
907:
650:
500:
480:
456:
39:with internal structure. It was first proposed by
3871:
3869:
3867:
3865:
3863:
3861:
3859:
274:and nuclear structure in the early 20th century.
5266:
4413:
4409:
3966:Notes and Records of the Royal Society of London
3435:
1382:is the number of corpuscles per unit volume and
4956:J. J. Thomson and the Discovery of the Electron
4759:
4651:
4551:
4407:
4405:
4403:
4401:
4399:
4397:
4395:
4393:
4391:
4389:
3802:
3800:
3735:
3667:
1947:is the number of electrons in the entire atom.
1152:For each electron within an arbitrary distance
229:
127:used experimental scattering data to propose a
4680:
4094:The British Journal for the History of Science
3856:
1126:
312:). In the conclusion of this paper he writes:
180:. Thomson discovered the electron by studying
5125:
5092:
4953:
4569:
4356:"LXX. On the number of corpuscles in an atom"
4303:
4126:
3956:
3908:Proceedings of the Royal Society of Edinburgh
3880:(Reprint ed.). Oxford: Clarendon Press
3788:
3644:
277:A few months after Thomson's paper appeared,
4817:
4716:
4386:
4036:
4034:
4032:
4006:
4004:
3797:
3748:
4765:
4347:
4169:Quantum Einstein, Bohr and the Great Debate
4120:
789:= number of electrons in the gold atom = 79
443:
226:experimentally known for several elements.
5132:
5118:
4769:The Basics of Nuclear and Particle Physics
4766:Belyaev, Alexander; Ross, Douglas (2021).
4658:(1 ed.). Cambridge University Press.
3962:
1399:Referring to Figure 2, it is obvious that
208:built the first quantum-based atom model.
4831:
4609:
4534:
4252:
4052:
4050:
4029:
4010:
4001:
3680:
347:of chemistry behind the structure of the
4508:
4314:
4308:
4087:
3927:
3815:
3684:
2478:
2309:
1445:{\displaystyle L=2{\sqrt {R^{2}-b^{2}}}}
1388:
1141:
171:fundamental unit quantity of electricity
18:
5051:
5017:
5000:
4972:
4496:
4484:
4472:
4460:
4353:
4291:
4222:
4154:
4075:
3900:
3729:
2582:The lateral component of this force is
1683:This means that the average deflection
204:spectra. That would have to wait until
43:in 1904 following his discovery of the
5267:
5062:
4954:Davis, E. A.; Falconer, I. J. (1997).
4686:
4047:
5113:
4420:Archive for History of Exact Sciences
4234:
4191:
4166:
3933:
3639:the Geiger-Mardsen experiment of 1909
3097:To find the average deflection angle
670:= positive charge of the gold atom =
4870:
4753:"Electric Field, Spherical Geometry"
3875:
3126:{\displaystyle {\bar {\theta }}_{2}}
2462:{\displaystyle {\bar {\theta }}_{2}}
1712:{\displaystyle {\bar {\theta }}_{1}}
1053:, then the average deflection after
67:. Based on experimental studies of
13:
4056:
3327:
2912:
2755:
1641:
409:1906 Estimating electrons per atom
390:Royal Institution of Great Britain
14:
5306:
5139:
3818:"J. J. Thomson and the Bohr atom"
3442:Rutherford scattering experiments
1951:Deflection by the positive sphere
693:= charge of the alpha particle =
322:1904 Mechanical model of the atom
5244:
5235:
5234:
5055:The Corpuscular Theory of Matter
5047:from the original on 2022-10-09.
4292:Thomson, J. J. (10 March 1905),
4015:. New York: Dover Publications.
3816:Heilbron, John L. (1977-04-01).
3431:Demise of the Plum Pudding model
3060:{\displaystyle \tan \theta _{2}}
1046:{\displaystyle {\bar {\theta }}}
746:= speed of the alpha particle =
438:the current measurement is 1,837
419:The Corpuscular Theory of Matter
374:
362:
4947:
4922:
4864:
4811:
4802:
4745:
4644:
4635:
4626:
4586:
4502:
4478:
4466:
4285:
4241:The European Physical Journal H
4228:
4216:
4185:
4160:
4081:
2739:The lateral change in momentum
759:= mass of the alpha particle =
457:Thomson's 1910 scattering model
266:non-integer atomic weightβe.g.
97:
4739:Perspectives of Modern Physics
4509:Crowther, J. A. (1910-09-15).
4088:Falconer, Isobel (July 1987).
3894:
3781:
3723:
3581:
3566:
3518:
3505:
3487:
3157:
3111:
2447:
1971:
1735:
1697:
1094:
1073:
1037:
977:
950:
932:
902: radians or 0.007 degrees
809:
524:
388:In a lecture delivered to the
211:
16:First modern model of the atom
1:
5018:Thomson, J. J. (March 1904).
4940:(8): 329β330. 25 August 1906.
3717:
3436:The Geiger-Marsden experiment
1456:is the distance of the chord
134:
5295:Obsolete theories in physics
5275:Foundational quantum physics
5223:(relativistic quantum model)
4604:(570): 226β247. 1910-09-15.
3668:Mathematical Thomson problem
733:= radius of the gold atom =
328:On the Structure of the Atom
238:, Thomson demonstrated that
230:1897 Corpuscles inside atoms
7:
4354:Thomson, J.J. (June 1906).
3087:{\displaystyle \theta _{2}}
2874:{\displaystyle \theta _{2}}
1538:{\displaystyle {\sqrt {L}}}
1127:Deflection by the electrons
481:{\displaystyle {\sqrt {N}}}
417:In 1907, Thomson published
157:Thomson's discovery of the
10:
5311:
5063:Ernest Rutherford (1911).
5058:. Charles Scribner's Sons.
4897:10.1103/PhysRevE.76.047702
4687:Ernest Rutherford (1911).
4271:10.1140/epjh/e2012-30009-7
4235:Baily, C. (January 2013).
3940:Princeton University Press
3648:
3645:Rutherford's nuclear model
3439:
3141:across the entire sphere:
138:
83:as the basis of the first
5230:
5206:
5163:vortex theory of the atom
5147:
5086:10.1080/14786440508637080
5038:10.1080/14786440409463107
4994:10.1080/14786449708621070
4850:10.1209/epl/i2003-00546-1
4808:Rutherford (1911). p. 677
4786:10.1007/978-3-030-80116-8
4710:10.1080/14786440508637080
4414:John L. Heilbron (1968).
4372:10.1080/14786440609463496
4333:10.1080/00033797600200141
4315:Snelders, H.A.M. (1976).
4304:Davis & Falconer 1997
4295:The Structure of the Atom
4106:10.1017/S0007087400023955
4040:Helge Kragh (Oct. 2010).
4011:Whittaker, E. T. (1989).
3921:10.1017/S0370164600045430
3901:Thomson, William (1869).
3789:Davis & Falconer 1997
3470:deflections is given by:
2292:is the impact parameter.
148:vortex theory of the atom
75:developed an alternative
69:alpha particle scattering
4958:. Taylor & Francis.
4934:The Chemist and Druggist
4664:10.1017/cbo9780511608797
4198:Foundations of Chemistry
3703:The Chemist and Druggist
444:1910 Multiple scattering
141:History of atomic theory
5052:Thomson, J. J. (1907).
5001:Thomson, J. J. (1899).
4973:Thomson, J. J. (1897).
4871:Roth, J. (2007-10-24).
4641:Heilbron (1968). p. 270
4632:Heilbron (1968). p. 278
4210:10.1023/A:1011448410646
3446:Between 1908 and 1913,
2469:over the whole sphere?
1135:along a path of length
5093:J. J. Thomson (1910).
5073:Philosophical Magazine
5025:Philosophical Magazine
5007:Philosophical Magazine
4982:Philosophical Magazine
4697:Philosophical Magazine
4611:10.1098/rspa.1910.0074
4570:J. J. Thomson (1910).
4536:10.1098/rspa.1910.0074
4167:Kumar, Manjit (2008).
4133:Philosophical Magazine
4127:J. J. Thomson (1899).
4063:University of Virginia
3979:10.1098/rsnr.1975.0018
3876:Pais, Abraham (2002).
3775:10.1002/andp.201300732
3712:
3694:
3681:Origin of the nickname
3628:
3533:
3419:
3338:
3127:
3088:
3061:
3018:
2875:
2846:
2731:
2574:
2486:
2463:
2421:
2317:
2257:
2183:
2152:
2050:
1935:
1834:
1713:
1675:
1539:
1515:
1446:
1396:
1367:
1250:
1149:
1111:
1047:
1011:
909:
652:
637: radians or
502:
482:
336:
319:
24:
5158:(billiard ball model)
4192:Kragh, Helge (2001).
3934:Kragh, Helge (2002).
3707:
3688:
3629:
3534:
3420:
3339:
3128:
3089:
3062:
3019:
2876:
2854:The deflection angle
2847:
2732:
2575:
2482:
2464:
2422:
2313:
2258:
2184:
2153:
2051:
1936:
1835:
1714:
1676:
1540:
1516:
1447:
1392:
1368:
1251:
1145:
1112:
1048:
1012:
910:
653:
503:
483:
332:
314:
22:
5215:electron cloud model
5172:(cubical atom model)
4059:"Models of the Atom"
3938:(Reprint ed.).
3555:
3476:
3349:
3147:
3101:
3071:
3038:
2887:
2858:
2752:
2588:
2495:
2437:
2326:
2303:equal to the radius
2197:
2168:
2067:
1961:
1845:
1725:
1687:
1551:
1525:
1464:
1403:
1264:
1181:
1063:
1028:
923:
799:
514:
492:
488:for encounters with
468:
294:photoelectric effect
169:had coined for the "
51:'s discovery of the
5199:(old quantum model)
4889:2007PhRvE..76d7702R
4842:2003EL.....63..415L
4778:2021bnpp.book.....B
4527:1910RSPSA..84..226C
4263:2013EPJH...38....1B
3834:1977PhT....30d..23H
3767:2013AnP...525A.129H
3208:
1590:
993:
966:
5221:DiracβGordon model
5184:plum pudding model
4499:, pp. 23, 26.
4432:10.1007/BF00411591
3942:. pp. 43β45.
3761:(8β9): A129βA133.
3755:Annalen der Physik
3695:
3624:
3529:
3415:
3334:
3194:
3133:, we must average
3123:
3084:
3067:as being equal to
3057:
3014:
2871:
2842:
2727:
2570:
2487:
2459:
2417:
2318:
2253:
2251:
2182:{\displaystyle m'}
2179:
2148:
2046:
1931:
1830:
1709:
1671:
1576:
1535:
1511:
1442:
1397:
1363:
1246:
1238:
1150:
1107:
1043:
1007:
970:
943:
905:
648:
498:
478:
450:J. Arnold Crowther
234:In a paper titled
85:quantum atom model
77:model for the atom
29:plum pudding model
25:
5262:
5261:
5192:(planetary model)
5179:(Saturnian model)
4930:"What is Matter?"
4877:Physical Review E
4795:978-3-030-80115-1
4673:978-0-521-35883-5
4321:Annals of Science
4057:Fowler, Michael.
4022:978-0-486-26126-3
3903:"On Vortex Atoms"
3887:978-0-19-851997-3
3842:10.1063/1.3037496
3691:Christmas pudding
3508:
3448:Ernest Rutherford
3413:
3363:
3309:
3291:
3285:
3249:
3192:
3160:
3114:
3012:
2994:
2981:
2936:
2840:
2827:
2725:
2668:
2641:
2568:
2541:
2476:from the center.
2450:
2415:
2400:
2286:elementary charge
2250:
2146:
2091:
2044:
1994:
1974:
1929:
1928:
1909:
1859:
1828:
1805:
1758:
1738:
1700:
1669:
1659:
1623:
1621:
1574:
1533:
1509:
1507:
1472:
1460:from the center.
1440:
1361:
1328:
1244:
1237:
1105:
1097:
1076:
1040:
1005:
994:
980:
953:
935:
903:
892:
879:
832:
812:
718:elementary charge
646:
638:
627:
626:
607:
594:
547:
527:
501:{\displaystyle N}
476:
279:George FitzGerald
125:Ernest Rutherford
73:Ernest Rutherford
49:Ernest Rutherford
5302:
5248:
5238:
5237:
5190:Rutherford model
5134:
5127:
5120:
5111:
5110:
5106:
5089:
5080:(125): 669β688.
5069:
5059:
5048:
5046:
5028:. Sixth series.
5014:
4997:
4988:(269): 293β316.
4979:
4969:
4942:
4941:
4926:
4920:
4919:
4868:
4862:
4861:
4835:
4833:cond-mat/0302524
4815:
4809:
4806:
4800:
4799:
4763:
4757:
4756:
4749:
4743:
4734:
4723:
4720:
4714:
4713:
4704:(125): 669β688.
4693:
4684:
4678:
4677:
4648:
4642:
4639:
4633:
4630:
4624:
4623:
4613:
4590:
4584:
4583:
4567:
4558:
4555:
4549:
4548:
4538:
4521:(570): 226β247.
4506:
4500:
4494:
4488:
4482:
4476:
4470:
4464:
4458:
4452:
4451:
4411:
4384:
4383:
4351:
4345:
4344:
4312:
4306:
4301:
4300:
4289:
4283:
4282:
4256:
4232:
4226:
4220:
4214:
4213:
4189:
4183:
4182:
4171:. W. W. Norton.
4164:
4158:
4152:
4143:
4140:
4124:
4118:
4117:
4085:
4079:
4073:
4067:
4066:
4054:
4045:
4038:
4027:
4026:
4008:
3999:
3998:
3960:
3954:
3953:
3931:
3925:
3924:
3898:
3892:
3891:
3873:
3854:
3853:
3813:
3807:
3804:
3795:
3785:
3779:
3778:
3746:
3733:
3727:
3705:in August 1906.
3651:Rutherford model
3633:
3631:
3630:
3625:
3623:
3622:
3607:
3606:
3591:
3590:
3589:
3588:
3576:
3538:
3536:
3535:
3530:
3528:
3527:
3526:
3525:
3516:
3515:
3510:
3509:
3501:
3497:
3424:
3422:
3421:
3416:
3414:
3412:
3408:
3407:
3394:
3393:
3392:
3383:
3382:
3369:
3364:
3356:
3343:
3341:
3340:
3335:
3330:
3310:
3308:
3297:
3292:
3287:
3286:
3284:
3283:
3271:
3270:
3261:
3255:
3250:
3248:
3247:
3238:
3237:
3236:
3227:
3226:
3210:
3207:
3202:
3193:
3191:
3190:
3189:
3173:
3168:
3167:
3162:
3161:
3153:
3132:
3130:
3129:
3124:
3122:
3121:
3116:
3115:
3107:
3093:
3091:
3090:
3085:
3083:
3082:
3066:
3064:
3063:
3058:
3056:
3055:
3023:
3021:
3020:
3015:
3013:
3011:
3000:
2995:
2987:
2982:
2980:
2979:
2970:
2969:
2968:
2959:
2958:
2942:
2937:
2935:
2934:
2925:
2924:
2923:
2910:
2905:
2904:
2880:
2878:
2877:
2872:
2870:
2869:
2851:
2849:
2848:
2843:
2841:
2833:
2828:
2826:
2825:
2816:
2815:
2814:
2805:
2804:
2788:
2780:
2779:
2767:
2766:
2736:
2734:
2733:
2728:
2726:
2724:
2723:
2714:
2713:
2712:
2703:
2702:
2686:
2669:
2667:
2666:
2657:
2656:
2647:
2642:
2640:
2639:
2630:
2629:
2628:
2619:
2618:
2605:
2600:
2599:
2579:
2577:
2576:
2571:
2569:
2567:
2566:
2557:
2556:
2547:
2542:
2540:
2539:
2530:
2529:
2528:
2519:
2518:
2505:
2468:
2466:
2465:
2460:
2458:
2457:
2452:
2451:
2443:
2426:
2424:
2423:
2418:
2416:
2413:
2405:
2401:
2399:
2395:
2394:
2381:
2380:
2379:
2370:
2369:
2356:
2338:
2337:
2262:
2260:
2259:
2254:
2252:
2249:
2248:
2247:
2235:
2234:
2224:
2223:
2222:
2213:
2212:
2202:
2188:
2186:
2185:
2180:
2178:
2157:
2155:
2154:
2149:
2147:
2145:
2141:
2140:
2131:
2122:
2121:
2120:
2111:
2110:
2097:
2092:
2087:
2086:
2077:
2055:
2053:
2052:
2047:
2045:
2043:
2039:
2038:
2025:
2024:
2023:
2014:
2013:
2000:
1995:
1987:
1982:
1981:
1976:
1975:
1967:
1940:
1938:
1937:
1932:
1930:
1924:
1916:
1915:
1910:
1908:
1904:
1903:
1890:
1889:
1888:
1879:
1878:
1865:
1860:
1852:
1839:
1837:
1836:
1831:
1829:
1821:
1820:
1811:
1806:
1804:
1803:
1802:
1789:
1788:
1787:
1778:
1777:
1764:
1759:
1751:
1746:
1745:
1740:
1739:
1731:
1718:
1716:
1715:
1710:
1708:
1707:
1702:
1701:
1693:
1680:
1678:
1677:
1672:
1670:
1662:
1660:
1652:
1644:
1624:
1622:
1620:
1619:
1607:
1606:
1597:
1592:
1589:
1584:
1575:
1573:
1572:
1571:
1555:
1544:
1542:
1541:
1536:
1534:
1529:
1520:
1518:
1517:
1512:
1510:
1508:
1506:
1505:
1493:
1492:
1483:
1478:
1473:
1468:
1451:
1449:
1448:
1443:
1441:
1439:
1438:
1426:
1425:
1416:
1372:
1370:
1369:
1364:
1362:
1357:
1356:
1344:
1343:
1334:
1329:
1327:
1323:
1322:
1309:
1308:
1307:
1298:
1297:
1281:
1276:
1275:
1255:
1253:
1252:
1247:
1245:
1243:
1239:
1230:
1227:
1226:
1213:
1212:
1211:
1202:
1201:
1185:
1171:
1169:
1168:
1165:
1162:
1116:
1114:
1113:
1108:
1106:
1101:
1099:
1098:
1090:
1084:
1083:
1078:
1077:
1069:
1052:
1050:
1049:
1044:
1042:
1041:
1033:
1016:
1014:
1013:
1008:
1006:
1003:
995:
992:
987:
982:
981:
973:
965:
960:
955:
954:
946:
942:
937:
936:
928:
914:
912:
911:
906:
904:
901:
893:
885:
880:
878:
877:
876:
863:
862:
861:
852:
851:
838:
833:
825:
820:
819:
814:
813:
805:
783:
781:
774:Coulomb constant
766:
764:
753:
751:
740:
738:
727:
725:
707:
705:
699:
684:
682:
676:
657:
655:
654:
649:
647:
644:
639:
636:
628:
622:
614:
613:
608:
600:
595:
593:
592:
591:
578:
577:
576:
567:
566:
553:
548:
540:
535:
534:
529:
528:
520:
507:
505:
504:
499:
487:
485:
484:
479:
477:
472:
378:
366:
311:
309:
308:
305:
302:
252:primordial atoms
129:new atomic model
61:emission spectra
33:scientific model
5310:
5309:
5305:
5304:
5303:
5301:
5300:
5299:
5265:
5264:
5263:
5258:
5226:
5202:
5148:Historic models
5143:
5138:
5067:
5044:
5032:(39): 237β265.
5013:(295): 547β567.
4977:
4966:
4950:
4945:
4928:
4927:
4923:
4869:
4865:
4816:
4812:
4807:
4803:
4796:
4764:
4760:
4751:
4750:
4746:
4736:Beiser (1969).
4735:
4726:
4721:
4717:
4691:
4685:
4681:
4674:
4649:
4645:
4640:
4636:
4631:
4627:
4592:
4591:
4587:
4568:
4561:
4556:
4552:
4507:
4503:
4495:
4491:
4483:
4479:
4471:
4467:
4459:
4455:
4412:
4387:
4366:(66): 769β781.
4352:
4348:
4313:
4309:
4302:. Reprinted in
4298:
4290:
4286:
4233:
4229:
4221:
4217:
4190:
4186:
4179:
4165:
4161:
4153:
4146:
4141:
4139:(295): 547β567.
4125:
4121:
4086:
4082:
4074:
4070:
4055:
4048:
4039:
4030:
4023:
4009:
4002:
3961:
3957:
3950:
3932:
3928:
3899:
3895:
3888:
3874:
3857:
3814:
3810:
3805:
3798:
3794:
3792:
3786:
3782:
3747:
3736:
3728:
3724:
3720:
3683:
3674:Thomson problem
3670:
3657:
3649:Main articles:
3647:
3615:
3611:
3599:
3595:
3584:
3580:
3572:
3562:
3558:
3556:
3553:
3552:
3521:
3517:
3511:
3500:
3499:
3498:
3493:
3483:
3479:
3477:
3474:
3473:
3444:
3438:
3433:
3403:
3399:
3395:
3388:
3384:
3378:
3374:
3370:
3368:
3355:
3350:
3347:
3346:
3326:
3301:
3296:
3279:
3275:
3266:
3262:
3260:
3256:
3254:
3243:
3239:
3232:
3228:
3222:
3218:
3211:
3209:
3203:
3198:
3185:
3181:
3177:
3172:
3163:
3152:
3151:
3150:
3148:
3145:
3144:
3117:
3106:
3105:
3104:
3102:
3099:
3098:
3078:
3074:
3072:
3069:
3068:
3051:
3047:
3039:
3036:
3035:
3032:
3004:
2999:
2986:
2975:
2971:
2964:
2960:
2954:
2950:
2943:
2941:
2930:
2926:
2919:
2915:
2911:
2909:
2900:
2896:
2888:
2885:
2884:
2865:
2861:
2859:
2856:
2855:
2832:
2821:
2817:
2810:
2806:
2800:
2796:
2789:
2787:
2775:
2771:
2762:
2758:
2753:
2750:
2749:
2745:
2719:
2715:
2708:
2704:
2698:
2694:
2687:
2685:
2662:
2658:
2652:
2648:
2646:
2635:
2631:
2624:
2620:
2614:
2610:
2606:
2604:
2595:
2591:
2589:
2586:
2585:
2562:
2558:
2552:
2548:
2546:
2535:
2531:
2524:
2520:
2514:
2510:
2506:
2504:
2496:
2493:
2492:
2453:
2442:
2441:
2440:
2438:
2435:
2434:
2412:
2390:
2386:
2382:
2375:
2371:
2365:
2361:
2357:
2355:
2351:
2333:
2329:
2327:
2324:
2323:
2307:as shown here:
2283:
2276:
2269:
2243:
2239:
2230:
2226:
2225:
2218:
2214:
2208:
2204:
2203:
2200:
2198:
2195:
2194:
2171:
2169:
2166:
2165:
2136:
2132:
2124:
2123:
2116:
2112:
2106:
2102:
2098:
2096:
2082:
2078:
2076:
2068:
2065:
2064:
2034:
2030:
2026:
2019:
2015:
2009:
2005:
2001:
1999:
1986:
1977:
1966:
1965:
1964:
1962:
1959:
1958:
1953:
1917:
1914:
1899:
1895:
1891:
1884:
1880:
1874:
1870:
1866:
1864:
1851:
1846:
1843:
1842:
1816:
1812:
1810:
1798:
1794:
1790:
1783:
1779:
1773:
1769:
1765:
1763:
1750:
1741:
1730:
1729:
1728:
1726:
1723:
1722:
1703:
1692:
1691:
1690:
1688:
1685:
1684:
1661:
1651:
1640:
1615:
1611:
1602:
1598:
1596:
1591:
1585:
1580:
1567:
1563:
1559:
1554:
1552:
1549:
1548:
1528:
1526:
1523:
1522:
1501:
1497:
1488:
1484:
1482:
1477:
1467:
1465:
1462:
1461:
1434:
1430:
1421:
1417:
1415:
1404:
1401:
1400:
1381:
1352:
1348:
1339:
1335:
1333:
1318:
1314:
1310:
1303:
1299:
1293:
1289:
1282:
1280:
1271:
1267:
1265:
1262:
1261:
1228:
1222:
1218:
1214:
1207:
1203:
1197:
1193:
1186:
1184:
1182:
1179:
1178:
1166:
1163:
1160:
1159:
1157:
1129:
1100:
1089:
1088:
1079:
1068:
1067:
1066:
1064:
1061:
1060:
1032:
1031:
1029:
1026:
1025:
1002:
988:
983:
972:
971:
961:
956:
945:
944:
941:
927:
926:
924:
921:
920:
900:
884:
872:
868:
864:
857:
853:
847:
843:
839:
837:
824:
815:
804:
803:
802:
800:
797:
796:
779:
777:
762:
760:
749:
747:
736:
734:
723:
721:
714:
703:
701:
694:
691:
680:
678:
671:
668:
643:
635:
615:
612:
599:
587:
583:
579:
572:
568:
562:
558:
554:
552:
539:
530:
519:
518:
517:
515:
512:
511:
493:
490:
489:
471:
469:
466:
465:
459:
446:
411:
394:Alfred M. Mayer
386:
385:
384:
383:
382:
379:
371:
370:
367:
324:
306:
303:
300:
299:
297:
287:Hendrik Lorentz
250:, calling them
232:
214:
194:alpha particles
186:Henri Becquerel
152:William Thomson
143:
137:
100:
17:
12:
11:
5:
5308:
5298:
5297:
5292:
5290:Periodic table
5287:
5282:
5277:
5260:
5259:
5257:
5256:
5250:Portal:Physics
5242:
5240:Category:Atoms
5231:
5228:
5227:
5225:
5224:
5217:
5210:
5208:
5207:Current models
5204:
5203:
5201:
5200:
5193:
5186:
5180:
5173:
5166:
5159:
5151:
5149:
5145:
5144:
5137:
5136:
5129:
5122:
5114:
5108:
5107:
5090:
5060:
5049:
5015:
4998:
4975:"Cathode rays"
4970:
4964:
4949:
4946:
4944:
4943:
4921:
4863:
4826:(3): 415β418.
4820:Europhys. Lett
4810:
4801:
4794:
4758:
4744:
4724:
4715:
4679:
4672:
4643:
4634:
4625:
4585:
4559:
4550:
4501:
4489:
4477:
4465:
4453:
4426:(4): 247β307.
4385:
4346:
4307:
4284:
4227:
4215:
4204:(2): 129β143.
4184:
4178:978-0393339888
4177:
4159:
4144:
4119:
4100:(3): 241β276.
4080:
4068:
4046:
4028:
4021:
4000:
3973:(2): 265β276.
3955:
3949:978-0691095523
3948:
3926:
3893:
3886:
3855:
3808:
3796:
3791:, p. 153:
3780:
3734:
3721:
3719:
3716:
3682:
3679:
3669:
3666:
3646:
3643:
3621:
3618:
3614:
3610:
3605:
3602:
3598:
3594:
3587:
3583:
3579:
3575:
3571:
3568:
3565:
3561:
3547:Euler's number
3524:
3520:
3514:
3507:
3504:
3496:
3492:
3489:
3486:
3482:
3456:Ernest Marsden
3440:Main article:
3437:
3434:
3432:
3429:
3411:
3406:
3402:
3398:
3391:
3387:
3381:
3377:
3373:
3367:
3362:
3359:
3354:
3333:
3329:
3325:
3322:
3319:
3316:
3313:
3307:
3304:
3300:
3295:
3290:
3282:
3278:
3274:
3269:
3265:
3259:
3253:
3246:
3242:
3235:
3231:
3225:
3221:
3217:
3214:
3206:
3201:
3197:
3188:
3184:
3180:
3176:
3171:
3166:
3159:
3156:
3120:
3113:
3110:
3081:
3077:
3054:
3050:
3046:
3043:
3030:
3010:
3007:
3003:
2998:
2993:
2990:
2985:
2978:
2974:
2967:
2963:
2957:
2953:
2949:
2946:
2940:
2933:
2929:
2922:
2918:
2914:
2908:
2903:
2899:
2895:
2892:
2868:
2864:
2839:
2836:
2831:
2824:
2820:
2813:
2809:
2803:
2799:
2795:
2792:
2786:
2783:
2778:
2774:
2770:
2765:
2761:
2757:
2743:
2722:
2718:
2711:
2707:
2701:
2697:
2693:
2690:
2684:
2681:
2678:
2675:
2672:
2665:
2661:
2655:
2651:
2645:
2638:
2634:
2627:
2623:
2617:
2613:
2609:
2603:
2598:
2594:
2565:
2561:
2555:
2551:
2545:
2538:
2534:
2527:
2523:
2517:
2513:
2509:
2503:
2500:
2456:
2449:
2446:
2411:
2408:
2404:
2398:
2393:
2389:
2385:
2378:
2374:
2368:
2364:
2360:
2354:
2350:
2347:
2344:
2341:
2336:
2332:
2281:
2274:
2267:
2246:
2242:
2238:
2233:
2229:
2221:
2217:
2211:
2207:
2177:
2174:
2164:). The factor
2144:
2139:
2135:
2130:
2127:
2119:
2115:
2109:
2105:
2101:
2095:
2090:
2085:
2081:
2075:
2072:
2042:
2037:
2033:
2029:
2022:
2018:
2012:
2008:
2004:
1998:
1993:
1990:
1985:
1980:
1973:
1970:
1952:
1949:
1927:
1923:
1920:
1913:
1907:
1902:
1898:
1894:
1887:
1883:
1877:
1873:
1869:
1863:
1858:
1855:
1850:
1827:
1824:
1819:
1815:
1809:
1801:
1797:
1793:
1786:
1782:
1776:
1772:
1768:
1762:
1757:
1754:
1749:
1744:
1737:
1734:
1706:
1699:
1696:
1668:
1665:
1658:
1655:
1650:
1647:
1643:
1639:
1636:
1633:
1630:
1627:
1618:
1614:
1610:
1605:
1601:
1595:
1588:
1583:
1579:
1570:
1566:
1562:
1558:
1532:
1521:. The mean of
1504:
1500:
1496:
1491:
1487:
1481:
1476:
1471:
1437:
1433:
1429:
1424:
1420:
1414:
1411:
1408:
1379:
1360:
1355:
1351:
1347:
1342:
1338:
1332:
1326:
1321:
1317:
1313:
1306:
1302:
1296:
1292:
1288:
1285:
1279:
1274:
1270:
1242:
1236:
1233:
1225:
1221:
1217:
1210:
1206:
1200:
1196:
1192:
1189:
1128:
1125:
1104:
1096:
1093:
1087:
1082:
1075:
1072:
1057:collisions is
1039:
1036:
1001:
998:
991:
986:
979:
976:
969:
964:
959:
952:
949:
940:
934:
931:
899:
896:
891:
888:
883:
875:
871:
867:
860:
856:
850:
846:
842:
836:
831:
828:
823:
818:
811:
808:
791:
790:
784:
767:
754:
741:
728:
712:
708:
689:
685:
666:
642:
634:
631:
625:
621:
618:
611:
606:
603:
598:
590:
586:
582:
575:
571:
565:
561:
557:
551:
546:
543:
538:
533:
526:
523:
497:
475:
458:
455:
445:
442:
410:
407:
380:
373:
372:
368:
361:
360:
359:
358:
357:
349:periodic table
323:
320:
231:
228:
224:spectral lines
213:
210:
201:atomic spectra
190:beta particles
184:, and in 1900
150:, proposed by
139:Main article:
136:
133:
116:periodic table
112:atomic physics
99:
96:
53:atomic nucleus
31:was the first
15:
9:
6:
4:
3:
2:
5307:
5296:
5293:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5272:
5270:
5255:
5251:
5247:
5243:
5241:
5233:
5232:
5229:
5222:
5218:
5216:
5212:
5211:
5209:
5205:
5198:
5194:
5191:
5187:
5185:
5181:
5178:
5177:Nagaoka model
5174:
5171:
5167:
5164:
5160:
5157:
5153:
5152:
5150:
5146:
5142:
5141:Atomic models
5135:
5130:
5128:
5123:
5121:
5116:
5115:
5112:
5104:
5100:
5096:
5091:
5087:
5083:
5079:
5075:
5074:
5066:
5061:
5057:
5056:
5050:
5043:
5039:
5035:
5031:
5027:
5026:
5021:
5016:
5012:
5008:
5004:
4999:
4995:
4991:
4987:
4983:
4976:
4971:
4967:
4965:0-203-79233-5
4961:
4957:
4952:
4951:
4939:
4935:
4931:
4925:
4918:
4914:
4910:
4906:
4902:
4898:
4894:
4890:
4886:
4883:(4): 047702.
4882:
4878:
4874:
4867:
4859:
4855:
4851:
4847:
4843:
4839:
4834:
4829:
4825:
4821:
4814:
4805:
4797:
4791:
4787:
4783:
4779:
4775:
4771:
4770:
4762:
4754:
4748:
4741:
4740:
4733:
4731:
4729:
4719:
4711:
4707:
4703:
4699:
4698:
4690:
4683:
4675:
4669:
4665:
4661:
4657:
4656:
4647:
4638:
4629:
4621:
4617:
4612:
4607:
4603:
4599:
4595:
4589:
4581:
4577:
4573:
4566:
4564:
4554:
4546:
4542:
4537:
4532:
4528:
4524:
4520:
4516:
4512:
4505:
4498:
4493:
4486:
4481:
4474:
4469:
4462:
4457:
4449:
4445:
4441:
4437:
4433:
4429:
4425:
4421:
4417:
4410:
4408:
4406:
4404:
4402:
4400:
4398:
4396:
4394:
4392:
4390:
4381:
4377:
4373:
4369:
4365:
4361:
4357:
4350:
4342:
4338:
4334:
4330:
4326:
4322:
4318:
4311:
4305:
4297:
4296:
4288:
4280:
4276:
4272:
4268:
4264:
4260:
4255:
4250:
4246:
4242:
4238:
4231:
4224:
4219:
4211:
4207:
4203:
4199:
4195:
4188:
4180:
4174:
4170:
4163:
4156:
4151:
4149:
4138:
4134:
4130:
4123:
4115:
4111:
4107:
4103:
4099:
4095:
4091:
4084:
4077:
4072:
4064:
4060:
4053:
4051:
4043:
4037:
4035:
4033:
4024:
4018:
4014:
4007:
4005:
3996:
3992:
3988:
3984:
3980:
3976:
3972:
3968:
3967:
3959:
3951:
3945:
3941:
3937:
3930:
3922:
3918:
3914:
3910:
3909:
3904:
3897:
3889:
3883:
3879:
3872:
3870:
3868:
3866:
3864:
3862:
3860:
3851:
3847:
3843:
3839:
3835:
3831:
3827:
3823:
3822:Physics Today
3819:
3812:
3803:
3801:
3790:
3784:
3776:
3772:
3768:
3764:
3760:
3756:
3752:
3745:
3743:
3741:
3739:
3731:
3726:
3722:
3715:
3711:
3706:
3704:
3700:
3692:
3687:
3678:
3675:
3665:
3663:
3656:
3652:
3642:
3640:
3634:
3619:
3616:
3612:
3608:
3603:
3600:
3596:
3592:
3585:
3577:
3573:
3569:
3563:
3559:
3550:
3548:
3544:
3539:
3522:
3512:
3502:
3494:
3490:
3484:
3480:
3471:
3469:
3463:
3461:
3457:
3453:
3449:
3443:
3428:
3425:
3409:
3404:
3400:
3396:
3389:
3385:
3379:
3375:
3371:
3365:
3360:
3357:
3352:
3344:
3331:
3323:
3320:
3317:
3314:
3311:
3305:
3302:
3298:
3293:
3288:
3280:
3276:
3272:
3267:
3263:
3257:
3251:
3244:
3240:
3233:
3229:
3223:
3219:
3215:
3212:
3204:
3199:
3195:
3186:
3182:
3178:
3174:
3169:
3164:
3154:
3142:
3140:
3136:
3118:
3108:
3095:
3079:
3075:
3052:
3048:
3044:
3041:
3029:
3024:
3008:
3005:
3001:
2996:
2991:
2988:
2983:
2976:
2972:
2965:
2961:
2955:
2951:
2947:
2944:
2938:
2931:
2927:
2920:
2916:
2906:
2901:
2897:
2893:
2890:
2882:
2866:
2862:
2852:
2837:
2834:
2829:
2822:
2818:
2811:
2807:
2801:
2797:
2793:
2790:
2784:
2781:
2776:
2772:
2768:
2763:
2759:
2747:
2746:is therefore
2742:
2737:
2720:
2716:
2709:
2705:
2699:
2695:
2691:
2688:
2682:
2679:
2676:
2673:
2670:
2663:
2659:
2653:
2649:
2643:
2636:
2632:
2625:
2621:
2615:
2611:
2607:
2601:
2596:
2592:
2583:
2580:
2563:
2559:
2553:
2549:
2543:
2536:
2532:
2525:
2521:
2515:
2511:
2507:
2501:
2498:
2490:
2485:
2481:
2477:
2475:
2470:
2454:
2444:
2431:
2427:
2414: degrees
2409:
2406:
2402:
2396:
2391:
2387:
2383:
2376:
2372:
2366:
2362:
2358:
2352:
2348:
2345:
2342:
2339:
2334:
2330:
2321:
2316:
2312:
2308:
2306:
2302:
2298:
2293:
2291:
2287:
2280:
2273:
2266:
2244:
2240:
2236:
2231:
2227:
2219:
2215:
2209:
2205:
2192:
2175:
2172:
2163:
2158:
2142:
2137:
2133:
2128:
2125:
2117:
2113:
2107:
2103:
2099:
2093:
2088:
2083:
2079:
2073:
2070:
2062:
2059:
2056:
2040:
2035:
2031:
2027:
2020:
2016:
2010:
2006:
2002:
1996:
1991:
1988:
1983:
1978:
1968:
1956:
1948:
1946:
1941:
1925:
1921:
1918:
1911:
1905:
1900:
1896:
1892:
1885:
1881:
1875:
1871:
1867:
1861:
1856:
1853:
1848:
1840:
1825:
1822:
1817:
1813:
1807:
1799:
1795:
1791:
1784:
1780:
1774:
1770:
1766:
1760:
1755:
1752:
1747:
1742:
1732:
1720:
1704:
1694:
1681:
1666:
1663:
1656:
1653:
1648:
1645:
1637:
1634:
1631:
1628:
1625:
1616:
1612:
1608:
1603:
1599:
1593:
1586:
1581:
1577:
1568:
1564:
1560:
1556:
1546:
1545:is therefore
1530:
1502:
1498:
1494:
1489:
1485:
1479:
1474:
1469:
1459:
1455:
1435:
1431:
1427:
1422:
1418:
1412:
1409:
1406:
1395:
1391:
1387:
1385:
1378:
1373:
1358:
1353:
1349:
1345:
1340:
1336:
1330:
1324:
1319:
1315:
1311:
1304:
1300:
1294:
1290:
1286:
1283:
1277:
1272:
1268:
1259:
1256:
1240:
1234:
1231:
1223:
1219:
1215:
1208:
1204:
1198:
1194:
1190:
1187:
1176:
1174:
1155:
1148:
1144:
1140:
1138:
1134:
1124:
1120:
1117:
1102:
1091:
1085:
1080:
1070:
1058:
1056:
1034:
1023:
1017:
1004: degrees
999:
996:
989:
984:
974:
967:
962:
957:
947:
938:
929:
918:
915:
897:
894:
889:
886:
881:
873:
869:
865:
858:
854:
848:
844:
840:
834:
829:
826:
821:
816:
806:
794:
788:
785:
782:10 NΒ·m/C
775:
771:
768:
758:
755:
745:
742:
732:
729:
719:
715:
709:
698:
692:
686:
675:
669:
663:
662:
661:
658:
645: degrees
640:
632:
629:
623:
619:
616:
609:
604:
601:
596:
588:
584:
580:
573:
569:
563:
559:
555:
549:
544:
541:
536:
531:
521:
509:
495:
473:
462:
454:
451:
441:
439:
434:
432:
431:August Becker
426:
422:
420:
415:
406:
402:
398:
395:
391:
377:
365:
356:
352:
350:
346:
340:
335:
331:
329:
318:
313:
295:
290:
288:
284:
283:Joseph Larmor
280:
275:
273:
269:
264:
263:William Prout
259:
257:
253:
249:
245:
241:
237:
227:
225:
220:
209:
207:
202:
197:
195:
191:
187:
183:
179:
178:radioactivity
174:
172:
168:
164:
160:
155:
153:
149:
142:
132:
130:
126:
122:
117:
113:
109:
105:
104:atomic models
95:
93:
88:
86:
82:
78:
74:
70:
66:
62:
57:
54:
50:
46:
42:
41:J. J. Thomson
38:
34:
30:
21:
5183:
5165:(knot model)
5156:Dalton model
5102:
5098:
5077:
5076:. Series 6.
5071:
5054:
5029:
5023:
5010:
5006:
4985:
4981:
4955:
4948:Bibliography
4937:
4933:
4924:
4916:
4880:
4876:
4866:
4823:
4819:
4813:
4804:
4768:
4761:
4747:
4738:
4718:
4701:
4700:. Series 6.
4695:
4682:
4654:
4646:
4637:
4628:
4601:
4597:
4588:
4579:
4575:
4553:
4518:
4514:
4504:
4497:Thomson 1907
4492:
4485:Thomson 1907
4480:
4475:, p. 27
4473:Thomson 1907
4468:
4461:Thomson 1907
4456:
4423:
4419:
4363:
4359:
4349:
4327:(1): 67β80.
4324:
4320:
4310:
4294:
4287:
4244:
4240:
4230:
4223:Thomson 1904
4218:
4201:
4197:
4187:
4168:
4162:
4155:Thomson 1904
4136:
4132:
4122:
4097:
4093:
4083:
4076:Thomson 1897
4071:
4062:
4012:
3970:
3964:
3958:
3935:
3929:
3912:
3906:
3896:
3877:
3828:(4): 23β30.
3825:
3821:
3811:
3783:
3758:
3754:
3730:Thomson 1907
3725:
3713:
3708:
3702:
3699:plum pudding
3696:
3671:
3658:
3635:
3551:
3542:
3540:
3472:
3467:
3464:
3445:
3426:
3345:
3143:
3138:
3134:
3096:
3027:
3025:
2883:
2881:is given by
2853:
2748:
2740:
2738:
2584:
2581:
2491:
2488:
2483:
2473:
2471:
2429:
2428:
2322:
2319:
2314:
2304:
2300:
2296:
2294:
2289:
2278:
2271:
2264:
2191:reduced mass
2159:
2063:
2060:
2057:
1957:
1954:
1944:
1942:
1841:
1721:
1682:
1547:
1457:
1453:
1398:
1393:
1383:
1376:
1374:
1260:
1257:
1177:
1172:
1153:
1151:
1146:
1136:
1132:
1130:
1121:
1118:
1059:
1054:
1018:
919:
916:
795:
792:
786:
769:
756:
743:
730:
710:
696:
687:
673:
664:
659:
510:
463:
460:
447:
435:
427:
423:
418:
416:
412:
403:
399:
387:
353:
345:periodic law
341:
337:
333:
327:
325:
315:
291:
276:
260:
255:
251:
247:
243:
240:cathode rays
236:Cathode Rays
235:
233:
219:polyelectron
218:
215:
198:
182:cathode rays
175:
167:G. J. Stoney
156:
144:
101:
98:Significance
92:plum pudding
89:
58:
28:
26:
5170:Lewis model
4247:(1): 1β38.
3637:results of
3452:Hans Geiger
1022:random walk
752:10 m/s
508:electrons:
212:Development
108:John Dalton
5269:Categories
5197:Bohr model
5105:: 465β471.
4582:: 465β471.
3915:: 94β105.
3718:References
3662:Niels Bohr
3655:Bohr model
765:10 kg
256:corpuscles
248:corpuscles
244:corpuscles
206:Niels Bohr
135:Background
81:Niels Bohr
5254:Chemistry
4905:1539-3755
4858:250764497
4620:0950-1207
4545:0950-1207
4440:0003-9519
4380:1941-5982
4341:0003-3790
4279:2102-6459
4254:1208.5262
4114:0007-0874
3995:145353314
3850:0031-9228
3617:−
3609:≈
3601:−
3593:≈
3564:−
3506:¯
3503:θ
3485:−
3366:⋅
3358:π
3324:⋅
3318:π
3312:⋅
3294:⋅
3273:−
3252:⋅
3196:∫
3179:π
3158:¯
3155:θ
3112:¯
3109:θ
3076:θ
3049:θ
3045:
2997:⋅
2984:⋅
2913:Δ
2898:θ
2894:
2863:θ
2830:⋅
2756:Δ
2680:φ
2677:
2671:⋅
2644:⋅
2544:⋅
2448:¯
2445:θ
2407:≈
2349:
2331:θ
2193:equal to
2080:θ
2074:
1997:⋅
1989:π
1972:¯
1969:θ
1912:⋅
1862:⋅
1823:π
1808:⋅
1761:⋅
1736:¯
1733:θ
1698:¯
1695:θ
1638:⋅
1632:π
1626:⋅
1609:−
1578:∫
1561:π
1495:−
1428:−
1346:π
1331:⋅
1269:θ
1095:¯
1092:θ
1074:¯
1071:θ
1038:¯
1035:θ
997:≈
978:¯
975:θ
951:¯
948:θ
933:¯
930:θ
895:≈
882:⋅
835:⋅
827:π
810:¯
807:θ
739:10 m
726:10 C
706:10 C
683:10 C
630:≈
610:⋅
597:⋅
550:⋅
525:¯
522:θ
163:particles
121:electrons
65:valencies
5285:Electron
5042:Archived
4913:17995142
4742:, p. 109
4448:41133273
2484:Figure 4
2315:Figure 3
2176:′
2129:′
1394:Figure 2
1147:Figure 1
672:79
272:isotopes
268:chlorine
159:electron
45:electron
4885:Bibcode
4838:Bibcode
4774:Bibcode
4523:Bibcode
4259:Bibcode
3830:Bibcode
3763:Bibcode
2284:is the
1170:
1158:
898:0.00013
695:2
633:0.00007
310:
298:
35:of the
4962:
4911:
4903:
4856:
4792:
4670:
4618:
4543:
4446:
4438:
4378:
4339:
4277:
4175:
4112:
4019:
3993:
3987:531468
3985:
3946:
3884:
3848:
3541:where
3454:, and
3026:where
2346:arctan
2263:where
2189:, the
1943:where
1452:where
1375:where
660:where
5280:Atoms
5219:1928
5213:1926
5195:1913
5188:1911
5182:1904
5175:1904
5168:1902
5161:1867
5154:1804
5068:(PDF)
5045:(PDF)
5009:. 5.
4978:(PDF)
4854:S2CID
4828:arXiv
4692:(PDF)
4444:JSTOR
4299:(PDF)
4249:arXiv
4135:. 5.
3991:S2CID
3983:JSTOR
3604:12656
1000:0.008
778:8.987
722:1.602
641:0.004
4960:ISBN
4909:PMID
4901:ISSN
4790:ISBN
4668:ISBN
4616:ISSN
4541:ISSN
4436:ISSN
4376:ISSN
4337:ISSN
4275:ISSN
4173:ISBN
4110:ISSN
4017:ISBN
3944:ISBN
3882:ISBN
3846:ISSN
3672:The
3653:and
3620:5946
3460:Gold
3137:and
2410:0.02
2288:and
2270:and
761:6.64
748:1.53
735:1.44
702:3.20
679:1.26
285:and
63:and
37:atom
27:The
5082:doi
5034:doi
4990:doi
4893:doi
4846:doi
4782:doi
4706:doi
4660:doi
4606:doi
4531:doi
4428:doi
4368:doi
4329:doi
4267:doi
4206:doi
4102:doi
3975:doi
3917:doi
3838:doi
3771:doi
3759:525
3578:0.8
3545:is
3042:tan
2891:tan
2674:cos
2071:tan
1719:is
307:714
5271::
5252:/
5103:15
5101:.
5097:.
5078:21
5070:.
5040:.
5022:.
5011:48
5005:.
4986:44
4984:.
4980:.
4938:69
4936:.
4932:.
4915:.
4907:.
4899:.
4891:.
4881:76
4879:.
4875:.
4852:.
4844:.
4836:.
4824:63
4822:.
4788:.
4780:.
4727:^
4702:21
4694:.
4666:.
4614:.
4602:84
4600:.
4596:.
4580:15
4578:.
4574:.
4562:^
4539:.
4529:.
4519:84
4517:.
4513:.
4442:.
4434:.
4422:.
4418:.
4388:^
4374:.
4364:11
4362:.
4358:.
4335:.
4325:33
4323:.
4319:.
4273:.
4265:.
4257:.
4245:38
4243:.
4239:.
4200:.
4196:.
4147:^
4137:48
4131:.
4108:.
4098:20
4096:.
4092:.
4061:.
4049:^
4031:^
4003:^
3989:.
3981:.
3971:29
3969:.
3911:.
3905:.
3858:^
3844:.
3836:.
3826:30
3824:.
3820:.
3799:^
3769:.
3757:.
3753:.
3737:^
3689:A
3664:.
3613:10
3570:90
3491:90
3450:,
3094:.
1854:16
1753:32
776:=
772:=
720:=
716:=
700:=
677:=
542:16
131:.
87:.
71:,
5133:e
5126:t
5119:v
5088:.
5084::
5036::
5030:7
4996:.
4992::
4968:.
4895::
4887::
4860:.
4848::
4840::
4830::
4798:.
4784::
4776::
4755:.
4712:.
4708::
4676:.
4662::
4622:.
4608::
4547:.
4533::
4525::
4463:.
4450:.
4430::
4424:4
4382:.
4370::
4343:.
4331::
4281:.
4269::
4261::
4251::
4212:.
4208::
4202:3
4181:.
4157:.
4116:.
4104::
4078:.
4065:.
4025:.
3997:.
3977::
3952:.
3923:.
3919::
3913:6
3890:.
3852:.
3840::
3832::
3777:.
3773::
3765::
3597:e
3586:2
3582:)
3574:/
3567:(
3560:e
3543:e
3523:2
3519:)
3513:n
3495:/
3488:(
3481:e
3468:n
3410:R
3405:2
3401:v
3397:m
3390:g
3386:q
3380:a
3376:q
3372:k
3361:4
3353:=
3332:b
3328:d
3321:b
3315:2
3306:v
3303:m
3299:1
3289:v
3281:2
3277:b
3268:2
3264:R
3258:2
3245:3
3241:R
3234:g
3230:q
3224:a
3220:q
3216:k
3213:b
3205:R
3200:0
3187:2
3183:R
3175:1
3170:=
3165:2
3139:L
3135:b
3119:2
3080:2
3053:2
3031:x
3028:p
3009:v
3006:m
3002:1
2992:v
2989:L
2977:3
2973:R
2966:g
2962:q
2956:a
2952:q
2948:k
2945:b
2939:=
2932:x
2928:p
2921:y
2917:p
2907:=
2902:2
2867:2
2838:v
2835:L
2823:3
2819:R
2812:g
2808:q
2802:a
2798:q
2794:k
2791:b
2785:=
2782:t
2777:y
2773:F
2769:=
2764:y
2760:p
2744:y
2741:p
2721:3
2717:R
2710:g
2706:q
2700:a
2696:q
2692:k
2689:b
2683:=
2664:3
2660:R
2654:3
2650:r
2637:2
2633:r
2626:g
2622:q
2616:a
2612:q
2608:k
2602:=
2597:y
2593:F
2564:3
2560:R
2554:3
2550:r
2537:2
2533:r
2526:g
2522:q
2516:a
2512:q
2508:k
2502:=
2499:F
2474:b
2455:2
2430:m
2403:)
2397:b
2392:2
2388:v
2384:m
2377:g
2373:q
2367:a
2363:q
2359:k
2353:(
2343:2
2340:=
2335:2
2305:R
2301:b
2297:R
2290:b
2282:e
2279:q
2275:2
2272:m
2268:1
2265:m
2245:2
2241:m
2237:+
2232:1
2228:m
2220:2
2216:m
2210:1
2206:m
2173:m
2143:b
2138:2
2134:v
2126:m
2118:e
2114:q
2108:e
2104:q
2100:k
2094:=
2089:2
2084:e
2041:R
2036:2
2032:v
2028:m
2021:g
2017:q
2011:a
2007:q
2003:k
1992:4
1984:=
1979:2
1945:N
1926:2
1922:N
1919:3
1906:R
1901:2
1897:v
1893:m
1886:e
1882:q
1876:a
1872:q
1868:k
1857:5
1849:=
1826:R
1818:0
1814:N
1800:2
1796:v
1792:m
1785:e
1781:q
1775:a
1771:q
1767:k
1756:5
1748:=
1743:1
1705:1
1667:R
1664:2
1657:5
1654:4
1649:=
1646:b
1642:d
1635:b
1629:2
1617:2
1613:b
1604:2
1600:R
1594:2
1587:R
1582:0
1569:2
1565:R
1557:1
1531:L
1503:2
1499:b
1490:2
1486:R
1480:2
1475:=
1470:L
1458:L
1454:b
1436:2
1432:b
1423:2
1419:R
1413:2
1410:=
1407:L
1384:L
1380:0
1377:N
1359:L
1354:2
1350:g
1341:0
1337:N
1325:g
1320:2
1316:v
1312:m
1305:e
1301:q
1295:a
1291:q
1287:k
1284:4
1278:=
1273:1
1241:g
1235:2
1232:1
1224:2
1220:v
1216:m
1209:e
1205:q
1199:a
1195:q
1191:k
1188:2
1173:g
1167:2
1164:/
1161:1
1154:g
1137:L
1133:R
1103:n
1086:=
1081:n
1055:n
990:2
985:2
968:+
963:2
958:1
939:=
890:R
887:1
874:2
870:v
866:m
859:g
855:q
849:a
845:q
841:k
830:4
822:=
817:2
787:N
780:Γ
770:k
763:Γ
757:m
750:Γ
744:v
737:Γ
731:R
724:Γ
713:e
711:q
704:Γ
697:e
690:a
688:q
681:Γ
674:e
667:g
665:q
624:2
620:N
617:3
605:R
602:1
589:2
585:v
581:m
574:e
570:q
564:a
560:q
556:k
545:5
537:=
532:1
496:N
474:N
304:/
301:1
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