J. J. Thomson

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Sir J. J. Thomson OM PRS
Born	Joseph John Thomson 18 December 1856 Cheetham Hill, Manchester, England
Died	30 August 1940 (aged 83) Cambridge, England
Nationality	English
Citizenship	British
Alma mater	Owens College (now the University of Manchester) Trinity College, Cambridge (BA)
Known for	Plum pudding model Discovery of electron Discovery of isotopes Mass spectrometer invention First m/e measurement Proposed first waveguide Thomson scattering Thomson problem Coining term 'delta ray' Coining term 'epsilon radiation' Thomson (unit)
Children	George Paget Thomson, Joan Paget Thomson
Awards	Smith's Prize (1880) Royal Medal (1894) Hughes Medal (1902) Nobel Prize in Physics (1906) Elliott Cresson Medal (1910) Copley Medal (1914) Albert Medal (1915) Franklin Medal (1922) Faraday Medal (1925)
Scientific career
Fields	Physics
Institutions	Trinity College, Cambridge
Academic advisors	John Strutt (Rayleigh) Edward John Routh
Notable students	Charles Glover Barkla Charles T. R. Wilson Ernest Rutherford Francis William Aston John Townsend J. Robert Oppenheimer Owen Richardson William Henry Bragg H. Stanley Allen John Zeleny Daniel Frost Comstock Max Born T. H. Laby Paul Langevin Balthasar van der Pol Geoffrey Ingram Taylor Niels Bohr George Paget Thomson
Signature

Sir Joseph John Thomson OM PRS (18 December 1856 – 30 August 1940) was an English physicist and Nobel Laureate in Physics, credited with the discovery and identification of the electron, the first subatomic particle to be discovered.

In 1897, Thomson showed that cathode rays were composed of previously unknown negatively charged particles (now called electrons), which he calculated must have bodies much smaller than atoms and a very large charge-to-mass ratio. Thomson is also credited with finding the first evidence for isotopes of a stable (non-radioactive) element in 1913, as part of his exploration into the composition of canal rays (positive ions). His experiments to determine the nature of positively charged particles, with Francis William Aston, were the first use of mass spectrometry and led to the development of the mass spectrograph.

Thomson was awarded the 1906 Nobel Prize in Physics for his work on the conduction of electricity in gases.

Education and personal life

Joseph John Thomson was born 18 December 1856 in Cheetham Hill, Manchester, Lancashire, England. His mother, Emma Swindells, came from a local textile family. His father, Joseph James Thomson, ran an antiquarian bookshop founded by a great-grandfather. He had a brother, Frederick Vernon Thomson, who was two years younger than he was. J. J. Thomson was a reserved yet devout Anglican.

His early education was in small private schools where he demonstrated outstanding talent and interest in science. In 1870, he was admitted to Owens College in Manchester (now University of Manchester) at the unusually young age of 14. His parents planned to enroll him as an apprentice engineer to Sharp-Stewart & Co, a locomotive manufacturer, but these plans were cut short when his father died in 1873.

He moved on to Trinity College, Cambridge, in 1876. In 1880, he obtained his Bachelor of Arts degree in mathematics (Second Wrangler in the Tripos and 2nd Smith's Prize). He applied for and became a Fellow of Trinity College in 1881. Thomson received his Master of Arts degree (with Adams Prize) in 1883.

Family

In 1890, Thomson married Rose Elisabeth Paget, one of his former students, daughter of Sir George Edward Paget, KCB, a physician and then Regius Professor of Physic at Cambridge at the church of St. Mary the Less. They had one son, George Paget Thomson, and one daughter, Joan Paget Thomson.

Career and research

Overview

On 22 December 1884, Thomson was appointed Cavendish Professor of Physics at the University of Cambridge. The appointment caused considerable surprise, given that candidates such as Osborne Reynolds or Richard Glazebrook were older and more experienced in laboratory work. Thomson was known for his work as a mathematician, where he was recognized as an exceptional talent.

He was awarded a Nobel Prize in 1906, "in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases." He was knighted in 1908 and appointed to the Order of Merit in 1912. In 1914, he gave the Romanes Lecture in Oxford on "The atomic theory". In 1918, he became Master of Trinity College, Cambridge, where he remained until his death. Joseph John Thomson died on 30 August 1940; his ashes rest in Westminster Abbey, near the graves of Sir Isaac Newton and his former student, Ernest Rutherford.

One of Thomson's greatest contributions to modern science was in his role as a highly gifted teacher. One of his students was Ernest Rutherford, who later succeeded him as Cavendish Professor of Physics. In addition to Thomson himself, six of his research assistants (Charles Glover Barkla, Niels Bohr, Max Born, William Henry Bragg, Owen Willans Richardson and Charles Thomson Rees Wilson) won Nobel Prizes in physics, and two (Francis William Aston and Ernest Rutherford) won Nobel prizes in chemistry. In addition, Thomson's son (George Paget Thomson) won the 1937 Nobel Prize in physics for proving the wave-like properties of electrons.

Early work

Thomson's prize-winning master's work, Treatise on the motion of vortex rings, shows his early interest in atomic structure. In it, Thomson mathematically described the motions of William Thomson's vortex theory of atoms.

Thomson published a number of papers addressing both mathematical and experimental issues of electromagnetism. He examined the electromagnetic theory of light of James Clerk Maxwell, introduced the concept of electromagnetic mass of a charged particle, and demonstrated that a moving charged body would apparently increase in mass.

Much of his work in mathematical modelling of chemical processes can be thought of as early computational chemistry. In further work, published in book form as Applications of dynamics to physics and chemistry (1888), Thomson addressed the transformation of energy in mathematical and theoretical terms, suggesting that all energy might be kinetic. His next book, Notes on recent researches in electricity and magnetism (1893), built upon Maxwell's Treatise upon electricity and magnetism, and was sometimes referred to as "the third volume of Maxwell". In it, Thomson emphasized physical methods and experimentation and included extensive figures and diagrams of apparatus, including a number for the passage of electricity through gases. His third book, Elements of the mathematical theory of electricity and magnetism (1895) was a readable introduction to a wide variety of subjects, and achieved considerable popularity as a textbook.

A series of four lectures, given by Thomson on a visit to Princeton University in 1896, were subsequently published as Discharge of electricity through gases (1897). Thomson also presented a series of six lectures at Yale University in 1904.

Discovery of the electron

Several scientists, such as William Prout and Norman Lockyer, had suggested that atoms were built up from a more fundamental unit, but they envisioned this unit to be the size of the smallest atom, hydrogen. Thomson in 1897 was the first to suggest that one of the fundamental units was more than 1,000 times smaller than an atom, suggesting the subatomic particle now known as the electron. Thomson discovered this through his explorations on the properties of cathode rays. Thomson made his suggestion on 30 April 1897 following his discovery that cathode rays (at the time known as Lenard rays) could travel much further through air than expected for an atom-sized particle. He estimated the mass of cathode rays by measuring the heat generated when the rays hit a thermal junction and comparing this with the magnetic deflection of the rays. His experiments suggested not only that cathode rays were over 1,000 times lighter than the hydrogen atom, but also that their mass was the same in whichever type of atom they came from. He concluded that the rays were composed of very light, negatively charged particles which were a universal building block of atoms. He called the particles "corpuscles", but later scientists preferred the name electron which had been suggested by George Johnstone Stoney in 1891, prior to Thomson's actual discovery.

In April 1897, Thomson had only early indications that the cathode rays could be deflected electrically (previous investigators such as Heinrich Hertz had thought they could not be). A month after Thomson's announcement of the corpuscle, he found that he could reliably deflect the rays by an electric field if he evacuated the discharge tube to a very low pressure. By comparing the deflection of a beam of cathode rays by electric and magnetic fields he obtained more robust measurements of the mass-to-charge ratio that confirmed his previous estimates. This became the classic means of measuring the charge-to-mass ratio of the electron. (The charge itself was not measured until Robert A. Millikan's oil drop experiment in 1909.) 

Thomson believed that the corpuscles emerged from the atoms of the trace gas inside his cathode ray tubes. He thus concluded that atoms were divisible, and that the corpuscles were their building blocks. In 1904, Thomson suggested a model of the atom, hypothesizing that it was a sphere of positive matter within which electrostatic forces determined the positioning of the corpuscles.^[2] To explain the overall neutral charge of the atom, he proposed that the corpuscles were distributed in a uniform sea of positive charge. In this "plum pudding" model, the electrons were seen as embedded in the positive charge like plums in a plum pudding (although in Thomson's model they were not stationary, but orbiting rapidly).

Isotopes and mass spectrometry

In the bottom right corner of this photographic plate are markings for the two isotopes of neon: neon-20 and neon-22.

 

In 1912, as part of his exploration into the composition of the streams of positively charged particles then known as canal rays, Thomson and his research assistant F. W. Aston channelled a stream of neon ions through a magnetic and an electric field and measured its deflection by placing a photographic plate in its path. They observed two patches of light on the photographic plate (see image on right), which suggested two different parabolas of deflection, and concluded that neon is composed of atoms of two different atomic masses (neon-20 and neon-22), that is to say of two isotopes. This was the first evidence for isotopes of a stable element; Frederick Soddy had previously proposed the existence of isotopes to explain the decay of certain radioactive elements. 

J. J. Thomson's separation of neon isotopes by their mass was the first example of mass spectrometry, which was subsequently improved and developed into a general method by F. W. Aston and by A. J. Dempster.

Experiments with cathode rays

Earlier, physicists debated whether cathode rays were immaterial like light ("some process in the aether") or were "in fact wholly material, and ... mark the paths of particles of matter charged with negative electricity", quoting Thomson. The aetherial hypothesis was vague, but the particle hypothesis was definite enough for Thomson to test.

Magnetic deflection

Thomson first investigated the magnetic deflection of cathode rays. Cathode rays were produced in the side tube on the left of the apparatus and passed through the anode into the main bell jar, where they were deflected by a magnet. Thomson detected their path by the fluorescence on a squared screen in the jar. He found that whatever the material of the anode and the gas in the jar, the deflection of the rays was the same, suggesting that the rays were of the same form whatever their origin.

Electrical charge

The cathode ray tube by which J. J. Thomson demonstrated that cathode rays could be deflected by a magnetic field, and that their negative charge was not a separate phenomenon.

 

While supporters of the aetherial theory accepted the possibility that negatively charged particles are produced in Crookes tubes, they believed that they are a mere by-product and that the cathode rays themselves are immaterial. Thomson set out to investigate whether or not he could actually separate the charge from the rays. 

Thomson constructed a Crookes tube with an electrometer set to one side, out of the direct path of the cathode rays. Thomson could trace the path of the ray by observing the phosphorescent patch it created where it hit the surface of the tube. Thomson observed that the electrometer registered a charge only when he deflected the cathode ray to it with a magnet. He concluded that the negative charge and the rays were one and the same.

Electrical deflection

Thomson's illustration of the Crookes tube by which he observed the deflection of cathode rays by an electric field (and later measured their mass-to-charge ratio). Cathode rays were emitted from the cathode C, passed through slits A (the anode) and B (grounded), then through the electric field generated between plates D and E, finally impacting the surface at the far end.

 

The cathode ray (blue line) was deflected by the electric field (yellow).

In May–June 1897, Thomson investigated whether or not the rays could be deflected by an electric field. Previous experimenters had failed to observe this, but Thomson believed their experiments were flawed because their tubes contained too much gas. 

Thomson constructed a Crookes tube with a better vacuum. At the start of the tube was the cathode from which the rays projected. The rays were sharpened to a beam by two metal slits – the first of these slits doubled as the anode, the second was connected to the earth. The beam then passed between two parallel aluminium plates, which produced an electric field between them when they were connected to a battery. The end of the tube was a large sphere where the beam would impact on the glass, created a glowing patch. Thomson pasted a scale to the surface of this sphere to measure the deflection of the beam. Note that any electron beam would collide with some residual gas atoms within the Crookes tube, thereby ionizing them and producing electrons and ions in the tube (space charge); in previous experiments this space charge electrically screened the externally applied electric field. However, in Thomson's Crookes tube the density of residual atoms was so low that the space charge from the electrons and ions was insufficient to electrically screen the externally applied electric field, which permitted Thomson to successfully observe electrical deflection. 

When the upper plate was connected to the negative pole of the battery and the lower plate to the positive pole, the glowing patch moved downwards, and when the polarity was reversed, the patch moved upwards.

Measurement of mass-to-charge ratio

In his classic experiment, Thomson measured the mass-to-charge ratio of the cathode rays by measuring how much they were deflected by a magnetic field and comparing this with the electric deflection. He used the same apparatus as in his previous experiment, but placed the discharge tube between the poles of a large electromagnet. He found that the mass-to-charge ratio was over a thousand times lower than that of a hydrogen ion (H⁺), suggesting either that the particles were very light and/or very highly charged. Significantly, the rays from every cathode yielded the same mass-to-charge ratio. This is in contrast to anode rays (now known to arise from positive ions emitted by the anode), where the mass-to-charge ratio varies from anode-to-anode. Thomson himself remained critical of what his work established, in his Nobel Prize acceptance speech referring to "corpuscles" rather than "electrons". 

Thomson's calculations can be summarised as follows (notice that we reproduce here Thomson's original notations, using F instead of E for the electric field and H instead of B for the magnetic field): 

The electric deflection is given by ${\displaystyle \Theta =Fel/mv^{2}}$, where Θ is the angular electric deflection, F is applied electric intensity, e is the charge of the cathode ray particles, l is the length of the electric plates, m is the mass of the cathode ray particles and v is the velocity of the cathode ray particles. The magnetic deflection is given by ${\displaystyle \phi =Hel/mv}$, where φ is the angular magnetic deflection and H is the applied magnetic field intensity. 

The magnetic field was varied until the magnetic and electric deflections were the same, when ${\displaystyle \Theta =\phi ,Fel/mv^{2}=Hel/mv}$. This can be simplified to give ${\displaystyle m/e=H^{2}l/F\Theta }$. The electric deflection was measured separately to give Θ and H, F and l were known, so m/e could be calculated.

Conclusions

As the cathode rays carry a charge of negative electricity, are deflected by an electrostatic force as if they were negatively electrified, and are acted on by a magnetic force in just the way in which this force would act on a negatively electrified body moving along the path of these rays, I can see no escape from the conclusion that they are charges of negative electricity carried by particles of matter.

— J. J. Thomson

As to the source of these particles, Thomson believed they emerged from the molecules of gas in the vicinity of the cathode.

If, in the very intense electric field in the neighbourhood of the cathode, the molecules of the gas are dissociated and are split up, not into the ordinary chemical atoms, but into these primordial atoms, which we shall for brevity call corpuscles; and if these corpuscles are charged with electricity and projected from the cathode by the electric field, they would behave exactly like the cathode rays.

— J. J. Thomson

Thomson imagined the atom as being made up of these corpuscles orbiting in a sea of positive charge; this was his plum pudding model. This model was later proved incorrect when his student Ernest Rutherford showed that the positive charge is concentrated in the nucleus of the atom.

Other work

In 1905, Thomson discovered the natural radioactivity of potassium.

In 1906, Thomson demonstrated that hydrogen had only a single electron per atom. Previous theories allowed various numbers of electrons.

Awards and honours

Plaque commemorating J. J. Thomson's discovery of the electron outside the old Cavendish Laboratory in Cambridge

 

Thomson was elected a Fellow of the Royal Society (FRS) and appointed to the Cavendish Professorship of Experimental Physics at the Cavendish Laboratory, University of Cambridge in 1884. Thomson won numerous awards and honours during his career including:

• Adams Prize (1882)
• Royal Medal (1894)
• Hughes Medal (1902)
• Hodgkins Medal (1902)
• Nobel Prize for Physics (1906)
• Elliott Cresson Medal (1910)
• Copley Medal (1914)
• Franklin Medal (1922)

Thomson was elected a Fellow of the Royal Society on 12 June 1884 and served as President of the Royal Society from 1915 to 1920. 

In November 1927, J. J. Thomson opened the Thomson building, named in his honour, in the Leys School, Cambridge.

Posthumous honours

In 1991, the thomson (symbol: Th) was proposed as a unit to measure mass-to-charge ratio in mass spectrometry in his honour.

J J Thomson Avenue, on the University of Cambridge's West Cambridge site, is named after Thomson.

Geiger–Marsden experiment (Gold foil experiment)

From Wikipedia, the free encyclopedia

 

A replica of one of Geiger and Marsden's apparatus

 

The Geiger–Marsden experiments (also called the Rutherford gold foil experiment) were a landmark series of experiments by which scientists discovered that every atom contains a nucleus where all of its positive charge and most of its mass are concentrated. They deduced this by measuring how an alpha particle beam is scattered when it strikes a thin metal foil. The experiments were performed between 1908 and 1913 by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester.

Summary

Contemporary theories of atomic structure

The plum pudding model of the atom, as envisioned by Thomson.

 

The popular theory of atomic structure at the time of Rutherford's experiment was the "plum pudding model". This model was devised by Lord Kelvin and further developed by J. J. Thomson. Thomson was the scientist who discovered the electron, and that it was a component of every atom. Thomson believed the atom was a sphere of positive charge throughout which the electrons were distributed, a bit like plums in a Christmas pudding. The existence of protons and neutrons was unknown at this time. They knew atoms were very tiny (Rutherford assumed they were in the order of 10⁻⁸ m in radius). This model was based entirely on classical (Newtonian) physics; the current accepted model uses quantum mechanics. 

Thomson's model was not universally accepted even before Rutherford's experiments. Thomson himself was never able to develop a complete and stable model of his concept. Japanese scientist Hantaro Nagaoka rejected Thomson's model on the grounds that opposing charges cannot penetrate each other. He proposed instead that electrons orbit the positive charge like the rings around Saturn.

Implications of the plum pudding model

An alpha particle is a sub-microscopic, positively charged particle of matter. According to Thomson's model, if an alpha particle were to collide with an atom, it would just fly straight through, its path being deflected by at most a fraction of a degree. At the atomic scale, the concept of "solid matter" is meaningless, so the alpha particle would not bounce off the atom like a marble. It would be affected only by the atom's electric fields, and Thomson's model predicted that the electric fields in an atom are too weak to affect a passing alpha particle much (alpha particles tend to move very fast). Both the negative and positive charges within the Thomson atom are spread out over the atom's entire volume. According to Coulomb's Law, the less concentrated a sphere of electric charge is, the weaker its electric field at its surface will be.

As a worked example, consider an alpha particle passing tangentially to a Thomson gold atom, where it will experience the electric field at its strongest and thus experience the maximum deflection θ. Since the electrons are very light compared to the alpha particle, their influence can be neglected and the atom can be seen as a heavy sphere of positive charge.

Q_n = positive charge of gold atom = 79 e = 1.266×10⁻¹⁷ C

Q_α = charge of alpha particle = 2 e = 3.204×10⁻¹⁹ C

r = radius of a gold atom = 1.44×10⁻¹⁰ m

v_α = velocity of alpha particle = 1.53×10⁷ m/s

m_α = mass of alpha particle = 6.645×10⁻²⁷ kg

k = Coulomb's constant = 8.998×10⁹ N·m²/C²

Using classical physics, the alpha particle's lateral change in momentum Δp can be approximated using the impulse of force relationship and the Coulomb force expression:

${\displaystyle \Delta p=F\Delta t=k\cdot {\frac {Q_{\alpha }Q_{n}}{r^{2}}}\cdot {\frac {2r}{v_{\alpha }}}}$

${\displaystyle \theta \approx {\frac {\Delta p}{p}}$

${\displaystyle \theta <0 .000326="" annotation="" circ="" mathrm="" or="" rad="">$

The above calculation is but an approximation of what happens when an alpha particle comes near a Thomson atom, but it is clear that the deflection at most will be in the order of a small fraction of a degree. If the alpha particle were to pass through a gold foil some 400 atoms thick and experience maximal deflection in the same direction (unlikely), it would still be a small deflection.

The outcome of the experiments

Left: Had Thomson's model been correct, all the alpha particles should have passed through the foil with minimal scattering. Right: What Geiger and Marsden observed was that a small fraction of the alpha particles experienced strong deflection.

 

At Rutherford's behest, Geiger and Marsden performed a series of experiments where they pointed a beam of alpha particles at a thin foil of metal and measured the scattering pattern by using a fluorescent screen. They spotted alpha particles bouncing off the metal foil in all directions, some right back at the source. This should have been impossible according to Thomson's model; the alpha particles should have all gone straight through. Obviously, those particles had encountered an electrostatic force far greater than Thomson's model suggested they would, which in turn implied that the atom's positive charge was concentrated in a much tinier volume than Thomson imagined.

When Geiger and Marsden shot alpha particles at their metal foil, they noticed only a tiny fraction of the alpha particles were deflected by more than 90°. Most flew straight through the foil. This suggested that those tiny spheres of intense positive charge were separated by vast gulfs of empty space. Most particles passed through the empty space and experienced negligible deviation, while a handful passed close to the nuclei of the atoms and were deflected through large angles. 

Rutherford thus rejected Thomson's model of the atom, and instead proposed a model where the atom consisted of mostly empty space, with all of its positive charge concentrated in its center in a very tiny volume, surrounded by a cloud of electrons.

Timeline

Background

Ernest Rutherford

 

Hans Geiger

 

Ernest Marsden

 

Ernest Rutherford was Langsworthy Professor of Physics at the Victoria University of Manchester (now the University of Manchester). He had already received numerous honours for his studies of radiation. He had discovered the existence of alpha rays, beta rays, and gamma rays, and had proved that these were the consequence of the disintegration of atoms. In 1906, he received a visit from a German physicist named Hans Geiger, and was so impressed that he asked Geiger to stay and help him with his research. Ernest Marsden was a physics undergraduate student studying under Geiger. 

Alpha particles are tiny, positively charged particles that are spontaneously emitted by certain substances such as uranium and radium. Rutherford had discovered them in 1899. In 1908, he was trying to precisely measure their charge-to-mass ratio. To do this, he first needed to know just how many alpha particles his sample of radium was giving off (after which he would measure their total charge and divide one by the other). Alpha particles are too tiny to be seen with a microscope, but Rutherford knew that alpha particles ionize air molecules, and if the air is within an electric field, the ions will produce an electric current. On this principle, Rutherford and Geiger designed a simple counting device which consisted of two electrodes in a glass tube. Every alpha particle that passed through the tube would create a pulse of electricity that could be counted. It was an early version of the Geiger counter.

The counter that Geiger and Rutherford built proved unreliable because the alpha particles were being too strongly deflected by their collisions with the molecules of air within the detection chamber. The highly variable trajectories of the alpha particles meant that they did not all generate the same number of ions as they passed through the gas, thus producing erratic readings. This puzzled Rutherford because he had thought that alpha particles were just too heavy to be deflected so strongly. Rutherford asked Geiger to investigate just how much matter could scatter alpha rays.

The experiments they designed involved bombarding a metal foil with alpha particles to observe how the foil scattered them in relation to their thickness and material. They used a fluorescent screen to measure the trajectories of the particles. Each impact of an alpha particle on the screen produced a tiny flash of light. Geiger worked in a darkened lab for hours on end, counting these tiny scintillations using a microscope. Rutherford lacked the endurance for this work, which is why he left it to his younger colleagues. For the metal foil, they tested a variety of metals, but they preferred gold because they could make the foil very thin, as gold is very malleable. As a source of alpha particles, Rutherford's substance of choice was radon, a substance several million times more radioactive than uranium.

The 1908 experiment

This apparatus was described in a 1908 paper by Hans Geiger. It could only measure deflections of a few degrees.

 

A 1908 paper by Geiger, On the Scattering of α-Particles by Matter, describes the following experiment. He constructed a long glass tube, nearly two meters in length. At one end of the tube was a quantity of "radium emanation" (R) that served as a source of alpha particles. The opposite end of the tube was covered with a phosphorescent screen (Z). In the middle of the tube was a 0.9 mm-wide slit. The alpha particles from R passed through the slit and created a glowing patch of light on the screen. A microscope (M) was used to count the scintillations on the screen and measure their spread. Geiger pumped all the air out of the tube so that the alpha particles would be unobstructed, and they left a neat and tight image on the screen that corresponded to the shape of the slit. Geiger then allowed some air in the tube, and the glowing patch became more diffuse. Geiger then pumped out the air and placed some gold foil over the slit at AA. This too caused the patch of light on the screen to become more spread out. This experiment demonstrated that both air and solid matter could markedly scatter alpha particles. The apparatus, however, could only observe small angles of deflection. Rutherford wanted to know if the alpha particles were being scattered by even larger angles—perhaps larger than 90°.

The 1909 experiment

In these experiments, alpha particles emitted by a radioactive source (A) were observed bouncing off a metal reflector (R) and onto a fluorescent screen (S) on the other side of a lead plate (P).

 

In a 1909 paper, On a Diffuse Reflection of the α-Particles, Geiger and Marsden described the experiment by which they proved that alpha particles can indeed be scattered by more than 90°. In their experiment, they prepared a small conical glass tube (AB) containing "radium emanation" (radon), "radium A" (actual radium), and "radium C" (bismuth-214); its open end sealed with mica. This was their alpha particle emitter. They then set up a lead plate (P), behind which they placed a fluorescent screen (S). The tube was held on the opposite side of plate, such that the alpha particles it emitted could not directly strike the screen. They noticed a few scintillations on the screen, because some alpha particles got around the plate by bouncing off air molecules. They then placed a metal foil (R) to the side of the lead plate. They pointed the tube at the foil to see if the alpha particles would bounce off it and strike the screen on the other side of the plate, and observed an increase in the number of scintillations on the screen. Counting the scintillations, they observed that metals with higher atomic mass, such as gold, reflected more alpha particles than lighter ones such as aluminium.

Geiger and Marsden then wanted to estimate the total number of alpha particles that were being reflected. The previous setup was unsuitable for doing this because the tube contained several radioactive substances (radium plus its decay products) and thus the alpha particles emitted had varying ranges, and because it was difficult for them to ascertain at what rate the tube was emitting alpha particles. This time, they placed a small quantity of radium C (bismuth-214) on the lead plate, which bounced off a platinum reflector (R) and onto the screen. They found that only a tiny fraction of the alpha particles that struck the reflector bounced onto the screen (in this case, 1 in 8000).

The 1910 experiment

This apparatus was described in 1910 paper by Geiger. It was designed to precisely measure how the scattering varied according to the substance and thickness of the foil.

 

A 1910 paper by Geiger, The Scattering of the α-Particles by Matter, describes an experiment by which he sought to measure how the most probable angle through which an a-particle is deflected varies with the material it passes through, the thickness of said material, and the velocity of the alpha particles. He constructed an airtight glass tube from which the air was pumped out. At one end was a bulb (B) containing "radium emanation" (radon-222). By means of mercury, the radon in B was pumped up the narrow glass pipe whose end at A was plugged with mica. At the other end of the tube was a fluorescent zinc sulfide screen (S). The microscope which he used to count the scintillations on the screen was affixed to a vertical millimeter scale with a vernier, which allowed Geiger to precisely measure where the flashes of light appeared on the screen and thus calculate the particles' angles of deflection. The alpha particles emitted from A was narrowed to a beam by a small circular hole at D. Geiger placed a metal foil in the path of the rays at D and E to observe how the zone of flashes changed. He could also vary the velocity of the alpha particles by placing extra sheets of mica or aluminium at A. 

From the measurements he took, Geiger came to the following conclusions:

• the most probable angle of deflection increases with the thickness of the material
• the most probable angle of deflection is proportional to the atomic mass of the substance
• the most probable angle of deflection decreases with the velocity of the alpha particles
• the probability that a particle will be deflected by more than 90° is vanishingly small

Rutherford mathematically models the scattering pattern

Considering the results of the above experiments, Rutherford published a landmark paper in 1911 titled "The Scattering of α and β Particles by Matter and the Structure of the Atom" wherein he proposed that the atom contains at its center a volume of electric charge that is very small and intense (in fact, Rutherford treats it as a point charge in his calculations). For the purpose of his mathematical calculations he assumed this central charge was positive, but he admitted he could not prove this and that he had to wait for other experiments to develop his theory. 

Rutherford developed a mathematical equation that modeled how the foil should scatter the alpha particles if all the positive charge and most of the atomic mass was concentrated in a single point at the center of an atom. 

${\displaystyle s={\frac {Xnt\csc ^{4}{\!\left({\tfrac {\phi }{2}}\right)}}{16r^{2}}}\cdot {\left({\frac {2Q_{n}Q_{\alpha }}{mv^{2}}}\right)}^{2}}$

s = the number of alpha particles falling on unit area at an angle of deflection Φ

r = distance from point of incidence of α rays on scattering material

X = total number of particles falling on the scattering material

n = number of atoms in a unit volume of the material

t = thickness of the foil

Q_n = positive charge of the atomic nucleus

Q_α = positive charge of the alpha particles

m = mass of an alpha particle

v = velocity of the alpha particle

From the scattering data, Rutherford estimated the central charge Q_n to be about +100 units.

The 1913 experiment

In a 1913 paper, The Laws of Deflexion of α Particles through Large Angles, Geiger and Marsden describe a series of experiments by which they sought to experimentally verify the above equation that Rutherford developed. Rutherford's equation predicted that the number of scintillations per minute s that will be observed at a given angle Φ should be proportional to:

1. csc⁴(Φ/2)
2. thickness of foil t
3. magnitude of central charge Q_n
4. 1/(mv²)²

Their 1913 paper describes four experiments by which they proved each of these four relationships. 

This apparatus was described in a 1913 paper by Geiger and Marsden. It was designed to accurately measure the scattering pattern of the alpha particles produced by the metal foil (F). The microscope (M) and screen (S) were affixed to a rotating cylinder and could be moved a full circle around the foil so that they could count scintillations from every angle.

 

To test how the scattering varied with the angle of deflection (i.e. if s ∝ csc⁴(Φ/2)) Geiger and Marsden built an apparatus that consisted of a hollow metal cylinder mounted on a turntable. Inside the cylinder was a metal foil (F) and a radiation source containing radon (R), mounted on a detached column (T) which allowed the cylinder to rotate independently. The column was also a tube by which air was pumped out of the cylinder. A microscope (M) with its objective lens covered by a fluorescent zinc sulfide screen (S) penetrated the wall of the cylinder and pointed at the metal foil. By turning the table, the microscope could be moved a full circle around the foil, allowing Geiger to observe and count alpha particles deflected by up to 150°. Correcting for experimental error, Geiger and Marsden found that the number of alpha particles that are deflected by a given angle Φ is indeed proportional to csc⁴(Φ/2).

This apparatus was used to measure how the alpha particle scattering pattern varied in relation to the thickness of the foil, the atomic weight of the material, and the velocity of the alpha particles. The rotating disc in the center had six holes which could be covered with foil.

 

Geiger and Marsden then tested how the scattering varied with the thickness of the foil (i.e. if s ∝ t). They constructed a disc (S) with six holes drilled in it. The holes were covered with metal foil (F) of varying thickness, or none for control. This disc was then sealed in a brass ring (A) between two glass plates (B and C). The disc could be rotated by means of a rod (P) to bring each window in front of the alpha particle source (R). On the rear glass pane was a zinc sulfide screen (Z). Geiger and Marsden found that the number of scintillations that appeared on the zinc sulfide screen was indeed proportional to the thickness as long as said thickness was small.

Geiger and Marsden reused the above apparatus to measure how the scattering pattern varied with the square of the nuclear charge (i.e. if s ∝ Q_n²). Geiger and Marsden didn't know what the positive charge of the nucleus of their metals were (they had only just discovered the nucleus existed at all), but they assumed it was proportional to the atomic weight, so they tested whether the scattering was proportional to the atomic weight squared. Geiger and Marsden covered the holes of the disc with foils of gold, tin, silver, copper, and aluminum. They measured each foil's stopping power by equating it to an equivalent thickness of air. They counted the number of scintillations per minute that each foil produced on the screen. They divided the number of scintillations per minute by the respective foil's air equivalent, then divided again by the square root of the atomic weight (Geiger and Marsden knew that for foils of equal stopping power, the number of atoms per unit area is proportional to the square root of the atomic weight). Thus, for each metal, Geiger and Marsden obtained the number of scintillations that a fixed number of atoms produce. For each metal, they then divided this number by the square of the atomic weight, and found that the ratios were more or less the same. Thus they proved that s ∝ Q_n².

Finally, Geiger and Marsden tested how the scattering varied with the velocity of the alpha particles (i.e. if s ∝ 1/v⁴). Using the same apparatus again, they slowed the alpha particles by placing extra sheets of mica in front of the alpha particle source. They found that, within the range of experimental error, that the number of scinitillations was indeed proportional to 1/v⁴.

Rutherford determines the nucleus is positively charged

In his 1911 paper, Rutherford assumed that the central charge of the atom was positive, but a negative charge would have fitted his scattering model just as well. In a 1913 paper, Rutherford declared that the "nucleus" (as he now called it) was indeed positively charged, based on the result of experiments exploring the scattering of alpha particles in various gases. 

In 1917, Rutherford and his assistant William Kay began exploring the passage of alpha particles through gases such as hydrogen and nitrogen. In an experiment where they shot a beam of alpha particles through hydrogen, the alpha particles knocked the hydrogen nuclei forwards in the direction of the beam, not backwards. In an experiment where they shot alpha particles through nitrogen, he discovered that the alpha particles knocked hydrogen nuclei (i.e. protons) out of the nitrogen nuclei.

Legacy

When Geiger reported to Rutherford that he had spotted alpha particles being strongly deflected, Rutherford was astounded. In a lecture Rutherford delivered at Cambridge University, he said:

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive centre, carrying a charge.

— Ernest Rutherford

Accolades soon flooded in. Hantaro Nagaoka, who had once proposed a Saturnian model of the atom, wrote to Rutherford from Tokyo in 1911: "Congratulations on the simpleness of the apparatus you employ and the brilliant results you obtained". The conclusions of these experiments revealed how all matter on Earth is structured and thus affected every scientific and engineering discipline, making it one of the most pivotal scientific discoveries of all time. The astronomer Arthur Eddington called Rutherford's discovery the most important scientific achievement since Democritus proposed the atom ages earlier.

Like most scientific models, Rutherford's atomic model was neither perfect nor complete. According to classical Newtonian physics, it was in fact impossible. Accelerating charged particles radiate electromagnetic waves, so an electron orbiting an atomic nucleus in theory would spiral into the nucleus as it loses energy. To fix this problem, scientists had to incorporate quantum mechanics into Rutherford's model.