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Rutherford atomic model

What is the model of the atom proposed by Ernest Rutherford?

What is the rutherford gold-foil experiment, what were the results of rutherford's experiment, what did ernest rutherford's atomic model get right and wrong, what was the impact of ernest rutherford's theory.

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Rutherford model

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  • UC Davis - The Rutherford Scattering Experiment
  • Chemistry LibreTexts - Rutherford's Experiment- The Nuclear Model of the Atom

Rutherford atomic model

The atom , as described by Ernest Rutherford , has a tiny, massive core called the nucleus . The nucleus has a positive charge. Electrons are particles with a negative charge. Electrons orbit the nucleus. The empty space between the nucleus and the electrons takes up most of the volume of the atom.

A piece of gold foil was hit with alpha particles , which have a positive charge. Most alpha particles went right through. This showed that the gold atoms were mostly empty space. Some particles had their paths bent at large angles. A few even bounced backward. The only way this would happen was if the atom had a small, heavy region of positive charge inside it.

The previous model of the atom, the Thomson atomic model , or the “plum pudding” model, in which negatively charged electrons were like the plums in the atom’s positively charged pudding, was disproved. The Rutherford atomic model relied on classical physics. The Bohr atomic model , relying on quantum mechanics, built upon the Rutherford model to explain the orbits of electrons.

The Rutherford atomic model was correct in that the atom is mostly empty space. Most of the mass is in the nucleus, and the nucleus is positively charged. Far from the nucleus are the negatively charged electrons. But the Rutherford atomic model used classical physics and not quantum mechanics. This meant that an electron circling the nucleus would give off electromagnetic radiation . The electron would lose energy and fall into the nucleus. In the Bohr model, which used quantum theory, the electrons exist only in specific orbits and can move between these orbits.​

The gold-foil experiment showed that the atom consists of a small, massive, positively charged nucleus with the negatively charged electrons being at a great distance from the centre. Niels Bohr built upon Rutherford’s model to make his own. In Bohr’s model the orbits of the electrons were explained by quantum mechanics.

Rutherford model , description of the structure of atoms proposed (1911) by the New Zealand-born physicist Ernest Rutherford . The model described the atom as a tiny, dense, positively charged core called a nucleus, in which nearly all the mass is concentrated, around which the light, negative constituents , called electrons , circulate at some distance, much like planets revolving around the Sun .

rutherford's scattering experiment demonstrated

The nucleus was postulated as small and dense to account for the scattering of alpha particles from thin gold foil, as observed in a series of experiments performed by undergraduate Ernest Marsden under the direction of Rutherford and German physicist Hans Geiger in 1909. A radioactive source emitting alpha particles (i.e., positively charged particles, identical to the helium atom nucleus and 7,000 times more massive than electrons) was enclosed within a protective lead shield. The radiation was focused into a narrow beam after passing through a slit in a lead screen. A thin section of gold foil was placed in front of the slit, and a screen coated with zinc sulfide to render it fluorescent served as a counter to detect alpha particles. As each alpha particle struck the fluorescent screen , it produced a burst of light called a scintillation, which was visible through a viewing microscope attached to the back of the screen. The screen itself was movable, allowing Rutherford and his associates to determine whether or not any alpha particles were being deflected by the gold foil.

atom. Orange and green illustration of protons and neutrons creating the nucleus of an atom.

Most alpha particles passed straight through the gold foil, which implied that atoms are mostly composed of open space. Some alpha particles were deflected slightly, suggesting interactions with other positively charged particles within the atom. Still other alpha particles were scattered at large angles, while a very few even bounced back toward the source. (Rutherford famously said later, “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.”) Only a positively charged and relatively heavy target particle, such as the proposed nucleus, could account for such strong repulsion. The negative electrons that balanced electrically the positive nuclear charge were regarded as traveling in circular orbits about the nucleus. The electrostatic force of attraction between electrons and nucleus was likened to the gravitational force of attraction between the revolving planets and the Sun. Most of this planetary atom was open space and offered no resistance to the passage of the alpha particles.

The Rutherford model supplanted the “plum-pudding” atomic model of English physicist Sir J.J. Thomson , in which the electrons were embedded in a positively charged atom like plums in a pudding. Based wholly on classical physics , the Rutherford model itself was superseded in a few years by the Bohr atomic model , which incorporated some early quantum theory . See also atomic model .

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Rutherford Scattering

Michael Fowler, University of Virginia

Rutherford as Alpha-Male

[Rutherford was] a "tribal chief", as a student said.

(Richard Rhodes, The Making of the Atomic Bomb, page 46)

In 1908 Rutherford was awarded the Nobel Prize—for chemistry! The award citation read: "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances." While at McGill University, he had discovered that the radioactive element thorium emitted a gas which was itself radioactive, but if the gas radioactivity was monitored separately from the thorium's, he found it decreased geometrically, losing approximately half its current strength for each minute that passed. The gas he had found was a short-lived isotope of radon, and this was the first determination of a "half-life" for a radioactive material. (Pais, Inward Bound , page 120).

The chemists were of course impressed that Rutherford was fulfilling their ancient alchemical dream of transmuting elements, or at least demonstrating that it happened. Rutherford himself remarked at the ceremony that he "had dealt with many different transformations with various time-periods, but the quickest he had met was his own transformation from a physicist to a chemist". Still, Nobel prizes of any kind are nice to get, so he played along, titling his official Nobel lecture: "The chemical nature of the alpha-particle from radioactive substances". (He established that his favorite particle was an ionized helium atom by collecting alphas in an evacuated container, where they picked up electrons. After compressing this very rarefied gas, he passed an electric discharge through it and observed the characteristic helium spectrum in the light emitted.)

Rutherford was the world leader in alpha-particle physics. In 1906, at McGill University, Montreal, he had been the first to detect slight deflections of alphas on passage through matter. In 1907, he became a professor at the University of Manchester, where he worked with Hans Geiger . This was just a year after Rutherford's old boss, J. J. Thomson , had written a paper on his plum pudding atomic model suggesting that the number of electrons in an atom was about the same as the atomic number. (Not long before, people had speculated that atoms might contain thousands of electrons. They were assuming that the electrons contributed a good fraction of the atom's mass.) The actual distribution of the electrons in the atom, though, was as mysterious as ever.  Mayer's floating magnets (see previous lecture) were fascinating, but had not led to any quantitative conclusions on electronic distributions in atoms.

Rutherford's 1906 discovery that his pet particles were slightly deflected on passing through atoms came about when he was finding their charge to mass ratio, by measuring the deflection in a magnetic field. He detected the alphas by letting them impact photographic film. When he had them pass through a thin sheet of mica before hitting the film (so the film didn't have to be in the vacuum?) he found the image was blurred at the edges, evidently the mica was deflecting the alphas through a degree or two. He also knew that the alphas wouldn't be deflected a detectable amount by the electrons in the atom, since the alphas weighed 8,000 times as much as the electrons, atoms contained only a few dozen electrons, and the alphas were very fast. The mass of the atom must be tied up somehow with the positive charge . Therefore, he reasoned, analyzing these small deflections might give some clue as to the distribution of positive charge and mass in the atom, and therefore give some insight into his old boss J. J.'s plum pudding. The electric fields necessary in the atom for the observed scattering already seemed surprisingly high to Rutherford (Pais, page 189).

Scattering Alphas

Rutherford's alpha scattering experiments were the first experiments in which individual particles were systematically scattered and detected. This is now the standard operating procedure of particle physics. To minimize alpha loss by scattering from air molecules, the experiment was carried out in a fairly good vacuum, the metal box being evacuated through a tube T (see below). The alphas came from a few milligrams of radium (to be precise, its decay product radon 222) at R in the figure below, from the original paper, which goes on:

" By means of a diaphragm placed at D, a pencil of alpha particles was directed normally on to the scattering foil F. By rotating the microscope [M] the alpha particles scattered in different directions could be observed on the screen S."

Actually, this was more difficult than it sounds. A single alpha caused a slight fluorescence on the zinc sulphide screen S at the end of the microscope. This could only be reliably seen by dark-adapted eyes (after half an hour in complete darkness) and one person could only count the flashes accurately for one minute before needing a break, and counts above 90 per minute were too fast for reliability. The experiment accumulated data from hundreds of thousands of flashes.

Rutherford's partner in the initial phase of this work was Hans Geiger, who later developed the Geiger counter to detect and count fast particles. Many hours of staring at the tiny zinc sulphide screen in the dark must have focused his mind on finding a better way!

In 1909, an undergraduate, Ernest Marsden, was being trained by Geiger. To quote Rutherford (a lecture he gave much later):

"I had observed the scattering of alpha-particles, and Dr. Geiger in my laboratory had examined it in detail. He found, in thin pieces of heavy metal, that the scattering was usually small, of the order of one degree.

"One day Geiger came to me and said, "Don't you think that young Marsden , whom I am training in radioactive methods, ought to begin a small research?" Now I had thought that, too, so I said, " Why not let him see if any alpha-particles can be scattered through a large angle?"

"I may tell you in confidence that I did not believe that they would be, since we knew the alpha-particle was a very fast, massive particle with a great deal of energy, and you could show that if the scattering was due to the accumulated effect of a number of small scatterings, the chance of an alpha-particle's being scattered backward was very small. Then I remember two or three days later Geiger coming to me in great excitement and saying "We have been able to get some of the alpha-particles coming backward …" It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

Disproof of the Pudding

The back scattered alpha-particles proved fatal to the plum pudding model. A central assumption of that model was that both the positive charge and the mass of the atom were more or less uniformly distributed over its size, approximately 10 -10  meters across or a little more. It is not difficult to calculate the magnitude of electric field from this charge distribution. (Recall that this is the field that must scatter the alphas, the electrons are so light they will jump out of the way with negligible impact on an alpha.)

To be specific, let us consider the gold atom, since the foil used by Rutherford was of gold, beaten into leaf about 400 atoms thick. The gold atom has a positive charge of 79 e (balanced of course by that of the 79 electrons in its normal state). Neglect the electrons—they'll be scattered away with negligible impact on the heavy alpha.

See the animation here !

The maximum electric force the alpha will encounter is that at the surface of the sphere of positive charge,

E ⋅ 2 e = 1 4 π ε 0 ⋅ 79 e ⋅ 2 e r 0 2 = 9 ⋅ 10 9 158 ⋅ ( 1.6 ⋅ 10 − 19 ) 10 − 20 = 3.64 ⋅ 10 − 6  Newtons .  

(In this model, once inside the sphere the electric force goes down, just as gravity goes down on going deep into the earth, to zero at the center. But the sideways component stays approximately constant if the path is nearly a straight line.)

If the alpha particle initially has momentum  p , for small deflections the angle of deflection (in radians) is given by Δ p / p ,  where  Δ p is the sideways momentum resulting from the electrically repulsive force of the positive sphere of charge.

A good estimate of the sideways deflection is given by taking the alpha to experience the surface  force given above for a time interval equal to the time it takes the alpha to cross the atom—say, a distance 2 r 0 .   (The force felt when outside the ball of charge is much smaller: it drops away as the inverse square, but at an angle that makes it effectively inverse cube. It can be shown to make only a small contribution.)

Note that since the alpha particle has mass 6.7x10 -27  kg, from  F = m a , the electric force at the atomic surface above will give it a sideways acceleration of 5.4x10 20  meters per sec per sec (compare  g = 10 !). But the force doesn't have long to act—the alpha is moving at 1.6x10 7  meters per second. So the time available for the force to act is the time interval a particle needs to cross an atom if the particle gets from New York to Australia in one second.

So the transit time for the alpha across the plum pudding atom is:

t 0 = 2 r 0 / v = 2 × 10 10 / 1.6 × 10 7 = 1.25 × 10 − 17  seconds .  

Now, the magnitude of the total sideways velocity picked up on crossing the atom is the sideways acceleration multiplied by the time,

1.25 × 10 − 17 × 5.4 × 10 20 = 6750   m /sec .  

This is a few ten-thousandths of the alpha's forward speed , so there is only a very tiny deflection . Even if the alpha hit 400 atoms in succession and they all deflected it the same way, an astronomically improbable event, the deflection would only be of order a degree. Therefore, the observed deflection through ninety degrees and more was completely inexplicable using Thomson's pudding model!

Emergence of the Nucleus

Rutherford pondered the problem for some months. He had been a believer in his former boss's pudding model, but he eventually decided there was simply no way it could generate the strength of electric field necessary to deflect the fast moving alphas. Yet it was difficult to credit there was much more positive charge around than that necessary to compensate for the electrons, and it was pretty well established that there were not more than a hundred or so electrons (we used 79, the correct value—that was not known exactly until a little later). The electric field from a sphere of charge reaches its maximum on the surface, as discussed above. Therefore, for a given charge, assumed spherically distributed, the only way to get a stronger field is to compress it into a smaller sphere . Rutherford concluded that he could only explain the large alpha deflections if the positive charge, and most of the mass of the atom, was in a sphere much smaller than the atom itself .

It is not difficult to estimate from the above discussion how small such a nucleus would have to be to give a substantial deflection. We found a sphere of radius 10 -10  meters gave a deflection of about 4x10 -4  radians. We need to increase this deflection by a factor of a few thousand. On decreasing the radius of the sphere of positive charge, the force at the surface increases as the inverse radius squared . On the other hand, the time over which the alpha experiences the sideways force decreases as the radius.

The total deflection , then, proportional to the product of force and time, increases as the inverse of the radius . This forces the conclusion that the positive charge is in a sphere of radius certainly less than 10 -13  meters, provided all the observed scattering is caused by one encounter with a nucleus.

Animation of scattering from a nuclear atom here !

Rutherford decided that the observed scattering was in fact from a single nucleus. He argued as follows: since the foil is only 400 atoms thick, it is difficult to see how ninety degree scatterings could arise unless the scattering by a single nucleus was at least one degree, say 100 times that predicted by the Thomson model. This would imply that the nucleus had a radius at most one-hundredth that of the atom, and therefore presented a target area for one-degree scattering (or more) to the incoming alphas only one ten-thousandth that of the atom. (In particle physics jargon, this target area is called the scattering cross section .) If an alpha goes through 400 layers of atoms, and in each layer it has a chance of one in ten thousand of getting close enough to the nucleus for a one-degree scatter, this is unlikely to happen twice. It follows that almost certainly only one scattering takes place. It then follows that all ninety or more degrees of scattering must be a single event, so the nucleus must be even smaller than one hundredth the radius of the atom -- it must be less than 10 -13 meters, as stated above.

Seeing the Nucleus

Having decided that the observed scattering of the alphas came from single encounters with nuclei, and assuming that the scattering force was just the electrostatic repulsion, Rutherford realized maybe just scaling down the radius in the plum pudding analysis given above wasn't quite right. Maybe the nucleus was so small that the alpha particle didn't even touch it. If that were the case, the alpha particle's entire trajectory was determined by a force law of inverse square repulsion, and could be analyzed precisely mathematically by the techniques already well-known to astronomers for finding paths of planets under inverse square attraction.

It turns out that the alpha will follow a hyperbolic path (see the animation). Imagine an alpha coming in along an almost straight line path, the perpendicular distance of the nucleus from this line is called the impact parameter (how close to the center the alpha particle would pass if the repulsion were switched off).  The standard planetary math is enough to find the angle at which the alpha comes out (the scattering angle), given the impact parameter and speed.  Although not exactly a hot shot theorist, Rutherford managed to figure this out after a few weeks.

The incoming stream of alphas all have the same velocity (including direction) , but random impact parameters: we assume the beam intensity doesn't vary much in the perpendicular direction, certainly on an atomic scale, so we average over impact parameters (with a factor 2 π p d p  for the annular region   p , p + d p  ).

The bottom line is that for a nucleus of charge  Z , and incident alpha particles of mass  m and speed  v , the rate of scattering to a point on the screen corresponding to a scattering angle of  θ (angle between incident velocity and final velocity of alpha) is proportional to:

scattering into small area at  θ   ∝ ( 1 4 π ε 0 ⋅ Z e 2 m v 2 ) 2 ⋅ 1 sin 4 ( θ / 2 ) .  

Analysis of the hundred thousand or more scattering events recorded for the alphas on gold fully confirmed the angular dependence predicted by the above analysis.

Modeling the Scattering

To visualize the path of the alpha in such a scattering, Rutherford "had a model made, a heavy electromagnet suspended as a pendulum on thirty feet of wire that grazed the face of another electromagnet set on a table. With the two grazing faces matched in polarity and therefore repelling each other, the pendulum was deflected" into a hyperbolic path.(Rhodes, page 50)

But it didn't work for Aluminum...

On replacing the gold foil by aluminum foil (some years later), it turned out that small angle scattering obeyed the above law, but large angle scattering didn't. Rutherford correctly deduced that in the large angle scattering, which corresponded to closer approach to the nucleus, the alpha was actually hitting the nucleus. This meant that the size of the nucleus could be worked out by finding the maximum angle for which the inverse square scattering formula worked, and finding how close to the center of the nucleus such an alpha came. Rutherford estimated the radius of the aluminum nucleus to be about 10 -14  meters.

The Beginnings of Nuclear Physics

The First World War lasted from 1914 to 1918. Geiger and Marsden were both at the Western front, on opposite sides. Rutherford had a large water tank installed on the ground floor of the building in Manchester, to carry out research on defense against submarine attack. Nevertheless, occasional research on alpha scattering continued. Scattering from heavy nuclei was fully accounted for by the electrostatic repulsion, so Rutherford concentrated on light nuclei, including hydrogen and nitrogen. In 1919, Rutherford established that an alpha impinging on a nitrogen nucleus can cause a hydrogen atom to appear! Newspaper headlines blared that Rutherford had "split the atom". (Rhodes, page 137)

Shortly after that experiment, Rutherford moved back to Cambridge to succeed J. J. Thomson as head of the Cavendish laboratory, working with one of his former students, James Chadwick , who had spent the war years interned in Germany. They discovered many unusual effects with alpha scattering from light nuclei. In 1921, Chadwick and co-author Bieler wrote: "The present experiments do not seem to throw any light on the nature of the law of variation of the forces at the seat of an electric charge, but merely show that the forces are of great intensity … It is our task to find some field of force which will reproduce these effects." I took this quote from Pais, page 240, who goes on to say that he considers this 1921 statement as marking the birth of the strong interactions.

In fact, Rutherford was beginning to focus his attention on the actual construction of the nucleus and the alpha particle. He coined the word "proton" to describe the hydrogen nucleus, it first appeared in print in 1920 (Pais). At first, he thought the alpha must be made up of four of these protons somehow bound together by having two electrons in the middle—this would get the mass and charge right, but of course nobody could construct a plausible electrostatic configuration. Then he had the idea that maybe there was a special very tightly bound state of a proton and an electron, much smaller than an atom. By 1924, he and Chadwick were discussing how to detect this neutron. It wasn't going to be easy—it probably wouldn't leave much of a track in a cloud chamber. In fact, Chadwick did discover the neutron, but not until 1932, and it wasn't much like their imagined proton-electron bound state. But it did usher in the modern era in nuclear physics.

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Experimental physics i & ii "junior lab", rutherford scattering, description.

rutherford's scattering experiment demonstrated

Rutherford scattering experiment equipment.

This is an experiment which studies scattering alpha particles on atomic nuclei. Nearly monoenergetic alpha particles (He nuclei) in a collimated beam from an source are scattered from thin foils of gold or titanium, and the intensities of the scattered alpha particles are measured with a silicon barrier detector at various scattering angles.

The energies of the incident alpha particles can be reduced by placing a gold foil in the beam. The differential scattering cross section of the target atoms is measured as a function of the angle of scattering, the energy of the particles, and the nuclear charge of the target atoms. The results are compared with the Rutherford theory of scattering by atomic nuclei.

Rutherford Scattering Lab Guide (PDF)

Rutherford, Ernest. “ The Scattering of Alpha and Beta Particles by Matter and the Structure of the Atom .” Philosophical Magazine 21 (1911): 669-688. Sixth Series.

Geiger, H. “ The Scattering of the Alpha-Particles by Matter .” Proceedings of the Royal Society of London 83, no. 565 (1910): 492-504.

Eisberg, Robert M. “The Discovery of the Atomic Nucleus.” In Fundamentals of Modern Physics. New York, NY: Wiley, 1963, pp. 87-109.

Melissinos, Adrian C. “Solid-State Particle Detectors.” In Experiments in Modern Physics. San Diego, CA: Academic Press, 1966, pp. 208-217.

———. “Rutherford Scattering.” In Experiments in Modern Physics. San Diego, CA: Academic Press, 1966, pp. 226-252.

Segre, Emilio. “The Passage of Radiations through Matter.” Chapter 2 in Nuclei and Particles. 2nd ed. Reading, MA: W. A. Benjamin, 1977, pp. 17-36. ISBN: 9780805386011.

Gasiorowiez, S. “The Born Approximation.” In Quantum Physics. 3rd ed. Hoboken, NJ: John Wiley, 2003, pp. 302-305. ISBN: 9780471429456.

———. “The Absorption of Radiation in Matter.” In Quantum Physics . 3rd ed. Hoboken, NJ: John Wiley, 2003, pp. 416-419. ISBN: 9780471429456.

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Rutherford scattering, what it shows:.

A qualitative demonstration of Rutherford's α-particle scattering experiment using magnetic pucks on an air table.

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Although designed to sit on a lecture bench, we have constructed a tripod table 70cm high so that it can be placed on the floor and be a good height for the lecturer to use. The air supply comes from two Air Source® blowers. The table should be leveled; do this by turning on the blowers and adjusting the legs until a puck sits stationary at the center.

The pucks only need a slight push—the magnets inside them are not strong and too much speed results in physical contact, which ruins the effect.

A more sophisticated setup is possible with all the technology at our disposal. A TV camera is mounted high above the air table on a fully extended tripod with its head reversed and looking down. The camera is linked to a storage oscilloscope that is adapted to behave as a television monitor (see description of the electronics in Single Photon Interference ). The pucks themselves have fluorescent markings, so the setup, when illuminated purely by UV light (4ft UV lamp fixtures duct-taped to the legs of the tripod), shows simply the pucks in space. Using the storage facility of the CRO, the track of the α-puck is recorded with text-book quality results!

1 Ealing-Daw Air Table 34-0000, Ealing Corp., Cambridge, MA

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rutherford's scattering experiment demonstrated

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rutherford's scattering experiment demonstrated

Contributed by: Enrique Zeleny   (June 20) Open content licensed under CC BY-NC-SA

rutherford's scattering experiment demonstrated

In order to get an initial distance 20 times the nuclear radius the initial position is taken as:

rutherford's scattering experiment demonstrated

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     by a thin sheet of gold foil. This experiment demonstrated that most particles passed through the foil completely undeflected, while a few were deflected at extremely large angles. This demonstrated that atoms consisted of mostly empty space with a very dense core (the ), thus debunking . , , New York: Wiley, pp. 89-95, 1985. New York: Wiley, pp. 11-14, 1987.

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Rutherford scattering.

Author: Tim & Eva

INTRODUCTION

It has been over a century since Ernest Rutherford interpreted the bizarre results of Hans Geiger and Ernest Marsden’s scattering experiments: the atom has a small hard positively charged nucleus surrounded by an electronic system – the true birth of nuclear physics! This is known as the “gold foil” experiment. Ever since reading about it in the beginning chapters of Richard Rhode’s book, Making of the Atomic Bomb , I wanted to perform this “simple” experiment for myself.

I place simple into quotes because it is far from simple. “Hindsight is 20/20,” does not apply, even though I knew what I was looking for, it took a while to find it. The principle is simple, but the experiment is tedious for the amateur when outfitted with only a small alpha source.

Having successfully performed the experiment, with all sorts of fancy nuclear instrumentation, it is now almost unbelievable that it was successfully done in 1913 in the first place! Please do not misunderstand my statement, I am not denying that these great physicists performed this experiment, I know they did, but it is amazing that they did.

Given that their initial experiments were performed manually, in again, unbelievable experimental conditions: staring with the naked eye in a dark room at faint scintillations from limited intensity alpha sources for hours, days, months on end, I now understand Geiger’s motivation for inventing the Geiger Counter and the then subsequently Lorded Rutherford’s request for a “copious supply” of charged particles (simply put, a particle accelerator). I sure wish I had a 5MeV accelerator too.

The experiment shines a thin beam of alpha particles onto an extremely thin metal foil, such as gold leaf used for gilding, and follows the path of the alpha particles passing through, more specifically, the angle that they scatter from interacting with the foil. The foil has to be of just the right thickness to present a sufficient number of atoms for the alphas to scatter off of in a reasonable amount of time, but not so thick to reduce the alpha energy below a detectable level or worse, causing the alphas come to a complete halt.

HOW THICK IS GOLD LEAF ?

Alpha particles are bare helium nuclei, and hence are relatively massive nuclear projectiles. As an energetic alpha particle enters matter, it immediately begins to interact and slow down. Over short distances, (fractions of a micrometer) the energy loss per distance traveled is linear, we can write that as dE/dx. After traversing some thickness of matter, Delta-X, the alpha particle will have lost Delta-E of energy. By measuring the initial and final energies of the alpha particle beam passing through the gold foil, we can infer the foil’s thickness.

For my version of the experiment I ordered a 100-pack of 2×2-inch squares of gold leaf from eBay for $15. There was no information on the actual thickness, or mass per unit area of sheet, so the first step was to measure the foil thickness by alpha energy attenuation. I used my Ortec Alpha King NIM-based alpha spectrometer and a low level front-surface calibration source. One-by-one, I stacked up sheets of gold leaf into a demountable cassette that I placed between the alpha source and the detector. I acquired data for as long as needed to achieve 25,000 counts under the spectral curve for each additionally layer added. The following plot is the resulting data. It is interesting to note, not only the reduction in energy, but the increased width of the spectral line.

Using NIST look-up tables for alpha particle ranges in gold (dE/dx), given in units of MeV.cm 2 /g, knowing the change in energy per sheet in MeV, and the density of gold (19.3g/cm 3 ), we can calculate the accruing thickness of the gold foil stack. There was some variation in a few sheets of the gold leaf sheets.

The alpha’s initial and final energy will be needed for analysis later on, so here is the same plot but with two different thicknesses of gold leaf foils added.

Eager to get started, I constructed the actual RBS gold foil target by using two more sheets of gold leaf, folded into quarters and stacked, producing a target 8 layers thick. I built this before I completed the previous measurement. In retrospect, I should have held off, as I then performed another thickness measurement by alpha energy shift and determined this arrangement was about 2.2um thick, too thick – most other RBS experiments use foils less than 1um thick, and as thin as 0.4um. Never the less, I proceeded to attempt the experiment with this thicker stack. It is worth noting that 7um of gold is sufficient to completely stop a 4MeV alpha particle. (Perhaps I will repeat this with a thinner foil).

SCATTERING EXPERIMENT

With exception of the gold leaf, the experimental apparatus made use of equipment and vacuum components that I have accumulated over two decades and have been lugging around ever since.

The scattering chamber is an octogonal chamber with two 6-inch con-flat (CF) ports on the top and bottom, and eight 2.75-inch CF ports on the side placed in 45-degree increments. Starting at the “3 o’clock” position in the above photo and rotating clock-wise the arrangement of the chamber is as follows: vacuum pumping port, with two valves in series to slowly pump the chamber so as not to rip the gold foil during pump down. Next, a variable leak valve for slowly bleeding up to atmosphere when venting the chamber, again, so as not to rip the gold. A CF blank directly facing us. Next a 2.75CF viewport, with it’s dark cover in place. Then, the alpha detector arm. Behind that is a lead shielded NaI(Tl) detector from the previous 237 Np alpha-gamma coincidence experiment. In the back, another CF blank, and finally, a Pirani vacuum gauge sensor. The top of the chamber is outfitted with a load-lock door, and the bottom has a linear-and-rotary motion feed through for positioning the foil-source structure.

I decided to mount the alpha particle “beam” and gold foil “target” assembly together in a fixed framework that would rotate with respect to the alpha detector. This is very similar to the 1913 Geiger-Marsden setup (had I a larger chamber, I would have liked to make the rotation of the source, the foil, and the detector(s) all independent). The alpha source is mounted to a stainless steel Kimball Physics eV square plate having an aperture in the center. A cajon stainless steel pipe fitting was spot welded to the other side of the stainless steel plate, creating the beam collimator: the source active diameter is 0.1 inches, the inside diameter of the collimator is 0.19 inches, and its length is about 1.32 inches long, creating a source divergence cone of 12.3 degrees.

A shaft was mounted to the bottom of the foil target and alpha beam assembly such that it would rotate about the centerline of the gold foil cassette. It was connected to the linear/rotary motion feed through and vertically adjusted to be centered in the chamber.

The alpha detector is an Ortec Si Surface Barrier Detector. At first I tried to improve the angular width by placing a slit on the face of the detector, making its azimuthal width about 2.5 degrees. The slits were removed since, as we will see, the alpha beam divergence itself was large, and the slits only reduced the counting rate without much benefit to angular resolution.

Two rotational scans were made without the target foil in place to determine the angular profile of the alpha “beam.” Clearly, without the slit on the detector face, the alpha beam was detectable as wide as +/- 12.5 degrees, which closely matched the expectation, the source divergence calculated to be 12.3 degrees, and the detector azimuthal “width” was also estimated to be 12.5 degrees, so edge-to-edge it is reasonable to see the width to be the sum of these two angle, or ~25 degrees (the black trace), The red trace is with the slit, of 2.5 degree width, would be 5 degrees summed with 12.3 degrees, or 17 degrees total.

The no-foil beam width set the limits of small angle scattering to start at +/-17 degrees. The foil cassette was placed into the target-source structure and scattering acquisition commenced. The first data collected was at 0 degrees, head on, so as to set the MCA’s region of interest (ROI) to the lowered alpha energy peak. Only the events in this ROI are counted as scattering events. Since the scattering is considered inelastic, and the disparate masses of the alpha (4) and the gold (197), the alpha will lose an imperceptible amount from the actual scattering event, arriving at the detector with almost it full energy (less the dE/dx loss), allowing scattered signal to be isolated from background “noise.”

First, the source-foil structure was aligned with the detector (0-degrees) to be able to set up the region of interest:

Then the alpha scattering was measured at four angles, 17, 22, 27, and 32 degrees. As describe earlier, it would make little sense to measure less than 17 degrees, and 32 degrees found the limits of my patience (aka impatience). Due to the exponentially falling scattering probability with increased angle, acquisition took over 2 days to accumulate a mere 500 events at 32 degrees.

A measurement at 37 degrees took about 10 days, and has been added to the final data plot below. The five measurements, expressed as the differential scattering cross section, reasonably matches the theoretical trend. The absolute numbers on average fall below the calculate theoretical curve up to a factor of two. This I do not understand yet, but will continue to refine the measurement.

Conclusion, with enough time and surplus equipment, one can “bounce” alpha particles off of the nuclei of heavy atoms for themselves.

This has been one of the more rewarding amateur nuclear projects for me, not only because it was the defining nuclear experiment of probing the nucleus, but because I struggled to find what I know I was looking for. This in turn has given me an even deeper respect for Rutherford, Geiger, and Marsden’s research abilities. And especially for young Rutherford, who had to stand up against convention and let the scientific data be his confidence when breaking the news to the world.

Rutherford Scattering ( AQA A Level Physics )

Revision note.

Katie M

Rutherford Scattering

  • Evidence for the structure of the atom was discovered by Ernest Rutherford at the beginning of the 20th century from the study of alpha particle scattering
  • The different angles of deflection of the alpha particles
  • The number of alpha particles that were deflected at each angle

Apparatus for the Rutherford Scattering Experiment

  • A source of alpha particles in a lead container
  • A thin sheet of gold foil
  • A movable detector 
  • An evacuated chamber

Alpha particle experiment diagram, downloadable AS & A Level Physics revision notes

Experimental set up for α-particle scattering

Purpose of the lead container

  • Alpha particles are emitted in all directions, so the source was placed in a lead container
  • This was to produce a collimated beam of alpha particles
  • This is because alpha particles are absorbed by lead, so a long narrow hole at the front allowed a concentrated beam of alpha particles to escape and be directed as needed

Purpose of the thin sheet of gold foil

  • The target material needed to be extremely thin , about 10 −6 m thick
  • This is because a thicker foil would stop the alpha particles completely
  • Gold was chosen due to its malleability , meaning it was easy to hammer into thin sheets

Purpose of the evacuated chamber

  • Alpha particles are highly ionising, meaning they only travel about 5 cm before interacting with molecules of air
  • So, the apparatus was placed in an evacuated chamber
  • This was to ensure that the alpha particles did not collide with any particles on their way to the foil target

Findings from the Rutherford Scattering Experiment

  • An alpha (α) particle is the nucleus of a helium atom, so it has a positive charge

Alpha particle scattering, downloadable AS & A Level Physics revision notes

When α-particles are fired at thin gold foil, most of them go straight through but a small number bounce straight back

  • The observations from Rutherford's experiment were:

A. The majority of α-particles passed straight through the foil undeflected

  • This suggests the atom is mostly empty space

B. Some α-particles deflected through small angles of <10°

  • This suggests there is a positive nucleus at the centre (since two positive charges would repel)

C. Only a small number of α-particles deflected straight back at angles of >90°

  • This suggests the nucleus is extremely small and is where most of the mass and charge of the atom are concentrated
  • This led to the conclusion that atoms consist of small, dense positively charged nuclei surrounded by negatively charged electrons

Atomic Structure, downloadable AS & A Level Physics revision notes

An atom: a small positive nucleus, surrounded by negative electrons

  • Note: The atom is around 100,000 times larger than the nucleus!

Worked example

In an α-particle scattering experiment, a student set up the apparatus below to determine the number n of α-particle incident per unit time on a detector held at various angles θ.

WE - Rutherford scattering question image 1, downloadable AS & A Level Physics revision notes

Which of the following graphs best represents the variation of n with θ from 0 to 90°?

WE - Rutherford scattering question image 2, downloadable AS & A Level Physics revision notes

     ANSWER:   A

  • The Rutherford scattering experiment directed parallel beams of α-particles at gold foil
  • Most of the α-particles went straight through the foil
  • The largest value of n will therefore be at small angles
  • Some of the α-particles were deflected through small angles
  • n drops quickly with increasing angle of deflection θ
  • These observations fit with graph A

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Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

  • Chemistry Class 9 Notes
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  • Analytical Chemistry
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  • Chemical Compounds
  • Chemical Formula
  • Real life Application of Chemistry
  • Chemistry Class 8 Notes
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Chapter 1: Matter in our Surroundings

  • Matter is Made of Tiny Particles
  • Why Solids, Liquids and Gases Have Different Properties
  • Classification of Matter
  • Brownian Movement
  • States of Matter: Solid, Liquid, Gas and Plasma
  • Evaporation
  • Effects of Relative Humidity and Wind Speed
  • How Does Evaporation Cause Cooling?
  • Effect of Change of Temperature
  • Melting Point
  • What is Vaporization?
  • Condensation
  • Effects of Change of Pressure
  • Difference between Rigidity and Fluidity of Matter
  • Prove That Liquids have No fixed Shape but have a Fixed Volume
  • Diffusion in Solids, Liquids, and Gases
  • What is the Unit of Temperature?
  • What is the Relationship Between Celsius and Kelvin Scale of Temperature?
  • Liquification of Gases
  • How to demonstrate the Presence of Water Vapour in Air?
  • What is Plasma and Bose-Einstein Condensate?

Chapter 2: Is Matter Around Us Pure?

  • Solution: Properties of Solution
  • Saturated and Unsaturated Solutions
  • Concentration of a Solution
  • Suspensions
  • How will you distinguish a Colloid from a Solution?
  • Classification of Colloids
  • Tyndall Effect
  • Separation of Mixtures
  • How to separate a Mixture of Two Solids?
  • Separation by a suitable solvent
  • Separation of Mixtures using Sublimation and Magnets
  • How to Separate a Mixture of a Solid and a Liquid?
  • Filtration: Definition, Process, Diagram and Examples
  • Water Purification
  • Centrifugation
  • How to Separate Cream from milk?
  • Difference Between Homogeneous and Heterogeneous Mixture
  • Difference Between Compound and Mixture
  • Factors affecting Solubility
  • Separation by Evaporation
  • Crystallization
  • Chromatography
  • Distillation
  • Separation of Mixtures of Two or More Liquids
  • Fractional Distillation
  • Pure and Impure Substances
  • What is an Element?
  • Metals, Non-Metals and Metalloids
  • Properties of Metals and Non-Metals

Chapter 3: Atoms and Molecules

  • Laws of Chemical Combination
  • Law of Conservation of Mass
  • Verification of the Law of Conservation of Mass in a Chemical Reaction
  • Law of Constant Proportions
  • What is Atom?
  • Atomic Mass
  • How Do Atoms Exist?
  • Cations vs Anions
  • What are Ionic Compounds?
  • What are Monovalent Ions?
  • What are Divalent Ions?
  • Trivalent Ions - Cations and Anions
  • Polyatomic Ions
  • Formulas of Ionic Compounds
  • Chemical Formula of Common Compounds
  • Molecular Mass
  • Mole Concept
  • Problems Based on Mole Concepts
  • Dalton's Atomic Theory
  • Drawbacks of Dalton's Atomic Theory
  • Significance of the Symbol of Elements
  • Difference Between Molecules and Compounds
  • How to Calculate Valency of Radicals?
  • What is the Significance of the Formula of a Substance?
  • Gram Atomic and Gram Molecular Mass

Chapter 4: Structure of the Atom

  • Charged Particles in Matter
  • Thomson's Atomic Model

Rutherford Atomic Model

  • Drawbacks of Rutherford's Atomic Model
  • Bohr's Model of an Atom
  • Valence Electrons
  • Mass Number
  • Relation Between Mass Number and Atomic Number
  • Why do all the Isotopes of an Element have similar Chemical Properties?
  • Why Isotopes have different Physical Properties?
  • What is Fractional Atomic Mass?
  • Radioactive Isotopes
  • Discovery of Electrons
  • What is a Proton?
  • Rutherford's Alpha Scattering Experiment
  • Atomic Nucleus
  • How did Neil Bohr explained the Stability of Atom?
  • Electron Configuration
  • Potassium and Calcium - Atomic Structure, Chemical Properties, Uses
  • What is meant by Chemical Combination?
  • Difference between Electrovalency and Covalency

Rutherford’s Alpha Scattering Experiment

Rutherford’s Alpha Scattering Experiment is the fundamental experiment done by Earnest Rutherford’s Alpha Scattering Experiment that gives the fundamental about the structure of the atom. Rutherford in his experiment directed high-energy streams of α-particles from a radioactive source at a thin sheet (100 nm thickness) of gold. Then the deflection of these alpha particles tells us about the structure of atoms.

In this article, we will study about constituents of atoms, Rutherford’s  Alpha Scattering Experiment,

What are Constituents of an Atom?

An atom consists of Electrons, Protons, and Neutrons are the fundamental particles or sub-atomic particles that build the structure of an atom. Let us understand each term.

  • Electron: In 1897, J. J. Thomson discovered negatively charged particles towards the anode, these rays are emitted by the cathode in a cathode ray experiment. Then these negatively charged particles are proposed as Electrons .
  • Protons: In 1886, Ernest Goldstein discovered that an anode emitted positively charged particles with a different condition in the same tube,  known as Canal rays or as Protons .
  • Neutrons: A subatomic particle with no charge and a mass equivalent to protons in the nucleus of all atoms was discovered by J. Chadwick. These neutrally charged particles are termed Neutrons .

The image added below shows the structure of an atom.

Learn more about, Atomic Structure

Structure-of-Atom

Structure of Atom

Isotopes are the elements that have the same atomic number but different mass. e.g. Isotopes of the Hydrogen atoms are Protium ( 1 H 1 ), Deuterium ( 2 H 1 ) and Tritium( 3 H 1 ). Isotopes of the Carbon atoms are 12 C 6 , 13 C 6 , 14 C 6 .

Isobars are the elements that have different atomic number but have same mass number. e.g. 19 K 40 , 18 Ar 40 , 20 Ca 40 , here all the elements having same mass number hence they are isobars.

He conduct an experiment by bombarding alpha particles into a thin sheet of gold and then notices their interaction with the gold foil and trajectory or path followed by these particles.

Rutherford's Alpha Scattering Experiment

In the experiment, Rutherford passes very high streams of alpha-particles from a radioactive source i.e. alpha-particle emitter, at a thin sheet of100 nm thickness of gold. In order to examine the deflection produced by the alpha particles, he placed a screen of fluorescent zinc sulphide around the thin gold foil. Rutherford made certain observations that oppose Thomson’s atomic model.

Observations of Rutherford’s Alpha Scattering Experiment

The observations of Rutherford’s Alpha Scattering Experiment are:

  • First, he observe that most of the α-particles that are bombarded towards the gold sheet pass away the foil without any deflection, and hence it shows most of the space is empty.
  • Out of all, some of the α-particles were deflected through the gold sheet by very small angles, and hence it shows the positive charge in an atom is non-uniformly distributed. The positive charge is concentrated in a very small volume in an atom.
  • Very few of the alpha-particles(1-2%) were deflected back, i.e. only a very less amount of α-particles had nearly 180° angle of deflection. this shows that the volume occupied by the positively charged particles is very small as compared to the total volume of an atom.

Rutherford proposed the atomic structure of elements, on the basis of his experiment. According to Rutherford’s atomic model:

  • Positively charged particle was concentrated in an extremely small volume and most of the mass of an atom was also in that volume. He called this a nucleus of an atom.
  • Rutherford proposed that there is negatively charged electrons around the nucleus of an atom. the electron surrounding the nucleus revolves around it in a circular path with very high speed. He named orbits to these circular paths.
  • Nucleus being a densely concentrated mass of positively charged particles and electrons being negatively charged are held together by a strong force of attraction called electrostatic forces of attraction.

Learn about, Rutherford Atomic Model

Limitations of Rutherford Atomic Model

The Rutherford atomic model is failed to explain certain things.

  • According to Maxwell, an electron revolving around the nucleus should emit electromagnetic radiation due to accelerated charged particles emit electromagnetic radiation. but Rutherford model says that the electrons revolve around the nucleus in fixed paths called orbits. The radiation would carry energy from the motion which led to the shrinking of orbit. Ultimately electrons would collapse inside the nucleus.
  • As per the Rutherford model, calculations have shown that an electron would collapse in the nucleus in less than 10 -8 seconds. So Rutherford model has created a high contradiction with Maxwell’s theory and Rutherford later could not explain the stability of an atom.
  • Rutherford also did not describe the arrangement of electrons in the orbit as one of the other drawbacks of his model.

Regardless of seeing the early atomic models were inaccurate and failed to explain certain experimental results, they were the base for future developments in the world of quantum mechanics.

Sample Questions on Rutherford’s Alpha Scattering Experiment

Some sample questions on Rutherford’s Alpha Scattering Experiment is,

Q1: Represent Element ‘X’ which contains 15 electrons and 16 neutrons.

Atomic number of element = No. of electron = 15 Mass number of element = no. of electrons + no. of neutrons = 15 + 16 = 31 Correct representation of element X is 31 X 15 .

Q2: Name particle and give its location in the atom which has no charge and has a mass nearly equal to that of a proton.

The particle which has no charge and has a mass nearly equal to that of a proton is a neutron and it is present in the nucleus of the atom.

Q3: An atom has both electron attribute negative charge and protons attribute positive charge but why there is no charge?

Positive and negative charges of protons and electrons are equal in magnitude, they cancel the effect of each other. So, the atom as a whole is electrically neutral.

Q4: What is Valency of Sodium Atom (Na)?

The atomic number of sodium = 11. Electronic configuration (2, 8, 1). By losing one electron it gains stability hence its valency is 1.

Q5: Which property do the following pairs show? 209 X 84 and 210 X 84

Atomic number of X is the same hence the pair shows an isotopic property. So, 209 X 84 and 210 X 84 are isotopes.
Dalton’s Atomic Theory Thomson’s Atomic Model Quantum Numbers

Rutherford’s Alpha Scattering Experiment FAQs

What is name of atom which has one electron, one proton and no neutron.

Atom with one electron, one proton and no neutron is Hydrogen, ( 1 H 1 ).

What is Ground State of an Atom?

It is the state of an atom where all the electrons in the atom are in their lowest energy state or levels is called the ground state.

What was Rutherford’s Alpha Particle Scattering Experiment?

Rutherford’s Alpha Particle Scattering Experiment is the fundamental experiment that gives the basic structure of an atom.

What was Conclusion of Rutherford’s Alpha Scattering Experiment?

Conclusion of Rutherford’s Alpha Scattering Experiment is, Atom is largely empty and has a heavy positive-charged body at the center called the nucleus. The central nucleus is positively charged and the negatively-charged electrons revolve around the nucleus.

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  1. Rutherford scattering experiments

    A replica of an apparatus used by Geiger and Marsden to measure alpha particle scattering in a 1913 experiment. The Rutherford scattering experiments were a landmark series of experiments by which scientists ... This too caused the patch of light on the screen to become more spread out. This experiment demonstrated that both air and solid ...

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  3. Rutherford model

    The nucleus was postulated as small and dense to account for the scattering of alpha particles from thin gold foil, as observed in a series of experiments performed by undergraduate Ernest Marsden under the direction of Rutherford and German physicist Hans Geiger in 1909. A radioactive source emitting alpha particles (i.e., positively charged particles, identical to the helium atom nucleus and ...

  4. PDF The Rutherford Scattering Experiment

    The scattering foil is an annulus located coaxially with the α-source and detector with inner and outer diameters, 46.0 and 56.7 mm respectively. The angle βis determined by a fixed distance from source to scattering foil. The scattering angle θis varied by changing the distance from the scattering plane to the plane of the detector.

  5. Rutherford Scattering

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  6. PDF Rutherford Scattering Lab Guide

    Rutherford showed [4] that the fraction of parti-cles scattered in thiswaythroughanangle θ or greater should decrease exponentially according to the equation. where θm is the mean multiple scattering angle. For a typical foil of gold leaf, θm ≈ 1 . Thus at θ = 30 , one finds Fθ on the order of exp(−30) or 10−13 .

  7. PDF The Rutherford Scattering Experiment

    of historical interest, but serves to demonstrate how scattering experiments provide the physicist with a powerful investigative technique. The essential idea of Rutherford's theory is to consider the -particle as a charged mass traveling according to the classical equations of motion in the Coulomb field of a nucleus. The dimensions

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  9. ‪Rutherford Scattering‬

    How did Rutherford discover the nucleus of the atom? Play with this simulation and see how alpha particles scatter off atoms.

  10. PhET: Rutherford Scattering

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  11. Rutherford Scattering

    Description. Rutherford scattering experiment equipment. This is an experiment which studies scattering alpha particles on atomic nuclei. Nearly monoenergetic alpha particles (He nuclei) in a collimated beam from an source are scattered from thin foils of gold or titanium, and the intensities of the scattered alpha particles are measured with a silicon barrier detector at various scattering ...

  12. Rutherford Scattering -- from Eric Weisstein's World of Physics

    The scattering of alpha particles by a thin sheet of gold foil. This experiment demonstrated that most particles passed through the foil completely undeflected, while a few were deflected at extremely large angles. This demonstrated that atoms consisted of mostly empty space with a very dense core (the nucleus), thus debunking Thomson's plum pudding model.

  13. Rutherford Scattering

    Simulate the famous experiment in which he disproved the Plum Pudding model of the atom by observing alpha particles bouncing off atoms and determining that they must have a small core. How did Rutherford figure out the structure of the atom without being able to see it? Simulate the famous experiment in which he disproved the Plum Pudding ...

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    Video transcript. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

  16. 3.4: Rutherford's Experiment- The Nuclear Model of the Atom

    In 1911, Rutherford and coworkers Hans Geiger and Ernest Marsden initiated a series of groundbreaking experiments that would completely change the accepted model of the atom. They bombarded very thin sheets of gold foil with fast moving alpha particles. Figure 3.4.2 3.4. 2 (a) The experimental setup for Rutherford's gold foil experiment: A ...

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    Scattering. Copying... Rutherford's classic experiment consisted in bombarding a thin gold foil with particles (helium nuclei). He expected that some particles would be slightly deflected by the positive charge inside the atoms. Most went through without much change, some were deflected, and surprisingly, some came straight back.

  18. Solved Rutherford's scattering experiment demonstrated A ...

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