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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.

Rutherford model

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

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 .

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.

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 .

• Structure of Atom
• Rutherford Atomic Model And Its Limitations

Rutherford Atomic Model and Limitations

Define rutherford atomic model.

Rutherford Atomic Model – The plum pudding model given by J. J. Thomson failed to explain certain experimental results associated with the atomic structure of elements. Ernest Rutherford, a British scientist conducted an experiment and based on the observations of this experiment, he explained the atomic structure of elements and proposed Rutherford’s Atomic Model.

Table of Contents

• Rutherfords Alpha Scattering Experiment

Observations of Rutherford’s Alpha Scattering Experiment

Rutherford atomic model, limitations of rutherford atomic model, recommended videos, frequently asked questions – faqs.

Rutherford’s Alpha Scattering Experiment

Rutherford conducted an experiment by bombarding a thin sheet of gold with α-particles and then studied the trajectory of these particles after their interaction with the gold foil.

Rutherford, in his experiment, directed high energy streams of α-particles from a radioactive source at a thin sheet (100 nm thickness) of gold. In order to study the deflection caused to the α-particles, he placed a fluorescent zinc sulphide screen around the thin gold foil. Rutherford made certain observations that contradicted Thomson’s atomic model .

The observations made by Rutherford led him to conclude that:

• A major fraction of the α-particles bombarded towards the gold sheet passed through the sheet without any deflection, and hence most of the space in an atom is empty .
• Some of the α-particles were deflected by the gold sheet by very small angles, and hence the positive charge in an atom is not uniformly distributed . The positive charge in an atom is concentrated in a very small volume .
• Very few of the α-particles were deflected back, that is only a few α-particles had nearly 180 o angle of deflection. So the volume occupied by the positively charged particles in an atom is very small as compared to the total volume of an atom .

Based on the above observations and conclusions, Rutherford proposed the atomic structure of elements. According to the Rutherford atomic model:

• The positive charge and most of the mass of an atom is concentrated in an extremely small volume. He called this region of the atom as a nucleus.
• Rutherford’s model proposed that the negatively charged electrons surround the nucleus of an atom. He also claimed that the electrons surrounding the nucleus revolve around it with very high speed in circular paths. He named these circular paths as orbits.
• Electrons being negatively charged and nucleus being a densely concentrated mass of positively charged particles are held together by a strong electrostatic force of attraction.

Although the Rutherford atomic model was based on experimental observations, it failed to explain certain things.

• Rutherford proposed that the electrons revolve around the nucleus in fixed paths called orbits. According to Maxwell, accelerated charged particles emit electromagnetic radiations and hence an electron revolving around the nucleus should emit electromagnetic radiation. This radiation would carry energy from the motion of the electron which would come at the cost of shrinking of orbits. Ultimately the electrons would collapse in the nucleus. Calculations have shown that as per the Rutherford model, an electron would collapse into the nucleus in less than 10 -8 seconds. So the Rutherford model was not in accordance with Maxwell’s theory and could not explain the stability of an atom .
• One of the drawbacks of the Rutherford model was also that he did not say anything about the arrangement of electrons in an atom which made his theory incomplete.
• Although the early atomic models were inaccurate and failed to explain certain experimental results, they formed the base  for future developments in the world of quantum mechanics .

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The Gold Foil Experiment

Structure of Atom Class 11 Chemistry

Drawbacks of Rutherford Atomic Model

What was the speciality of Rutherford’s atomic model?

Rutherford was the first to determine the presence of a nucleus in an atom. He bombarded α-particles on a gold sheet, which made him encounter the presence of positively charged specie inside the atom.

What is Rutherford’s atomic model?

Rutherford proposed the atomic structure of elements. He explained that a positively charged particle is present inside the atom, and most of the mass of an atom is concentrated over there. He also stated that negatively charged particles rotate around the nucleus, and there is an electrostatic force of attraction between them.

What are the limitations of Rutherford’s atomic model?

Rutherford failed to explain the arrangement of electrons in an atom. Like Maxwell, he was unable to explain the stability of the atom.

What kind of experiment did Rutherford’s perform?

Rutherford performed an alpha scattering experiment. He bombarded α-particles on a gold sheet and then studied the trajectory of these α-particles.

What was the primary observation of Rutherford’s atomic model?

Rutherford observed that a microscopic positively charged particle is present inside the atom, and most of the mass of an atom is concentrated over there.

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I am very happy with the answer that I obtained, however Ernest Rutherford’s Atomic Model never had any neutrons in the nucleus. James Chadwick discovered the neutron later in 1932. However, the limitations and observations of his theory on this web page seem to be correct.

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Experimental physics i & ii "junior lab", 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 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.

Selected Resources

Stopping Power and Range Tables for Helium Ions

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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.

Rutherford Experiment and Atomic Collisions

Claimed by: Lia McSweeney (Fall 2023)

• 1.1 A Mathematical Model
• 1.2 A Computational Model
• 2.2 Middling
• 2.3 Difficult
• 3 Connectedness
• 5.1 Further Reading
• 5.2 External Links
• 6 References

The Main Idea

Rutherford's Gold Foil Experiment helped detect that there was a large positively charged mass in the center of an atom: the nucleus. The experiment was done through the use of atomic collisions. Under the instruction of Rutherford, Hans Geiger and Ernest Marsden pointed a beam of alpha particles at a thin foil of metal and measured the scattering pattern by using a fluorescent screen. The scientists noted that some alpha particles bounced in random directions. This was not originally hypothesized due to the idea that, at most the alpha particle should experience only a 90° scattering angle. This helped lead to the discovery of the nucleus and a highly compact positively charged center.

Rutherford studied the particles that uranium and its derivatives emitted and how these particles affected certain materials. Rutherford created a method to record the position of each alpha particle by circling the bombarded object with a ZnS coated sheet. This sheet would emit a flash of light when hit by an alpha particle, allowing Rutherford to accurately measure the deflection of each alpha particle. This gave Rutherford a counting mechanism for theses particles he wanted to study. Rutherford then began to study the angles that negatively charged particles deflected when they collided with a thin metal foil. This was the beginning of his most famous study: the gold foil experiment. Knowing the relative mass of these negatively charged particles and their quick speed, he hypothesized that they would pierce the metal foil but then collide with the atoms dispersed inside the foil resulting in the small deflections. These deflections were extremely small, usually by a degree. In 1911, Ernest Rutherford took this experiment further and worked with his assistants, Hans Geiger and Ernest Marsden, to carry out an experiment that tested the plum pudding model. They shot alpha (helium 2+) particles at gold foil in order to measure the deflection of the particles as they come off of the other side. They decided to see if these deflections could occur at larger angles greater than 90 degrees. Through countless trials, they found an extremely small portion of these deflections to occur at angles larger than 90 degrees. Rutherford wondered how these large deflections occurred and concluded that there existed an extremely small and positively charged area in the atom that resulted in these huge deflections. He eventually named this area the nucleus. What happened during these deflections was that most particles would become slightly deflected by small angles due to the positive atoms. However, some would collide directly with nucleus resulting in the deflections that were greater than 90 degrees. These occurred rarely because the nucleus was such a small size so the probability of these atoms hitting the nucleus was very low. This experiment helped indicate that the atom is made predominantly of empty space with a small nucleus with protons and electrons placed extremely far away from the nucleus in their own cloud. Rutherford devised the name “proton” to describe the positive particles in the nucleus. He thought that a neutral particle existed in the nucleus too, but its existence wasn’t confirmed until 1932 when James Chadwick proved it.

A Mathematical Model

Rutherford modeled the effect the alpha particle has on the electrons of the gold atom. He did this by calculating the potential electric energy between the particle and the atom using the formula below. Rutherford came up with several equations to numerically describe these deflections. Based on the equations below, the number of particles scattered at a certain angle is directly proportional to the thickness of the metal foil and the square of the nucleus’ charge but inversely proportional to the particle’s velocity raised to the fourth power.

[math]\displaystyle{ {U_{elec}} = {\frac{1}{4πε_0}}{\frac{q_{α}q_{Au}}{r}} }[/math]

r = center to center distance between particle and atom

[math]\displaystyle{ {\frac{1}{4πε_0}} = {9*10^9}{\frac {N*m^2}{C^2}} }[/math]

[math]\displaystyle{ {q_α} }[/math] = charge of alpha particle

[math]\displaystyle{ {q_{Au}} }[/math] = charge of gold nucleus

In this instance the charge of the alpha particle is equal to 2e and the charge of the gold particle is equal to 79e.

Another important part of atomic collisions is that they are inelastic collisions. This is shown by the conservation of both momentum and kinetic energy. Take the alpha particle and gold particle for example.

[math]\displaystyle{ {\vec{p_{α,i}}} = {\vec{p_{α,f}}}+ {\vec{p_{Au,f}}} }[/math]

[math]\displaystyle{ {\vec{K_{α,i}}} = {\vec{K_{α,f}}}+ {\vec{K_{Au,f}}} }[/math]

Where [math]\displaystyle{ {\vec{p}} }[/math] is momentum and [math]\displaystyle{ {\vec{K}} }[/math] is kinetic energy.

A Computational Model

Much like the mathematical model, the collision can be modeled computationally using the same formulas. Here is a video of a VPython mode of a continuous stream of alpha particles with exaggerated interaction for easy viewing:

Example Problems

The scattering of alpha particles from nuclei is mathematically modeled from the Coulomb force and treated as an orbit. For a ZnS detector at a specific angle with respect to the incident beam, the number of particles per unit area striking the detector is given by the Rutherford formula: [math]\displaystyle{ N(θ) = {\frac{N_inLZ^2k^2e^4}{4r^2KE^2sin^4(θ/2)}} }[/math] where [math]\displaystyle{ N_i = \text {number of incident alpha particles} }[/math] [math]\displaystyle{ n = \text {atoms per unit volume in target} }[/math] [math]\displaystyle{ L = \text {thickness of target} }[/math] [math]\displaystyle{ Z = \text {atomic number of target} }[/math] [math]\displaystyle{ e = \text {electron charge} }[/math] [math]\displaystyle{ k = \text {Coulomb's constant} }[/math] [math]\displaystyle{ r = \text {target to detector distance} }[/math] [math]\displaystyle{ KE = \text {kinetic energy of alpha} }[/math] [math]\displaystyle{ θ = \text {scattering angle} }[/math]

Find the number of particles per unit area striking the detector given the following values: [math]\displaystyle{ N_i = 5 }[/math] alpha particles [math]\displaystyle{ n = 8.4866 * 10^{22} \text {atoms in 1} cm^3 }[/math] [math]\displaystyle{ L = 1 cm }[/math] [math]\displaystyle{ Z = 26 }[/math] [math]\displaystyle{ e = -1 }[/math] [math]\displaystyle{ k = 8.988 * 10^9 }[/math] [math]\displaystyle{ r = 10 cm }[/math] [math]\displaystyle{ KE = (1/2)*m*v^2 }[/math] where [math]\displaystyle{ v_a = 1.53 * 10^7 m/s \text {and mass of the alpha particle is} 6.64424*10^27 kg }[/math] [math]\displaystyle{ θ = 0.18 degrees }[/math]

Plug each number into the equation (make sure units cancel).

[math]\displaystyle{ N(0.18) = {\frac{5*8.4866*10^{22}*1*26^2*{(8.988*10^9)}^2*-1^4}{4*10^2*{((1/2)(6.64424*10^27){(1.53*10^-7)}^2)}^2*sin^4(0.18/2)}} }[/math]

= 1.57341 * 10^27 particles striking the surface per cm

Rutherford found that the fraction of particles scattered at an angle [math]\displaystyle{ θ }[/math] or greater can be modeled by the equation [math]\displaystyle{ F_{θ} ≈ e^{(−θ/θ^2_m)} }[/math] . At what angle would Rutherford have found a fraction of [math]\displaystyle{ 10^{45} }[/math] particles to be at that angle or greater than? ( [math]\displaystyle{ θ_m ≈ 1 }[/math] for a gold leaf foil)

Using the formula [math]\displaystyle{ F_{θ} ≈ e^{(−θ/θ^2_m)} }[/math] , we can rearrange to solve for θ by taking the log of both sides:

[math]\displaystyle{ log(F_{θ}) = −θ/θ^2_m }[/math]

Then, we can multiple by [math]\displaystyle{ -θ^2_m }[/math] to find:

[math]\displaystyle{ θ = −(θ^2_m)log(F_{θ}) }[/math]

Plugging in the given information, [math]\displaystyle{ θ = −(1^2)log(10^{45}) = 45 }[/math] . Therefore, a fraction of [math]\displaystyle{ 10^{45} }[/math] particles are scattered at about an angle of 45 degrees or greater.

A proton and an electron are a distance [math]\displaystyle{ {7.2*10^{-9}m} }[/math] apart. What is the electric potential energy of the system consisting of the proton and the electron?

[math]\displaystyle{ {U_{elec}} = {\frac{1}{4πε_0}}{\frac{q_{+}q_{-}}{r}} }[/math]

[math]\displaystyle{ {U_{elec}} = {9*10^{9}}{\frac {N*m^2}{C^2}}*{\frac{1.6*10^{-19}*(-1.6*10^{-19})}{7.2*10^{-9}}} = {-3.2*10^{-28}}{J} }[/math]

Connectedness

This topic is related to the study of chemical engineering. Without the discovery of the nucleus, any progress in this field would be limited based on the interaction of atomic particles. This would also hinder the medical field for very similar reason. Much of the understanding of sciences has its roots in the understanding of the atom and its functions. This experiment and the idea of atomic collisions helped to widen the atomic grasp. One of the best industrial examples of atomic collisions is the Large Hadron Collider.

Around the early 1900s, very little was known about atoms besides the ground breaking experiments conducted by J.J. Thompson in 1897. Thompson discovered what we call the electron. He hypothesized that electrons were negatively charged particles. It was also speculated that there must be a positive charge to balance out the negative charge from the electron. This "Plum Pudding Model" was invented by Thompson. This model assumed that matter consists of atoms which are overall positively charged, but with some type of negative electron charge throughout it. The electrons function as the "plum" which was evenly distributed through a positively charged "pudding".

With the knowledge of the plum pudding model of the atom, Ernst Rutherford and a small group of scientists set out to discover the properties behind alpha particles. The experiment, now known as the Gold Foil Experiment, was used to test this in 1911. It involved launching alpha particles at a small piece of gold foil. It was hypothesized that the alpha particle would be deflected at times, but at an angle because it was assumed that the alpha particle was more dense than the gold foil atom. They registered deflected particles through light emissions that would occur when the alpha particle hit the light source. Much to their surprise, some of the alpha particles they launched bounced straight back. This demonstrated that the gold particle was more massive than expected. It led to the discovery that the atom contained a positively charged nucleus. This was a major break through in the study of the atom in that it showed what the atom's composition was and how it act around other atoms.

Collisions is a related helpful page to get a foundation in collisions. Elastic Collisions and Inelastic Collisions are also useful, and Scattering: Collisions in 2D and 3D takes a broader look at the principles involved in the Rutherford Experiment.

Further Reading

Another page on Rutherford's Experiment.

External Links

MIT video of an experiment confirming Rutherford's model.

Chabay, R.W., & Sherwood, B.A. (2015). Collisions. In Fiorillo, J. Editor & Rentrop, A. Editor (Eds.), Matter and Interactions (383-410). John Wiley & Sons, Inc.

“Ernest Rutherford.” New Page 2, chemed.chem.purdue.edu/genchem/history/gold.html.

"History of Rutherford Experiment". HyperPhysics. Web. 03 Dec. 2015. Retrieved from: < http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html >.

“Rutherford Scattering.” MIT OpenCourseWare, MIT Department of Physics , ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2016-spring-2017/experiments/rutherford-scattering/MIT8_13-14F16-S17exp15.pdf.

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Syllabus Edition

First teaching 2014

Last exams 2024

Rutherford Scattering & Nuclear Radius ( DP IB Physics: HL )

Revision note.

Rutherford Scattering & Nuclear Radius

• In the Rutherford scattering experiment, alpha particles are fired at a thin gold foil
• Initially, before interacting with the foil, the particles have kinetic energy, 
• Some of the alpha particles are found to come straight back from the gold foil
• This indicates that there is electrostatic repulsion between the alpha particles and the gold nucleus

Experimental set up of the Rutherford alpha scattering experiment

• At this point, the initial kinetic energy of an alpha particle, E k , is equal to electric potential energy, E p
• The radius of the closest approach can be found be equating the initial kinetic energy to the electric potential energy
• Charge of an alpha particle, Q = 2e
• Charge of a target nucleus, q = Ze
• Z = proton number
• e = charge on an electron (or proton)
• Substituting into the equation:
• This gives an expression for the potential energy at the point of repulsion:
• This expression also gives the initial kinetic energy possessed by the alpha particle
• Rearranging and calculating for the distance, d , gives a value for the radius of the nucleus when the alpha particle is fired with high energy

The closest approach method of determining the size of a gold nucleus

Nuclear Radius

• The radius of nuclei depends on the nucleon number,  A  of the atom
• This makes sense because as more nucleons are added to a nucleus, more space is occupied by the nucleus, hence giving it a larger radius
• The exact relationship between the radius and nucleon number can be determined from experimental data
• By doing this, physicists were able to deduce the following relationship:

• R = nuclear radius (m)
• A = nucleon / mass number
• R 0 = constant of proportionality = 1.20 fm

Nuclear Density

• Assuming that the nucleus is spherical, its volume is equal to:

• Where R is the nuclear radius, which is related to mass number, A , by the equation:
• Where R 0 is a constant of proportionality
• Combining these equations gives:

• Therefore, the nuclear volume, V , is proportional to the mass of the nucleus, A
• Mass (m), volume (V), and density (ρ) are related by the equation:

• The mass, m , of a nucleus is equal to:
• A = the mass number
• u = –27 kg)" data-title="Atomic Mass Unit" data-toggle="popover">atomic mass unit
• Using the equations for mass and volume, nuclear density is equal to:

• Since the mass number A cancels out, the remaining quantities in the equation are all constant
• Independent of the radius
• The fact that nuclear density is constant shows that nucleons are evenly separated throughout the nucleus regardless of their size
• The accuracy of nuclear density depends on the accuracy of the constant R 0 , as a guide nuclear density should always be of the order 10 17 kg m –3
• The majority of the atom’s mass is contained in the nucleus
• The nucleus is very small compared to the atom
• Atoms must be predominantly empty space

Worked example

Determine the value of nuclear density. You may take the constant of proportionality, R 0 , to be 1.20 × 10 –15 m.

• Using the equation derived above, the density of the nucleus is:
• Atomic mass unit, u = 1.661 × 10 –27 kg
• Constant of proportionality, R 0 = 1.20 × 10 –15 m

Make sure you're comfortable with the calculations involved with the alpha particle closest approach method, as this is a common exam question. You will be expected to remember that the charge of an α is the charge of 2 protons (2 × the charge of an electron)

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The Rutherford scattering formula

The Rutherford scattering formula describes the final direction $\theta$ that a particle will scatter in the presence of a repulsive inverse square force between it and a stationary point mass (see figure). This is precisely the situation encountered in Rutherford's famous gold foil experiment when a beam of alpha particles approach heavy nuclei. One version of the formula relates the deflection angle ($\theta$) to the particle's initial speed ($v_0$) and the so-called scattering parameter $b$, which is the shortest distance between the two particles that would occur if the particle were to continue undeflected.

We begin with the impulse momentum relation in the $y$-direction:

Considering a particle approaching from the left ($\psi = \pi$), the inital $y$-momentum is zero. Since the scattering is elastic, the particle's final speed will be equal to its initial speed. Therfore,

Meanwhile, the component of the force in the $y$-direction is given by

Substitution of \eqref{eq:momentum} and \eqref{eq:force} into \eqref{eq:impulse-momentum} yields

At this point, we perform a change of variables $t \to \psi$

We can rewrite this equation in terms of $b$ and $v_0$ by applying the conservation of angular momentum ($r^2 \dot \psi = b v_0$)

After noting that $E = \frac{1}{2}mv_0^2$ and applying the trig identity

This formula can be also be derived from the equation of motion .

Differential scattering cross section

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Rutherford Atomic Model

Last updated at April 16, 2024 by Teachoo

As per Rutherford Nuclear Model of Atom ,

• Every atom has a nucleus .
• The size of the nucleus is very small . It is 1/10 the size of an atom .
• This nucleus is positively charged .
• Even though the nucleus is of small size, it has a very high mass . Nearly all the mass of an atom is inside the nucleus.
• Electrons revolve around the nucleus in a circular path .

How was the Rutherford Model formed?

• It was formed by the scientist Ernest Rutherford .

He designed the model after performing Alpha Particle Scattering Experiment on a gold foil .

What is an alpha particle?

• Alpha particles are nucleus of helium atoms . It has a charge of +2 . The fast moving alpha particles have a good amount of energy.
• The mass of an alpha - particle is 4u .

Why did Rutherford use a gold foil?

• He selected a gold foil because he wanted as thin a layer as possible . This gold foil was about 1000 atoms thick .

What did Rutherford expect before the experiment?

• Mass of the alpha particles was 4u while that of the proton is 1u. Hence, they were much heavier than the proton.
• Rutherford expected that alpha particles would deflect a little by the subatomic particles (protons and electrons) in the gold atoms.
• But since alpha particles were much heavier than protons , he did not expect to see large deflections.

What was Rutherford's Alpha Particle Scattering Experiment?

• In this experiment, Rutherford made fast moving alpha particles to fall on a gold foil .
• He observed that:
• Many of fast moving alpha particles pass straight through the gold foil with no deflection at all
• Some of the alpha particles were deflected by foil at small angles.
• Very less alpha particles(1 out of every 12000) were reflected back  at 180 degree (rebound)

Rutherford’s observations from his experiment: -

• Most of spaces inside atom was empty This is because most of the fast moving alpha particles pass straight through the gold foil.
• Positive charge of atom occupies very little space This is because only some of the alpha particles were deflected by the foil at small angles.
• All mass of atom and positive charged was concentrated in very small volume of atom called Nucleus This is because very less alpha particles were reflected back at 180 degree (rebound).

Note: From his experiment, he estimated that, radius of an atom is about 10 5   more than the radius of a nucleus.

What was Rutherford's model of an atom?

Rutherford's model of an atom stated that:

• There is a positively charged centre in an atom called the nucleus . Nearly all the mass of an atom resides in the nucleus .
• The electrons (negatively charged particles) revolve around the nucleus in circular paths.
• The size of the nucleus is very small as compared to the size of the atom .

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What did Rutherford expect in his alpha scattering experiments? [closed]

At the time when Rutherford's gold foil experiment was performed, Thomson's plum pudding model was believed to be true (at least by Rutherford himself and his students).

With this model in mind Rutherford predicted that most of the alpha particles will be deflected by at most a fraction of a degree (sourced by this Wikipedia page ), but why?

In my opinion, since according to the plum pudding model the mass of an atom was assumed to be uniformly distributed and the atomic mass of gold is nearly 50 times larger than the mass of an alpha particle, and gold is solid, therefore much less intermolecular space will be present, so, most of the alpha particles should rebound or get deflected by a large angle.

• experimental-chemistry

• 3 $\begingroup$ Perhaps see this answer to get started: chemistry.stackexchange.com/a/10392/79678 . Search for “Rutherford” here for more information. $\endgroup$ –  Ed V Commented Jul 21, 2020 at 12:36
• 3 $\begingroup$ Strongly related (almost duplicate): chemistry.stackexchange.com/questions/106819/… $\endgroup$ –  Nilay Ghosh Commented Jul 21, 2020 at 12:48
• $\begingroup$ en.wikipedia.org/wiki/Rutherford_scattering $\endgroup$ –  Buck Thorn ♦ Commented Jul 21, 2020 at 13:21
• 1 $\begingroup$ What is the alpha particle bouncing off of? What are the kinematics of that situation? Without using backspin, you don't get backscattering in pool/snooker because the balls are all the same mass. $\endgroup$ –  Jon Custer Commented Jul 21, 2020 at 13:51
• 3 $\begingroup$ Further, given that Thompson's model was proposed after $\alpha$ backscattering was observed, it is clear that the assumption in the first sentence is not valid. $\endgroup$ –  Jon Custer Commented Jul 21, 2020 at 14:35

The nucleus has a radius roughly 10⁴ times smaller than the size of the atom itself (imagine a sports ball in a stadium). That would mean that its volume were 10¹² smaller than the volume of an atom. Sure the gold nucleus is ~30 times as charged and is ~50 times heavier. But dilute that charge and mass by a factor of a trillion, and suddenly those don't seem so significant anymore.

That's the worst thing about those schematic diagrams that you see for the Rutherford experiment. They blow up the size of the nucleus to prove a point, but those diagrams are definitely "Not to Scale™".

• $\begingroup$ I know that but I asked what led Rutherford think that Alpha particle should pass through the gold foil keeping in mind plum pudding model $\endgroup$ –  Tushar Commented Jul 21, 2020 at 13:14
• $\begingroup$ he expectesdthis i.e. before conducting the experiment $\endgroup$ –  Tushar Commented Jul 21, 2020 at 13:15
• $\begingroup$ That's what I'm saying to you. Rutherford is able to divide, so he can already estimate the density of matter and charge within the gold foil, and it's not that dense. $\endgroup$ –  Zhe Commented Jul 21, 2020 at 13:59
• 2 $\begingroup$ Why is a question with 3 upvotes closed? Surely there was a known difference between an alpha particle and gold and this had to be in his mind. Ostensibly one conducts experiments to answer a question, What was the question? The 16in projectile analogy is foolish; shooting a pingpong ball at a pillow filled with pingpong balls and having it bounce back is more appropriate and more exciting. $\endgroup$ –  jimchmst Commented Aug 29, 2023 at 21:00
• $\begingroup$ @jimchmst I would expect that most ping pong ball collisions result in its bouncing back. That seems less than exciting. $\endgroup$ –  Zhe Commented Aug 31, 2023 at 17:52

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