evidence from the alpha particle scattering experiment

What is the 'Gold Foil Experiment'? The Geiger-Marsden experiments explained

Physicists got their first look at the structure of the atomic nucleus.

J.J. Thomson model of the atom

Gold foil experiments, rutherford model of the atom.

• The real atomic model

Additional Resources

Bibliography.

The Geiger-Marsden experiment, also called the gold foil experiment or the α-particle scattering experiments, refers to a series of early-20th-century experiments that gave physicists their first view of the structure of the atomic nucleus and the physics underlying the everyday world. It was first proposed by Nobel Prize -winning physicist Ernest Rutherford.

As familiar as terms like electron, proton and neutron are to us now, in the early 1900s, scientists had very little concept of the fundamental particles that made up atoms . 

In fact, until 1897, scientists believed that atoms had no internal structure and believed that they were an indivisible unit of matter. Even the label "atom" gives this impression, given that it's derived from the Greek word "atomos," meaning "indivisible." 

But that year, University of Cambridge physicist Joseph John Thomson discovered the electron and disproved the concept of the atom being unsplittable, according to Britannica . Thomson found that metals emitted negatively charged particles when illuminated with high-frequency light. 

His discovery of electrons also suggested that there were more elements to atomic structure. That's because matter is usually electrically neutral; so if atoms contain negatively charged particles, they must also contain a source of equivalent positive charge to balance out the negative charge.

By 1904, Thomson had suggested a "plum pudding model" of the atom in which an atom comprises a number of negatively charged electrons in a sphere of uniform positive charge,  distributed like blueberries in a muffin. 

The model had serious shortcomings, however — primarily the mysterious nature of this positively charged sphere. One scientist who was skeptical of this model of atoms was Rutherford, who won the Nobel Prize in chemistry for his 1899 discovery of a form of radioactive decay via α-particles — two protons and two neutrons bound together and identical to a helium -4 nucleus, even if the researchers of the time didn't know this.

Rutherford's Nobel-winning discovery of α particles formed the basis of the gold foil experiment, which cast doubt on the plum pudding model. His experiment would probe atomic structure with high-velocity α-particles emitted by a radioactive source. He initially handed off his investigation to two of his protégés, Ernest Marsden and Hans Geiger, according to Britannica . 

Rutherford reasoned that if Thomson's plum pudding model was correct, then when an α-particle hit a thin foil of gold, the particle should pass through with only the tiniest of deflections. This is because α-particles are 7,000 times more massive than the electrons that presumably made up the interior of the atom.

Marsden and Geiger conducted the experiments primarily at the Physical Laboratories of the University of Manchester in the U.K. between 1908 and 1913. 

The duo used a radioactive source of α-particles facing a thin sheet of gold or platinum surrounded by fluorescent screens that glowed when struck by the deflected particles, thus allowing the scientists to measure the angle of deflection. 

The research team calculated that if Thomson's model was correct, the maximum deflection should occur when the α-particle grazed an atom it encountered and thus experienced the maximum transverse electrostatic force. Even in this case, the plum pudding model predicted a maximum deflection angle of just 0.06 degrees. 

Of course, an α-particle passing through an extremely thin gold foil would still encounter about 1,000 atoms, and thus its deflections would be essentially random. Even with this random scattering, the maximum angle of refraction if Thomson's model was correct would be just over half a degree. The chance of an α-particle being reflected back was just 1 in 10^1,000 (1 followed by a thousand zeroes). 

Yet, when Geiger and Marsden conducted their eponymous experiment, they found that in about 2% of cases, the α-particle underwent large deflections. Even more shocking, around 1 in 10,000 α-particles were reflected directly back from the gold foil.

Rutherford explained just how extraordinary this result was, likening it to firing a 15-inch (38 centimeters) shell (projectile) at a sheet of tissue paper and having it bounce back at you, according to Britannica  

Extraordinary though they were, the results of the Geiger-Marsden experiments did not immediately cause a sensation in the physics community. Initially, the data were unnoticed or even ignored, according to the book "Quantum Physics: An Introduction" by J. Manners.

The results did have a profound effect on Rutherford, however, who in 1910 set about determining a model of atomic structure that would supersede Thomson's plum pudding model, Manners wrote in his book.

The Rutherford model of the atom, put forward in 1911, proposed a nucleus, where the majority of the particle's mass was concentrated, according to Britannica . Surrounding this tiny central core were electrons, and the distance at which they orbited determined the size of the atom. The model suggested that most of the atom was empty space.

When the α-particle approaches within 10^-13 meters of the compact nucleus of Rutherford's atomic model, it experiences a repulsive force around a million times more powerful than it would experience in the plum pudding model. This explains the large-angle scatterings seen in the Geiger-Marsden experiments.

Later Geiger-Marsden experiments were also instrumental; the 1913 tests helped determine the upper limits of the size of an atomic nucleus. These experiments revealed that the angle of scattering of the α-particle was proportional to the square of the charge of the atomic nucleus, or Z, according to the book "Quantum Physics of Matter," published in 2000 and edited by Alan Durrant.  

In 1920, James Chadwick used a similar experimental setup to determine the Z value for a number of metals. The British physicist went on to discover the neutron in 1932, delineating it as a separate particle from the proton, the American Physical Society said . 

What did the Rutherford model get right and wrong?

Yet the Rutherford model shared a critical problem with the earlier plum pudding model of the atom: The orbiting electrons in both models should be continuously emitting electromagnetic energy, which would cause them to lose energy and eventually spiral into the nucleus. In fact, the electrons in Rutherford's model should have lasted less than 10^-5 seconds. 

Another problem presented by Rutherford's model is that it doesn't account for the sizes of atoms. 

Despite these failings, the Rutherford model derived from the Geiger-Marsden experiments would become the inspiration for Niels Bohr 's atomic model of hydrogen , for which he won a Nobel Prize in Physics .

Bohr united Rutherford's atomic model with the quantum theories of Max Planck to determine that electrons in an atom can only take discrete energy values, thereby explaining why they remain stable around a nucleus unless emitting or absorbing a photon, or light particle.

Thus, the work of Rutherford, Geiger  (who later became famous for his invention of a radiation detector)  and Marsden helped to form the foundations of both quantum mechanics and particle physics. 

Rutherford's idea of firing a beam at a target was adapted to particle accelerators during the 20th century. Perhaps the ultimate example of this type of experiment is the Large Hadron Collider near Geneva, which accelerates beams of particles to near light speed and slams them together. 

• See a modern reconstruction of the Geiger-Marsden gold foil experiment conducted by BackstageScience and explained by particle physicist Bruce Kennedy . 
• Find out more about the Bohr model of the atom which would eventually replace the Rutherford atomic model. 
• Rutherford's protege Hans Gieger would eventually become famous for the invention of a radioactive detector, the Gieger counter. SciShow explains how they work .

Thomson's Atomic Model , Lumens Chemistry for Non-Majors,.

Rutherford Model, Britannica, https://www.britannica.com/science/Rutherford-model

Alpha particle, U.S NRC, https://www.nrc.gov/reading-rm/basic-ref/glossary/alpha-particle.html

Manners. J., et al, 'Quantum Physics: An Introduction,' Open University, 2008. 

Durrant, A., et al, 'Quantum Physics of Matter,' Open University, 2008

Ernest Rutherford, Britannica , https://www.britannica.com/biography/Ernest-Rutherford

Niels Bohr, The Nobel Prize, https://www.nobelprize.org/prizes/physics/1922/bohr/facts/

House. J. E., 'Origins of Quantum Theory,' Fundamentals of Quantum Mechanics (Third Edition) , 2018

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Robert Lea is a science journalist in the U.K. who specializes in science, space, physics, astronomy, astrophysics, cosmology, quantum mechanics and technology. Rob's articles have been published in Physics World, New Scientist, Astronomy Magazine, All About Space and ZME Science. He also writes about science communication for Elsevier and the European Journal of Physics. Rob holds a bachelor of science degree in physics and astronomy from the U.K.’s Open University

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PhysicsOpenLab Modern DIY Physics Laboratory for Science Enthusiasts

The rutherford-geiger-marsden experiment.

April 11, 2017 Alpha Spectroscopy , English Posts 85,393 Views

What made by Rutherford and his assistants Geiger and Marsden is perhaps one of the most important experiments of nuclear physics.

The experiments were performed between 1908 and 1913 by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester.

In the experiment, Rutherford sent a beam of alpha particles (helium nuclei) emitted from a radioactive source against a thin gold foil (the thickness of about 0.0004 mm, corresponding to about 1000 atoms).

Surrounding the gold foil it was placed a zinc sulfide screen that would show a small flash of light when hit by a scattered alpha particle. The idea was to determine the structure of the atom and understand if it were what supposed by Thomson (atom without a nucleus, also known as pudding model ) or if there was something different.

In particular, if the atom had an internal nucleus separated from external electrons, then they would have been able to observe events, or particles, with large angle of deviation . Obtained, actually, these results, the New Zealand physicist concluded that the atom was formed by a small and compact nucleus , but with high charge density, surrounded by an electron cloud. In the image below it is depicted the interaction of the alpha particles beam with the nuclei of the thin gold foil; one can see how the majority of the particles passes undisturbed, or with small angles of deflection, through the “empty” atom, some particles, however, passing close to the nucleus are diverted with a high angle or even bounced backwards.

The interaction between an alpha particle and the nucleus (elastic collision) is also known as Coulomb scattering , because the interaction in the collision is due to the Coulomb force. In the diagram below it is shown the detail of the interaction between an alpha particle and the nucleus of an atom.

Experimental Setup

In the PhysicsOpenLab “laboratory” we tried to replicate the famous Rutherford experiment. With the equipment already used in alpha spectroscopy we built a setup based on an alpha solid-state detector , a 0.9 μCi Am 241 source and a gold foil as a scatterer. In these post we describe the equipment used : Alpha Spectrometer , Gold Leaf Thickness  . The main purpose is not to make precision measurements but to make a qualitative assessment of the scattering as a function of deflection. The images below show the experimental setup:

The alpha source is actually 0.9 μCi of Am 241 (from smoke detector) which emits alpha particles with energy of 5.4 MeV. The alpha particle beam is collimated by a simple hole in a wooden screen. Source and collimator are fixed on a arm free to rotate around a pivot, which hosts the gold foil that acts as a scatterer. The whole is placed inside a sealed box that acts as a vacuum chamber with the help of an ordinary oil rotary vacuum pump. The images below show the “vacuum chamber” and the electronic part for amplification and acquisition connected to the PC for counting events.

Linear Scale :

Semilog Scale

The results obtained in our experiment approach, albeit with obvious limitations, to the expected theoretical results, represented in the following graph:

For completeness, we report also at the side the formula that describes the distribution of the number of the counted particles in function of the scattering angle. Interestingly, this depends on the power of two the atomic number of the target and is inversely proportional to the fourth power of the sin (θ/2).

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Tags Alpha spectrometer Rutherford

Gamma Spectroscopy with KC761B

Abstract: in this article, we continue the presentation of the new KC761B device. In the previous post, we described the apparatus in general terms. Now we mainly focus on the gamma spectrometer functionality.

Experimental Evidence for the Structure of the Atom

George sivulka march 23, 2017, submitted as coursework for ph241 , stanford university, winter 2017, introduction.

The Rutherford Gold Foil Experiment offered the first experimental evidence that led to the discovery of the nucleus of the atom as a small, dense, and positively charged atomic core. Also known as the Geiger-Marsden Experiments, the discovery actually involved a series of experiments performed by Hans Geiger and Ernest Marsden under Ernest Rutherford. With Geiger and Marsden's experimental evidence, Rutherford deduced a model of the atom, discovering the atomic nucleus. His "Rutherford Model", outlining a tiny positively charged atomic center surrounded by orbiting electrons, was a pivotal scientific discovery revealing the structure of the atoms that comprise all the matter in the universe.

The experimental evidence behind the discovery involved the scattering of a particle beam after passing through a thin gold foil obstruction. The particles used for the experiment - alpha particles - are positive, dense, and can be emitted by a radioactive source. Ernest Rutherford discovered the alpha particle as a positive radioactive emission in 1899, and deduced its charge and mass properties in 1913 by analyzing the charge it induced in the air around it. [1] As these alpha particles have a significant positive charge, any significant potential interference would have to be caused by a large concentration of electrostatic force somewhere in the structure of the atom. [2]

Previous Model of the Atom

The scattering of an alpha particle beam should have been impossible according to the accepted model of the atom at the time. This model, outlined by Lord Kelvin and expanded upon by J. J. Thompson following his discovery of the electron, held that atoms were comprised of a sphere of positive electric charge dotted by the presence of negatively charged electrons. [3] Describing an atomic model similar to "plum pudding," it was assumed that electrons were distributed throughout this positive charge field, like plums distributed in the dessert. However, this plum pudding model lacked the presence of any significant concentration of electromagnetic force that could tangibly affect any alpha particles passing through atoms. As such, alpha particles should show no signs of scattering when passing through thin matter. [4] (see Fig. 2)

The Geiger Marsden Experiments

Testing this accepted theory, Hans Geiger and Ernest Marsden discovered that atoms indeed scattered alpha particles, a experimental result completely contrary to Thompson's model of the atom. In 1908, the first paper of the series of experiments was published, outlining the apparatus used to determine this scattering and the scattering results at small angles. Geiger constructed a two meter long glass tube, capped off on one end by radium source of alpha particles and on the other end by a phosphorescent screen that emitted light when hit by a particle. (see Fig. 3) Alpha particles traveled down the length of the tube, through a slit in the middle and hit the screen detector, producing scintillations of light that marked their point of incidence. Geiger noted that "in a good vacuum, hardly and scintillations were observed outside of the geometric image of the slit, "while when the slit was covered by gold leaf, the area of the observed scintillations was much broader and "the difference in distribution could be noted with the naked eye." [5]

On Rutherford's request, Geiger and Marsden continued to test for scattering at larger angles and under different experimental parameters, collecting the data that enabled Rutherford to further his own conclusions about the nature of the nucleus. By 1909, Geiger and Marsden showed the reflection of alpha particles at angles greater than 90 degrees by angling the alpha particle source towards a foil sheet reflector that then would theoretically reflect incident particles at the detection screen. Separating the particle source and the detector screen by a lead barrier to reduce stray emission, they noted that 1 in every 8000 alpha particles indeed reflected at the obtuse angles required by the reflection of metal sheet and onto the screen on the other side. [6] Moreover, in 1910, Geiger improved the design of his first vacuum tube experiment, making it easier to measure deflection distance, vary foil types and thicknesses, and adjust the alpha particle stream' velocity with mica and aluminum obstructions. Here he discovered that both thicker foil and foils made of elements of increased atomic weight resulted in an increased most probable scattering angle. Additionally, he confirmed that the probability for an angle of reflection greater than 90 degrees was "vanishingly small" and noted that increased particle velocity decreased the most probably scattering angle. [7]

Rutherford's Atom

Backed by this experimental evidence, Rutherford outlined his model of the atom's structure, reasoning that as atoms clearly scattered incident alpha particles, the structure contained a much larger electrostatic force than earlier anticipated; as large angle scattering was a rare occurrence, the electrostatic charge source was only contained within a fraction of the total volume of the atom. As he concludes this reasoning with the "simplest explanation" in his 1911 paper, the "atom contains a central charge distributed through a very small volume" and "the large single deflexions are due to the central charge as a whole." In fact, he mathematically modeled the scattering patterns predicted by this model with this small central "nucleus" to be a point charge. Geiger and Marsden later experimentally verified each of the relationships predicted in Rutherford's mathematical model with techniques and scattering apparatuses that improved upon their prior work, confirming Rutherford's atomic structure. [4, 8, 9] (see Fig. 1)

With the experimentally analyzed nature of deflection of alpha rays by thin gold foil, the truth outlining the structure of the atom falls into place. Though later slightly corrected by Quantum Mechanics effects, the understanding of the structure of the the atom today almost entirely follows form Rutherford's conclusions on the Geiger and Marsden experiments. This landmark discovery fundamentally furthered all fields of science, forever changing mankind's understanding of the world around us.

© George Sivulka. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] E. Rutherford, "Uranium Radiation and the Electrical Conduction Produced By It," Philos. Mag. 47 , 109 (1899).

[2] E. Rutherford, "The Structure of the Atom," Philos. Mag. 27 , 488 (1914).

[3] J. J. Thomson, "On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a Number of Corpuscles Arranged at Equal Intervals Around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure," Philos. Mag. 7 , 237 (1904).

[4] E. Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom," Philos. Mag. 21 , 669 (1911).

[5] H. Geiger, "On the Scattering of the α Particles by Matter," Proc. R. Soc. A 81 , 174 (1908).

[6] H. Geiger and E. Marsden, "On a Diffuse Reflection of the α-Particles," Proc. R. Soc. A 82 , 495 (1909).

[7] H. Geiger, "The Scattering of the α Particles by Matter," Proc. R. Soc. A 83 , 492 (1910).

[8] E. Rutherford, "The Origin of α and β Rays From Radioactive Substances," Philos. Mag. 24 , 453 (1912).

[9] H. Geiger and E. Marsden, "The Laws of Deflexion of α Particles Through Large Angles," Philos. Mag. 25 , 604 (1913).

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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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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 .

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• The ɑ-particle Scattering Experiment
• Simple Model of The Atom
• Atomic Mass
• Mass-energy Relation
• The Mass Defect
• Binding Energy
• Binding Energy Per Nucleon And Nuclear Stability
• Nuclear Reactions
• Nuclear Fission
• Nuclear Fusion
• Radioactivity & Radioactive Decay
• Characteristics Of Alpha/Beta Particles & Gamma Rays
• Activity, Half-life And Decay constant
• Effects of Radiation On Living Organism
• Geiger-Muller Tube/Counter

J.J. Thomson proposed a model of the atom – Plum-pudding model of the atom

Characteristic of plum-pudding model of the atom

• Positive charge of the atom is spread out through the entire volume of the atom
• Electrons are distributed throughout this volume
• Electrons vibrate about their equilibrium positions within the sphere of charge

The ɑ-particle scattering experiment Using a beam of positively charged alpha particles to fire on a thin gold foil

Video of the experiment:

•  ɑ-particles carry a charge of +2e and are about 7300 more massive than electrons.
• If Thomson’s model was correct, maximum deflecting force on the ɑ-particle as it passes near a positive charge will be far too small to deflect the particle by even 1 o .
• Electrons in the atom would also have very little effect on the massive, energetic ɑ-particle.

Actual Results:

• Most of the particles went straight through or were scattered through very small angles.
• But a very small fraction (less than 1%) of the particles were scattered through very large angles, some of which were close to 180 o .

Interpretation of the actual results:

1. Large deflection of ɑ-particles

• To produce such a large deflection, there must be a large force.
• Such a large force is only possible if we assume that the atom consists of a positively charged nucleus of very small dimensions compared with the ordinarily accepted magnitude of the diameter of the atom.
• When an ɑ-particles gets close to the centre of the concentration of positive charges(nucleus), it cannot penetrate the nucleus but gets deflected instead due to the large repulsive force between it and the positively charged nucleus.

2. Most particles passed through undeflected or with a small deflection

• Since very few of the particles were scattered through large angles, the probability of the particle getting close to the centre of the positive charge is small. This shows that the nucleus occupies only a small proportion of the available space.

3. Few particles are deflected backwards, through an angle close to 180o.

• The nucleus is small and very massive.

Simulation of the experiment: http://phet.colorado.edu/en/simulation/rutherford-scattering

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• Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom

In 1911, Rutherford, along with his assistants, H. Geiger and E. Marsden, performed the Alpha Particle scattering experiment , which led to the birth of the ‘nuclear model of an atom ’ – a major step towards how we see the atom today.

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J.j thomson’s plum-pudding model.

In 1897-98, the first model of an atom was proposed by J.J. Thomson. Famously known as the Plum-pudding model or the watermelon model, he proposed that an atom is made up of a positively charged ball with electrons embedded in it. Further, the negative and positive charges were equal in number , making the atom electrically neutral.

Figure 1 shows what Thomson’s plum-pudding model of an atom looked like. Ernest Rutherford, a former research student working with J.J. Thomson, proposed an experiment of scattering of alpha particles by atoms to understand the structure of an atom.

Rutherford, along with his assistants – H. Geiger and E. Marsden – started performing experiments to study the structure of an atom. In 1911, they performed the Alpha particle scattering experiment, which led to the birth of the ‘nuclear model of an atom’ – a major step towards how we see the atom today.

Figure 1. Source: Wikipedia

Browse more Topics under Atoms

• Atomic Spectra
• Bohr Model of the Hydrogen Atom

The Alpha Particle Scattering Experiment

They took a thin gold foil having a thickness of 2.1×10 -7 m and placed it in the centre of a rotatable detector made of zinc sulfide and a microscope. Then, they directed a beam of 5.5MeV alpha particles emitted from a radioactive source at the foil. Lead bricks collimated these alpha particles as they passed through them.

After hitting the foil, the scattering of these alpha particles could be studied by the brief flashes on the screen. Rutherford and his team expected to learn more about the structure of the atom from the results of this experiment.

Source: Wikipedia

Observations

Here is what they found:

• Most of the alpha particles passed through the foil without suffering any collisions
• Around 0.14% of the incident alpha particles scattered by more than 1 o
• Around 1 in 8000 alpha particles deflected by more than 90 o

These observations led to many arguments and conclusions which laid down the structure of the nuclear model on an atom.

Conclusions and arguments

The results of this experiment were not in sync with the plum-pudding model of the atom as suggested by Thomson. Rutherford concluded that since alpha particles are positively charged, for them to be deflected back, they needed a large repelling force. He further argued that for this to happen, the positive charge of the atom needs to be concentrated in the centre, unlike scattered in the earlier accepted model.

Hence, when the incident alpha particle came very close to the positive mass in the centre of the atom, it would repel leading to a deflection. On the other hand, if it passes through at a fair distance from this mass, then there would be no deflection and it would simply pass through.

He then suggested the ‘nuclear model of an atom’ wherein the entire positive charge and most of the mass of the atom is concentrated in the nucleus. Also, the electrons are moving in orbits around the nucleus akin to the planets and the sun. Further, Rutherford also concluded from his experiments that the size of the nucleus is between 10 -15 and 10 -14 m.

According to Kinetic theory, the size of an atom is around 10 -10 m or around 10,000 to 100,000 times the size of the nucleus proposed by Rutherford. Hence, the distance of the electrons from the nucleus should be around 10,000 to 100,000 times the size of the nucleus.

This eventually implies that most of the atom is empty space and explains why most alpha particles went right through the foil. And, these particles are deflected or scattered through a large angle on coming close to the nucleus. Also, the electrons having negligible mass, do not affect the trajectory of these incident alpha particles.

Alpha Particle Trajectory

The trajectory traced by an alpha particle depends on the impact parameter of the collision. The impact parameter is simply the perpendicular distance of each alpha particle from the centre of the nucleus. Since in a beam all alpha particles have the same kinetic energy, the scattering of these particles depends solely on the impact parameter.

Hence, the particles with a small impact parameter or the particles closer to the nucleus, experience large angle of scattering. On the other hand, those with a large impact parameter suffer no deflection or scattering at all. Finally, those particles having ~zero impact parameter or a head-on collision with the nucleus rebound back.

Coming to the experiment, Rutherford and his team observed that a really small fraction of the incident alpha particles was rebounding back. Hence, only a small number of particles were colliding head-on with the nucleus. This, subsequently, led them to believe that the mass of the atom is concentrated in a very small volume.

Electron Orbits

In a nutshell, Rutherford’s nuclear model of the atom describes it as:

• A small and positively charged nucleus at the centre
• Surrounded by revolving electrons in their dynamically stable orbits

The centripetal force that keeps the electrons in their orbits is an outcome of:

• The positively charged nucleus and
• The negatively charged revolving electrons.

Solved Example for You

Question: Rutherford, Geiger and Marsden, directed a beam of alpha particles on a foil of which metal

Solution: Gold

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Rutherford Scattering ( AQA A Level Physics )

Revision note.

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

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

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

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.

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

     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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