geiger and marsden alpha 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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18.3: The Geiger-Marsden Experiment

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In 1908 Hans Geiger and Ernest Marsden, working with Ernest Rutherford of the Physical Laboratories at the University of Manchester, measured the angular distribution of alpha particles scattered from a thin gold foil in an experiment illustrated in figure 18.3. In order to understand this experiment, we need to compute the de Broglie wavelength of alpha particles resulting from radioactive decay. Typical alpha particle kinetic energies are of order \(5 \mathrm{MeV}=8 \times 10^{-13} \mathrm{~J}\). Since the alpha particle consists of two protons and two neutrons, its mass is about \(\mathrm{M}_{\mathrm{a}}=6.7 \times 10^{-27} \mathrm{~kg}\). This implies a velocity of about \(\mathrm{v}=1.1 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}\), a momentum of about p = mv = 7.4 × 10 -20 N s, and a de Broglie wavelength of about \(\lambda=\mathrm{h} / \mathrm{p}=9.0 \times 10^{-15} \mathrm{~m}\).

Other evidence indicates that atoms have dimensions of order \(10 -10 m\), so the de Broglie wavelength of an alpha particle is about a factor of \(10^{4}\) smaller than a typical atomic dimension. Thus, the typical diffraction scattering angle of alpha particles off of atoms ought to be very small, of order \(a=\lambda /(2 d) \approx 10^{-4} \text { radian } \approx 0.01^{\circ}\).

Imagine the surprise of Geiger and Marsden when they found that while most alpha particles suffered only small deflections when passing through the gold foil, a small fraction of the incident particles scattered through large angles, some in excess of 90 ∘ !

Ernest Rutherford calculated the probability for an alpha particle, considered to be a positive point charge, to be scattered through various angles by a stationary atomic nucleus, assumed also to be a positive point charge. The calculation was done classically, though interestingly enough a quantum mechanical calculation gives the same answer. The relative probability for scattering with a momentum transfer to the alpha particle of q is proportional to | q | -4 ≡ q -4 according to Rutherford’s calculation. (Do not confuse this q with charge!) As figure 18.4 indicates, a larger momentum transfer corresponds to a larger scattering angle. The maximum momentum transfer for an incident alpha particle with momentum p is 2| p |, or just twice the initial momentum. This corresponds to a head-on collision between the alpha particle and the nucleus followed by a recoil of the alpha particle directly backwards. Since this collision is elastic, the kinetic energy of the alpha particle after the collision is approximately the same as before, as long as the nucleus is much more massive than the alpha particle.

Rutherford’s calculation agreed quite closely with the experimental results of Geiger and Marsden. Though the probability for scattering through a large angle is small even in the Rutherford theory, it is still much larger than would be expected if there were no small scale atomic nucleus.

PhysicsOpenLab Modern DIY Physics Laboratory for Science Enthusiasts

The rutherford-geiger-marsden experiment.

April 11, 2017 Alpha Spectroscopy , English Posts 84,081 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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Abstract: in this article, we present an interesting new apparatus dedicated to gamma spectrometry and dosimetry measurements. It is a device based on a CsI(Tl) scintillator coupled to solid-state photomultipliers: SiPM. In addition to the scintillation sensor, the instrument has a PIN diode sensitive to beta radiation.

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4.14: Gold Foil Experiment

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How much space do bricks occupy?

As we look at the world around us, it looks pretty solid. We hit a wall with our hand and the hand stops – it does not (normally) go through the wall. We think of matter as occupying space. But there is a lot of empty space in matter. In fact, most of the matter  is  empty space.

The Gold Foil Experiment

In 1911, Rutherford and coworkers Hans Geiger and Ernest Marsden initiated a series of groundbreaking experiments that would completely change the accepted model of the atom. They bombarded very thin sheets of gold foil with fast moving alpha particles . Alpha particles, a type of natural radioactive particle, are positively charged particles with a mass about four times that of a hydrogen atom.

According to the accepted atomic model—in which an atom's mass and charge are uniformly distributed throughout the atom—the scientists hypothesized that all of the alpha particles would pass through the gold foil with only a slight deflection, or none at all. Surprisingly, while most of the alpha particles were indeed not deflected, a very small percentage (about 1 in 8000 particles) bounced off the gold foil at very large angles. Some were even redirected back toward the source. No prior knowledge had prepared them for this discovery. In a famous quote, Rutherford exclaimed that it was "as if you had fired a 15-inch [artillery] shell at a piece of tissue and it came back and hit you."

Rutherford needed to come up with an entirely new model of the atom in order to explain his results. Because the vast majority of the alpha particles had passed through the gold, he reasoned that most of the atom was empty space. In contrast, the particles that were highly deflected must have experienced a tremendously powerful force within the atom. He concluded that all of the positive charge and the majority of the mass of the atom must be concentrated in a very small space in the atom's interior, which he called the nucleus. The nucleus is the tiny, dense, central core of the atom and is composed of protons and neutrons.

Rutherford's atomic model became known as the nuclear model . In the nuclear atom, the protons and neutrons, which comprise nearly all of the mass of the atom, are located in the nucleus at the center of the atom. The electrons are distributed around the nucleus and occupy most of the volume of the atom. It is worth emphasizing just how small the nucleus is compared to the rest of the atom. If we could blow up an atom to be the size of a large professional football stadium, the nucleus would be about the size of a marble.

Rutherford's model proved to be an important step towards a full understanding of the atom. However, it did not completely address the nature of the electrons and the way in which they occupied the vast space around the nucleus. It was not until some years later that a full understanding of the electron was achieved. This proved to be the key to understanding the chemical properties of elements.

• Bombardment of gold foil with alpha particles showed that a very small percentage of alpha particles were deflected.
• The nuclear model of the atom consists of a small and dense positively charged interior surrounded by a cloud of electrons. 
• What is an alpha particle?
• What did Rutherford observe from shooting thousands and thousands of alpha particles at a thin piece of gold foil?
• How did Rutherford explain the observation that most alpha particles went straight through the gold foil?
• What did he say about the particles that were deflected?
• Describe Rutherford’s nuclear model.

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).

• 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

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• 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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On a Diffuse Reflection of the α-Particles

(I) The relative amount of reflection from different metals. (II) The relative amount of reflection from a metal of varying thickness. (III) The fraction of the incident α-particles which are reflected.

Geiger-Marsden's Gold Foil Experiment & Rutherford's Model of the Atom

Hsc physics syllabus.

investigate, assess and model the experimental evidence supporting the nuclear model of the atom, including:

assess the limitations of the Rutherford and Bohr atomic models

Geiger-Marsden's Gold Foil Experiment

Geiger and Marsden performed an experiment using a thin gold foil to investigate the structure of the atom.

Rutherford’s Model of the Atom

Rutherford's model of the atom is characterised by a few key features:

• a highly concentrated positively charged region in the centre of the atom, called the nucleus
• most of the atom is empty space
• electrons orbit the nucleus

Geiger and Marsden fired alpha particles (helium nuclei) at a thin gold foil. The gold foil was surrounded by a screen that would cause scintillations when alpha particles hit it. 

What Did the Gold Foil Experiment Show?

• Observation 1: Most alpha particles passed through the gold foil undeflected as most scintillations were observed directly behind the gold foil. 

This observation supported Rutherford's postulate that an atom is mostly empty space. 

• Observation 2: A few alpha particles were deflected and some of which were reflected back (large angle deflections). The angle of deflection was measured by the position at which they were detected on the fluorescent screen.

This observation supported the presence of a region in the atom of highly concentrated positive charge (nucleus). In an atom of gold, the charge and mass of the nucleus are substantially greater than that of an alpha particles. As a result, when an alpha particle collided with the nucleus, it was reflected.

Geiger and Marsden's gold foil experiment not only provided evidence for Rutherford's model of the atom, it rejected the preceding atomic model proposed by Thomson . Although Thomson's model predicted that all, if not most, alpha particles would pass through the gold foil undeflected, it could not account for the few alpha particles that were reflected. 

How was the Proton Discovered?

After Geiger and Marsden's gold foil experiment, Rutherford tried to investigate the content of the nucleus. 

Rutherford fired alpha particles at a sample of nitrogen gas, which resulted in a transmutation reaction producing protons. 

Rutherford conducted a similar experiment as Thomson to determine the value of the charge to mass ratio of a proton. He showed that a proton is positively charged and much heavier than an electron. 

Although Rutherford demonstrated that the charge of proton(s) accounts for the positive nature of the nucleus, he wasn't able to account for the nuclear mass.

Limitations of Rutherford's Model of the Atom

There are three main limitations to Rutherford's atomic model:

1. The model fails to explain the stability of electrons' orbital motion.

Rutherford proposed that electrons must be orbiting the positively charged nucleus like how satellites orbit the Earth, otherwise they would clash into the nucleus due to the electrostatic attraction towards the nucleus. However, by Maxwell's electromagnetic theory, electrons should emit radiation when they experience centripetal acceleration. By the law of conservation of energy, an electron's kinetic energy should gradually decrease, leading to its spiralling motion into the nucleus. 

Previous section: Millikan's Oil Drop Experiment

Next section: Chadwick's Discovery of The Neutron

BACK TO MODULE 8: FROM THE UNIVERSE TO THE ATOM

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Rutherford Scattering ( AQA GCSE Physics )

Revision note.

Physics Project Lead

Rutherford Scattering

Alpha scattering.

• Physicist, Ernest Rutherford was instructing two of his students, Hans Geiger and Ernest Marsden to carry out the experiment
• They were directing a beam of alpha particles (He 2+ ions) at a thin gold foil
• They expected the alpha particles to travel through the gold foil, and maybe change direction a small amount
• Most of the alpha particles passed straight through the foil
• Some of the alpha particles changed direction but continued through the foil
• A few of the alpha particles bounced back off the gold foil
• The bouncing back could not be explained by the Plum Pudding model, so a new model had to be created

When alpha particles are fired at thin gold foil, most of them go straight through, some are deflected and a very small number bounce straight back

The Nuclear Model

• Ernest Rutherford made different conclusions from the findings of the experiment
• The table below describes the findings and conclusions of A, B and C from the image above:

Alpha Scattering Findings and Conclusions Table

• Rutherford proposed the nuclear model of the atom
• Nearly all of the mass of the atom is concentrated in the centre of the atom (in the nucleus)
• The nucleus is positively charged
• Negatively charged electrons orbit the nucleus at a distance
• The nuclear model could explain experimental observations better than the Plum Pudding model

The Nuclear model replaced the Plum Pudding model as it could better explain the observations of Rutherford’s Scattering Experiment

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How can we derive the maximum scattering angle from the experiment of Geiger and Marsden?

Schematic diagram of apparatus used by Geiger and Marsden to observe scattering of $\alpha$ particles past 90°. "A small frac­tion of the $\alpha$ particles falling upon a metal foil have their di­rections changed to such an ex­ tent that they emerge again at the side of incidence." The scattered $\alpha$ particle struck a scintillating screen where the brief flash was observed through the microscope. From H. Geiger and E. Marsden, Pro­ceedings of Royal Society (London) 82, 495 (1909).

This is about the alpha-particle scattering experiment. The book says that some alpha-particles were scattered with the angle larger than 90 degree, which is impossible if the particles were colliding with electrons of small mass. There's the formula of the maximum scattering angle at the bottom of the second image. I don't get how the formula is derived. What does the angle have to do with the momentum?

• quantum-mechanics
• homework-and-exercises
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• atomic-physics

• $\begingroup$ Please don't abuse screenshots and type your question completely and clearly. Also, use Mathjax syntax for equations. Thank you. $\endgroup$ –  Miyase Commented Oct 18, 2022 at 15:36
• $\begingroup$ This is classical kinematics. Conserve momentum and energy in the center-of-mass frame. You can’t backscatter if the incident particle is more massive than the other particle. $\endgroup$ –  Jon Custer Commented Oct 18, 2022 at 15:43

The equation use this approximation when $\theta \ll 1$

$$ \theta \approx \tan \theta = \frac{\Delta P_{\alpha}}{P_\alpha} $$

You can find the error of the approximation from Small-angle approximation - Wikipedia .

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