what was the purpose of rutherford gold foil experiment

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About Rutherford's Gold Foil Experiment

Five Types of Atomic Models

Ernest Rutherford, originally from New Zealand, is credited as being the father of nuclear physics for his discoveries in atomic structure, even though Hantaro Nagaoka, a physicist from the Imperial University of Tokyo, first proposed the theory of the nucleus as it is known today. Rutherford's "gold foil experiment" led to the discovery that most of an atom's mass is located in a dense region now called the nucleus. Prior to the groundbreaking gold foil experiment, Rutherford was granted the Nobel Prize for other key contributions in the field of chemistry.

The popular theory of atomic structure at the time of Rutherford's experiment was the "plum pudding model." This model was developed in 1904 by J.J. Thompson, the scientist who discovered the electron. This theory held that the negatively charged electrons in an atom were floating in a sea of positive charge--the electrons being akin to plums in a bowl of pudding. Although Dr. Nagaoka had published his competing theory that electrons orbit a positive nucleus, akin to the way the planet Saturn is orbited by its rings, in 1904, the plum pudding model was the prevailing theory on the structure of the atom until it was disproved by Ernest Rutherford in 1911.

The gold foil experiment was conducted under the supervision of Rutherford at the University of Manchester in 1909 by scientist Hans Geiger (whose work eventually led to the development of the Geiger counter) and undergraduate student Ernest Marsden. Rutherford, chair of the Manchester physics department at the time of the experiment, is given primary credit for the experiment, as the theories that resulted are primarily his work. Rutherford's gold foil experiment is also sometimes referred to as the Geiger-Marsden experiment.

The gold foil experiment consisted of a series of tests in which a positively charged helium particle was shot at a very thin layer of gold foil. The expected result was that the positive particles would be moved just a few degrees from their path as they passed through the sea of positive charge proposed in the plum pudding model. The result, however, was that the positive particles were repelled off of the gold foil by nearly 180 degrees in a very small region of the atom, while most of the remaining particles were not deflected at all but rather passed right through the atom.

Significance

The data generated from the gold foil experiment demonstrated that the plum pudding model of the atom was incorrect. The way in which the positive particles bounced off the thin foil indicated that the majority of the mass of an atom was concentrated in one small region. Because the majority of the positive particles continued on their original path unmoved, Rutherford correctly deducted that most of the remainder of the atom was empty space. Rutherford termed his discovery "the central charge," a region later named the nucleus.

Rutherford's discovery of the nucleus and proposed atomic structure was later refined by physicist Niels Bohr in 1913. Bohr's model of the atom, also referred to as the Rutherford Bohr model, is the basic atomic model used today. Rutherford's description of the atom set the foundation for all future atomic models and the development of nuclear physics.

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

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

The gold foil experiments gave physicists their first view of the structure of the atomic nucleus and the physics underlying the everyday world.

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.

Here, an illustration of Rutherford's particle scattering device used in his gold foil experiment.

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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Who did the Gold Foil Experiment?

The gold foil experiment was a pathbreaking work conducted by scientists Hans Geiger and Ernest Marsden under the supervision of Nobel laureate physicist Ernest Rutherford that led to the discovery of the proper structure of an atom . Known as the Geiger-Marsden experiment, it was performed at the Physical Laboratories of the University of Manchester between 1908 and 1913.

The prevalent atomic theory at the time of the research was the plum pudding model that was developed by Lord Kelvin and further improved by J.J. Thomson. According to the theory, an atom was a positively charged sphere with the electrons embedded in it like plums in a Christmas pudding.

With neutrons and protons yet to be discovered, the theory was derived following the classical Newtonian Physics. However, in the absence of experimental proof, this approach lacked proper acceptance by the scientific community.

What is the Gold Foil Experiment?

Description.

The method used by scientists included the following experimental steps and procedure. They bombarded a thin gold foil of thickness approximately 8.6 x 10 -6 cm with a beam of alpha particles in a vacuum. Alpha particles are positively charged particles with a mass of about four times that of a hydrogen atom and are found in radioactive natural substances. They used gold since it is highly malleable, producing sheets that can be only a few atoms thick, thereby ensuring smooth passage of the alpha particles. A circular screen coated with zinc sulfide surrounded the foil. Since the positively charged alpha particles possess mass and move very fast, it was hypothesized that they would penetrate the thin gold foil and land themselves on the screen, producing fluorescence in the part they struck.

Like the plum pudding model, since the positive charge of atoms was evenly distributed and too small as compared to that of the alpha particles, the deflection of the particulate matter was predicted to be less than a small fraction of a degree.

Observation

Though most of the alpha particles behaved as expected, there was a noticeable fraction of particles that got scattered by angles greater than 90 degrees. There were about 1 in every 2000 particles that got scattered by a full 180 degree, i.e., they retraced their path after hitting the gold foil.

Simulation of Rutherford’s Gold Foil Experiment Courtesy: University of Colorado Boulder

The unexpected outcome could have only one explanation – a highly concentrated positive charge at the center of an atom that caused an electrostatic repulsion of the particles strong enough to bounce them back to their source. The particles that got deflected by huge angles passed close to the said concentrated mass. Most of the particles moved undeviated as there was no obstruction to their path, proving that the majority of an atom is empty.

In addition to the above, Rutherford concluded that since the central core could deflect the dense alpha particles, it shows that almost the entire mass of the atom is concentrated there. Rutherford named it the “nucleus” after experimenting with various gases. He also used materials other than gold for the foil, though the gold foil version gained the most popularity.

He further went on to reject the plum pudding model and developed a new atomic structure called the planetary model. In this model, a vastly empty atom holds a tiny nucleus at the center surrounded by a cloud of electrons. As a result of his gold foil experiment, Rutherford’s atomic theory holds good even today.

Rutherford’s Atomic Model

Rutherford’s Gold Foil Experiment Animation

Rutherford demonstrated his experiment on bombarding thin gold foil with alpha particles contributed immensely to the atomic theory by proposing his nuclear atomic model.
The nuclear model of the atom consists of a small and dense positively charged interior surrounded by a cloud of electrons.
The significance and purpose of the gold foil experiment are still prevalent today. The discovery of the nucleus paved the way for further research, unraveling a list of unknown fundamental particles.
Chemed.chem.purdue.edu
Chem.libretexts.org
Large.stanford.edu
Radioa ctivity.eu.com

Article was last reviewed on Friday, February 3, 2023

5 responses to “Gold Foil Experiment”

Super very much helpful to me,clear explanation about every act done by our Rutherford that is under different sub headings ,which is very much clear to ,to study .very much thanks to the science facts.com.thank u so much.

Good explanation,very helpful ,thank u ,so much

very clear and helpful, perfect for my science project!

Thank you for sharing the interactive program on the effects of the type of atom on the experiment! Looking forward to sharing this with my ninth graders!

Rutherford spearheaded with a team of scientist in his experiment of gold foil to capture the particles of the year 1911. It’s the beginning of explaining particles that float and are compacted . Rutherford discovered this atom through countless experiments which was the revolutionary discovery of the atomic nuclear . Rutherford name the atom as a positive charge and the the center is the nucleus.

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What is the model of the atom proposed by Ernest Rutherford?
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What did Ernest Rutherford's atomic model get right and wrong?
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What is the Rutherford gold-foil experiment?

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.

Discovering the Nucleus: Rutherford’s Gold Foil Experiment

what was the purpose of rutherford gold foil experiment

History of Chemistry: Rutherford Gold Foil Experiment

In this article, you will learn the history behind the Rutherford Gold Foil Experiment and the events that led to the discovery of the atomic nucleus. If you enjoy this article, check out our other history of chemistry articles linked below!

Rutherford Atomic Model
JJ Thompson cathode-ray tube
Rutherfords Jar Experiment
Molecular Geometry tutorial
The structure of an atom
Bohr Atomic Model
Nuclear Reactions

Who was Ernest Rutherford?

Biography of Physicist Ernest Rutherford

Ernest Rutherford is known as the father of nuclear physics. Born in Brightwater, New Zealand on August 30th, 1871, Rutherford was the fourth of twelve children. His father was a farmer and his mother a school teacher. From a very early age, Rutherford understood the importance of hard work and the power of education. In school, he excelled greatly and at the age of fifteen won an academic scholarship to study at Nelson Collegiate School. Then, at the age of 19, he won another academic scholarship to study at Canterbury College in Christchurch. A few years later he won another scholarship, the exhibition science scholarship, and he left New Zealand to study at Trinity College, Cambridge in England. While there, he conducted research at the Cavendish Laboratory under his advisor J.J. Thomson .

Rutherford's Nuclear World: The Story of the Discovery of the Nucleus | Young Rutherford | American Institute of Physics

During his time at Cavendish Lab, Rutherford faced adversity from his peers. Because he was from New Zealand, he was often ostracized by fellow students. In the end, he used this as motivation to succeed. Which he did as he made a multitude of great discoveries through his research in gases and radioactivity. These included the discovery of different types of radiation, radiometric dating, and the nucleus of an atom.

The Rutherford Gold Foil Experiment

The experiment.

While working as a chair at the University of Manchester, Rutherford conducted the gold-foil experiment alongside Hans Geiger and Ernest Marsden. In this experiment, they shot alpha particles –which Rutherford had discovered years prior– directly at a piece of thin gold foil . As the alpha particles passed through, they would hit the phosphorescent screen encasing the foil. When the particles came into contact with the screen, there would be a flash.

Observations

Going into the experiment, Rutherford had formed preconceptions for the experiment based on J.J. Thomson’s plum pudding model . He predicted the alpha particles would shoot through the foil with ease. Some of the particles did manage to pass directly through the foil, but some veered from the path either bouncing back or deflecting. Rutherford found this to be an exciting observation and compared it to shooting a bullet at a piece of tissue and having it bounce back.

From this observation, two deductions were made. Firstly, he concluded most of the atom is composed of empty space. Secondly, he concluded there must be something small, dense, and positive inside the atom to repel the positively charged alpha particles. This became the nucleus, which in Latin means the seed inside of a fruit.

The Nuclear Model

The gold-foil experiment disproved J.J. Thomsons plum pudding model, which hypothesized the atom was positively charged spaced with electrons embedded inside. Therefore, giving way to the nuclear model. In this model, Rutherford theorized the atomic structure was similar to that of the solar system. Where the nucleus was in this middle and surrounded by empty space with orbiting electrons.

KentChemistry HOME

Dalton's Model of the Atom / J.J. Thomson / Millikan's Oil Drop Experiment / Rutherford / Niels Bohr / DeBroglie / Heisenberg / Planck / Schrödinger / Chadwick

From MIT 3.091-Lec 3 Donald Sadoway 17:00 min

Earnest Rutherford- From New Zealand, one of 12 children born on a farm. Rutherford was a scholarship research student under J.J. Thomson at Cavendish Lab at Cambridge University. Did thesis research on the properties of charged particles. Identified alpha particle as a Helium nucleus (protons and neutrons, no electrons) and beta particle as an electron.

After this he worked at McGill University in Montreal, Canada. He worked on the origin of alpha particles (from the disintegration of elements) and won the Noble Prize .

He became a Professor of Physics at Victoria University in Manchester, UK.

The experiment to probe the structure of the atom performed by Hans Geiger (Geiger counter) and Ernest Marsden in 1909, under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester.

(Rutherford gets all the credit, while his graduate students did the work.)

The Experiment

A beam of alpha particles, generated by the radioactive decay of radium, was directed onto a sheet of very thin gold foil.

The gold foil was surrounded by a circular sheet of zinc sulfide (ZnS) which was used as a detector: The ZnS sheet would light up when hit with alpha particles.

The Results


	Atoms are mostly made of open space
a very small percentage of particles were deflected through angles much larger than 90 degrees	massive center with a + charge (the nucleus)

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

Problems with the new model resulted in a strong negative reaction in the scientific community

1. Nuclear Collapse	Negative particles revolving around a positive nucleus should collapse ...."Collumbic attraction" between +ive and -ive particles.
2. Energy Deficit	Revolving electrons changes direction, which means there is acceleration. What powers the accelerating electron?

Adjustment to the Model of the Atom- Now with open space & positive nucleus

J.J. Thomson	Rutherford

Rutherford Experiment and Atomic Collisions

Claimed by: Lia McSweeney (Fall 2023)

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

The Main Idea

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

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

A Mathematical Model

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

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

r = center to center distance between particle and atom

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

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

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

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

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

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

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

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

A Computational Model

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

Example Problems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Connectedness

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

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

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

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

External Links

MIT video of an experiment confirming Rutherford's model.

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

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

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

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

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