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Geiger–Marsden Experiments
(Rutherford Gold Foil Experiment)
Kaiyue Wang
COSMOS Cluster 2
Final Research Paper
30 July 2015
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Ernest Rutherford
Abstract
The main subject of this paper is the discovery of the nucleus of the atom as well as the
structure of it using alpha particles by Ernest Rutherford. The methods and preparation of the
experiment will be elaborated as well as its effects. The main experiment is the gold foil
experiment where the nucleus was discovered with Rutherford’s theory backing it up.
Rutherford’s theory would then be verified by a further experiment. He is the man who brought
nuclear physics to the surface of the world wide world.
Ernest Rutherford, known as “the father of the atom”, “greatest experimentalist physicist
since Faraday”, is mostly recognized for his gold foil experiment in finding the nuclei. Although
this discovery may seem minimal, it laid the ground work for countless of experiments later in
the discovery of subatomic particles and their natures. His work in radiation in nuclear physics
along with his gold foil experiment helped him come up with the Rutherford model of the atom.
A small structure in the atom that held charged particles. Rutherford’s discovery did not really
emulate a genius nature about him, but he was a man of outstanding charisma. He was a genius
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at finding the best scientists to gather around him and develop healthful relationships along with
his constant findings and discoveries. His ability to overcome hardships while producing results
serves as an inspiration to many. “He is a very great man whom few can emulate, but everybody
can admire” (11, The Great Nobel Prizes)
. Ernest lived a very fortunate life as education started to become free as he started to
grow up. Many schools he would attend in the future started to take shape as he was just born.
His parents, James and Martha Rutherford new that education was essential and made many
sacrifices for him to become educated. Rutherford himself was not viewed as a prodigy or genius
as he child, he was a lively boy as he attended Foxhill for his primary education. However, what
really propelled him into the interest and world of science was a small primer of science by
Balfour Stewart he had in 1881. He would love his science classes and apply concepts he learned
to different ideas. He learned to calculate the distance away from a canon from hearing the noise
and applied it to finding the distance away from a flashing light. The idea of simplicity in the
books he read about the fundamentals really became apparent as his most famous experiments
had very simplistic models. Rutherford grew and scored very well on his entrance exams and
attended Nelson College, scoring 580 out 600 on it. Here the headmaster, Mr W. J. Ford, who
came from Cambridge and was a former master at Marlborough in New England, was an
extremely influential character in Rutherford’s life as he laid down the foundation of his further
inquiries in science. Rutherford really became the epitome of being well-rounded, not only was
he on the rugby team, he also received countless awards in mathematics and even subjects such
as History, English Literature, French and Latin. This was result from his immense genius ability
to concentrate in physical endeavors as well as mental. Rutherford studied at Nelson College for
three years until his abnormal skill level in concentration finally was rewarded. Rutherford tried
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out for a Junior University Scholarship which would enable him to take work in the University of
New Zealand. Rutherford went to take the examination as he was urged by his headmaster and
was by no means certain of the results. He, in fact, under-estimated himself. Once he heard news
that he got it, he was extremely emphatic, making this his first large step that would propel him
into the heads of science. There students described him by no means a genius, but a frank likable
guy who pursed his goals like a hawk. There he would get a bachelors in arts and his bachelor’s
in science. Here he really established his line of work as a physicist.
Ernest Rutherford’s journey and dreams of pursing his interests at top facilities come true
when J.J. Thomson, a professor at the Cavendish Laboratory at Cambridge, invited him to this
top physics lab in the world to work with him. The program he entered was the first of its kind. It
was a graduate program for people that did not attend Cambridge University. Ernest and
Thomson started with work regarding the magnetic detection of Hertzian waves. They got to the
point where they could detect waves from half a mile away. This, however, did not gain enough
recognition because the extent of communication using these would only give a chirp of static.
This point was the turning point as he really started to get into nuclear physics. The science
community was headed into a new direction as the X-Ray was introduced by Professor Routgen.
Rutherford’s and Thomson started to investigate why the X-Ray was able to make air an
electrical conductor, when it normally acts as an insulator. The two great minds realized the XRay turned air molecules into electrified molecules, some positive and some negative. This
became the basis of Thomson’s discovery of the electron when he found that the mysterious
cathode rays were in fact corpuscles of negative characterizes.
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Rutherford, on the other hand was working on his ultraviolet light and discovered the
light caused the same ionization of ions behaved the same way as x-rays. He measured the
velocity of the ions by an ingenious piece of experimentation as shown:
Rutherford used an electrometer instead of an electric plate as the plate created limitations. There
is a uniform layer of uranium on plate A. The ultraviolet ray is shot through and ionizes the
particles between the plate A and B. The amount of ionization measure is called “saturation
current” received at B when the potential difference between A and B is great enough to pull all
ions to the plate before they recombine. Rutherford then covered the uranium with aluminum
sheets in order to measure the current with his electrometer. Rutherford was checking to see if
Becquerel, an earlier experimentalist who tested the uranium with metal plates, was right about
uranium radiation having two distinct parts (This was apparent because rays were unequally
absorbed). Rutherford did find two “rays”* with this experiment and identified them as alpha and
beta particles. The equation he used at the time was:
1. r = exp (-λd)
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In this case the “r” represents the intensity of the radiation after passing through a
distance of “d” through the substance to the intensity when it is removed.
An equation that is better understandable is:
2. I = Io exp (-λt)
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Io is the current with nothing covering the uranium plate.
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I is the current at each thickness
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t is thickness of the aluminum
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λ is the coefficient on absorption.
Explanation: If uranium rays are homogenous, consisting of one part, then λ will remain
constant as t is increased and I goes down. This, however, did not happen. He found that λ did
stay constant for only a few values and then suddenly dropped to another value, where it
remained as the thickness of aluminum increased. As a result he concluded there are two parts of
uranium, and alpha particle and a beta particle.
The Three Particles: Rutherford at the time thought the alpha and beta particles he discovered
were actually rays and not particles. He did however know that there was a certain charge to
these particles. The Alpha particle is the largest out and slowest out of the particles, it has the
least penetrating ability as it instead knocks off electrons ionizing the particle while losing all its
energy. The beta particle was much smaller and faster, however, it is charged and slows down is
decelerated by electromagnetic interactions. The last particle is the gamma ray, the most
penetrating as it contains no charge. Rutherford found that this particle to be X-rays, which had
the same effect in activating gasses for X-rays.
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This discovery really catapulted Ernest Rutherford into the global community. Wanting
to pursue his marriage with his wife Mary Newton, he moved over to McGill University in
Canada. There he would continue his investigation on radioactivity. His discovery of the element
Radon was a big factor in his further research in Canada. The element was involved in him
winning the Nobel Prize regarding his work on “hos investigation into the disintegration of the
elements and the chemistry of radioactive substances”. This however was the Nobel Prize of
Chemistry. McGill is the place where he discovered a peculiar property of thorium, a resultant of
the decay of radium. Along with thorium emitting alpha and beta “rays” he found that it emitted
a third “ray”. This was eventually called the gamma ray. Rutherford also discovered the decay of
thorium and this would establish the grounds of definite physical methods in identifying
elements because of their unique exponential decay life or half-life. This was explained in
Rutherford’s and Soddy’s theory of radioactive disintegration which consisted of these
postulates:
1. The atomic nuclei of the radioactive elements are unstable and liable to disintegrate any
moment.
2. The disintegration is spontaneous, i.e., constantly breaking. The rate of breaking is not
affected by external factors like temperature, pressure, chemical combination etc.
3. During disintegration, atoms of new elements called daughter elements having different
physical and chemical properties than the parent elements come into existence.
4. During disintegration, either alpha or beta particles are emitted from the nucleus.
The disintegration process may proceed in one of the following two ways,
Alpha radiation:
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An alpha particle is essentially and helium nucleus.
Beta radiation:
Gamma Radiation: Essentially the emission of a neutron. Gamma rays are emitted especially
when large elements decay and are essential to modern nuclear technology.
Rutherford continued one this radioactive disintegration and focused on the role of the
alpha particle on it. He suggested that the atom was essentially composed of helium nuclei and
could not be separated by molecular forces unless through mass heat emission of decay. He
proved that the heat emitted were the alpha particles. Rutherford would eventually move from
Canada back to England where he would be able to start his most prolific experiments in history,
really paving the way for future scientists. Manchester was very enticing and moved there to do
research and teach as a professor.
Manchester’s facilities were not as good as the ones in McGill, but they were still better
than many others. Ernest Rutherford’s presence made the physics department of the school world
renowned attracting Otto Hahn from Cavendish and Moseley from Oxford. Here Rutherford still
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focused on his beloved alpha particle in dealing with a behavior called scattering. This was quite
contrary to Thomson’s model as he claimed that alpha particles should not scatter at all and pass
right though the metal foil. Rutherford was actually not the man to first conduct the gold foil
experiment, he was the man that gave meaning to it. Geiger and Marsden conducted this
experiment using the scintillation method to measure the scattering of the alpha particles. Geiger
preformed the prototype of the experiment using a narrow flat beam of particles produced by a
suitable slit, which was allowed to fall on a screen of phosphorescent zinc sulfide, the whole
being enclosed in a vacuum to avoid any scattering by air. A piece of metal was then place in
front of the source and there was scattering. This experiment only allowed slight angles of
scattering. However it did show that the amount of scattering increased as the thickness of the
foil increased and with the atomic weight of the metal. With further experiments regarding this,
they created the most famous setup in 1913. This is his 1910 experiment:
Bulb B contains the radium emanation and is pumped up through the use of mercury up the tube
into the narrow tube A. S contains the a fluorescent zinc sulfide screen. The ray is then narrowed
even more by the slit at D. The metal foil is then placed at D and E to observe how the zone of
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flashes changed. He could also adjust the velocity of the rays by adding more sheets of mica or
aluminum at point A.
He arrived with these sets of rules:
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the most probable angle of deflection increases with the thickness of the material
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the most probable angle of deflection is proportional to the atomic mass of the
substance
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the most probable angle of deflection decreases with the velocity of the alpha
particles
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the probability that a particle will be deflected by more than 90° is vanishingly small
Rutherford was extremely intrigued by this and created his own theory about the structure of the
atom. He published a paper called The Scattering of α and β Particles by Matter and the
Structure of the Atom. In this paper he theorized that each of the large-angle deflections of the
alpha particles must be due to a single encounter and that the only single collision that could
produce such a deflection would be one with a very small, heavy charged particle. The atom, he
theorized must contain a central particle, very small in comparison to the atom itself. This area
would be where close to all of the mass is concentrated. He also said that the atom must have a
large charge, many times greater than electronic charge. So, to render the atom neutral, he
theorized that the central particle must be surrounded by a sphere of electrification thinly spread
of the opposite charge. This was the first conception he offered about the structure of the atom.
Rutherford was mainly concerned about the scattering of the alpha particles and just
assumed that the nucleus was positive, although he could not prove it because both charges fit
his model.
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Single Reflection
Rutherford showed that the path of the alpha particle must be a curve of the kind know as a
hyperbola. The more closely the particle is aimed at the atom, the more sharply it comes back.
The diagram on the right shows the Thomson path of the particle as the bolded dotted line, while
the solid bold line is actual path the alpha particle followed. Rutherford was able to model an
equation regarding the probability of a given direction of single scattering with an alpha particle
of given velocity striking a foil of material of known atomic mass and velocity. The equation is
show below:
s = the number of alpha particles falling on unit area at an angle of deflection Φ
r = distance from point of incidence of α rays on scattering material (radius)
X = total number of particles falling on the scattering material
n = number of atoms in a unit volume of the material (moles)
t = thickness of the foil (in this case, gold or aluminum foil).
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Qn = positive charge of the atomic nucleus
Qα = positive charge of the alpha particles
m = mass of an alpha particle
v = velocity of the alpha particle
Geiger and Marsden would undertake a detailed experiment to investigate how the
scattering angle varied with the different quantities involved in Rutherford’s equation. This
experiment is one of the better known of all the experiments performed, the iconic Gold Foil
Experiment. They found the results of the experiment agreed very well with his experiments and
theory. This was all explained in their paper, The Laws of Deflection of α Particles Through
Large Angles. They tested that the number of scintillations observed at a given angle Φ should
be proportional to these parts of the equation:
1. csc4Φ/2
2. thickness of foil t
3. magnitude of central charge Qn
4. 1/(mv2)2
The 1913 paper published by the two researchers did four experiments to prove these
relationships.
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To test the variation of scattering of the angle of deflection, csc4Φ/2, They constructed a
hollow cylindrical apparatus on a turn table. Inside the cylinder is mounted a metal foil (F) where
it is mounted on a rod (T) which is detached from the turn table so the turn table could rotate. Air
could be also pumped up from the rod (T). A Microscope (M) is attached to the cylinder to view
the deflection. The Microscope is covered by a fluorescent zinc sulfide screen (S) as the
objective lens. Geigor could move the turn table in a full circle and could observe and count
particles deflected up to 150 degrees. After correcting for experimental error, the number of
particles that are deflected at a given angle Φ where proportional to csc4Φ/2.
Geiger and Marsden the tested how the scattering varied different thicknesses. There
apparatus is show here:
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The Scientists drilled six holes into a disc (S). The holes were then covered by metal foil
(F) of varying thickness or none for a control. The disc was covered by two glass plates (B and
C). A disk could be rotated on a rod (P) to bring each metal foil (F) to the alpha ray sources (R).
Zinc Sulfide screen is placed behind the disc to record the number of scintillations. They found
through this experimentation that the thickness was proportional to Rutherford’s equation.
Geiger and Marsden used the same apparatus above to measure how the scattering pattern
varied with the square of the nuclear charge. They did not know whether the charge was positive
or not, but they assumed it was proportional to atomic weight. So, they whether the scattering
was proportional to the weight squared. They placed different metals inside the holes including
gold, aluminum, tin, silver, and copper. To measure this, they counted the number of
scintillations per minute over the respective foils air equivalent and then divided by the square
root of the atomic number. They knew that the number of atoms was proportional to the square
root of the atomic weight. The ratios they found were very close to that of the ones calculated by
the equation. s ∝ Qn2
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Lastly they wanted to test how the velocity of the alpha particle affected the scattering of
them. They wanted to see of s ∝ 1/v4 as this isolates the equation for velocity. To slow the alpha
particle down, they placed mica in front of the alpha ray to slow the particles down. Again, they
found that the number of scintillations was proportional to 1/v4.
Rutherford catapulted nuclear physics as one of the leading scientific fields in the world.
His discovering of the nucleus and his model of the atom really help the field of chemistry grow.
His finding that the nucleus contained a positively charged particle, proton, and his eventual
discovery of the neutron gave a legitimist structure of the atom. This model is still widely
accepted as a basis and is the first thing chemistry students are taught. It can be thought of as the
basis of chemistry. His discovering also lead to the widely popular field today known as quantum
mechanics. His discovering really created a ripple that is still existent in today’s society. As the
father of nuclear physics, one can assume that any develops there one are somehow linked to his
discovery and work. It really bring weight today society as the discovery of the existence of the
nucleus is apparent in today’s use of nuclear technology and how it affects the world politically
and keeps countries in check. To an extent, his work is keeping peace in the world because of the
fear of nuclear warfare.
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Work Cited
Andrade, E. N. Da C. Rutherford and the Nature of the Atom. Garden City, NY: Doubleday,
1964. Print.
Birks, J. B. Rutherford at Manchester. New York: W.A. Benjamin, 1963. Print.
Boltz, Cecil Leonard. Ernest Rutherford. London: Distributed by Heron, 1970. Print.
Rowland, John. Ernest Rutherford. Atom Pioneer. Laurie: London, 1955. Print.
Rutherford, Ernest; Ratcliffe, John A. (1938). "Forty Years of Physics". In Needham, Joseph;
Pagel, Walter.
Tibbetts, Gary (2007). How the Great Scientists Reasoned: The Scientific Method in Action.