Rutherford scattering experiments
The Rutherford scattering experiments were a landmark series of experiments by which scientists learned that every atom has a nucleus where all of its positive charge and most of its mass is concentrated. They deduced this after measuring how an alpha particle beam is scattered when it strikes a thin metal foil. 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.
Summary[edit]
Contemporary theories of atomic structure[edit]
The prevailing model of atomic structure before Rutherford's experiments was devised by J. J. Thomson. Thomson had discovered the electron through his work on cathode rays and concluded that an electric current is electrons flowing from one atom to an adjacent atom in a series. When no electric current is in effect, electrons remain embedded within atoms. To explain why atoms are electrically neutral, he proposed the existence of a commensurate amount of positive charge that balanced the negative charge of the electrons. Having no idea what was the source of this positive charge, he tentatively proposed that the positive charge was everywhere in the atom, the atom being spherical in shape.[1] Thomson wasn't quite satisfied with this simplistic idea and hoped to dispense with it as he refined his model.[2] Thomson's model of the atom is popularly referred to as the plum pudding model, although neither Thomson nor his colleagues ever used this analogy.[3]
Thomson's model was not universally accepted even before Rutherford's experiments. Thomson was never able to develop a complete and stable model of his concept.[4] The Japanese scientist Hantaro Nagaoka rejected Thomson's model on the grounds that opposing charges cannot penetrate each other.[5] He proposed instead that electrons orbit the positive charge like the rings around Saturn.[6]
An alpha particle is a sub-microscopic, positively charged particle of matter that is spontaneously emitted from certain radioactive elements. Rutherford discovered their existence in 1899 and in 1906 he deduced that they were essentially helium atoms stripped of their electrons—they had a charge of 2 e and an atomic weight of 4.[7] Protons and neutrons had yet to be discovered, so Rutherford knew nothing about the structure of alpha particles.
According to Thomson's model, if an alpha particle were to collide with an atom, it would just fly straight through, its path being deflected by at most a fraction of a degree. At the atomic scale, the concept of "solid matter" is meaningless. The Thomson atom is a sphere of electric charge anchored in space by its mass, with mass by definition being resistance to acceleration. Thus the alpha particle will not bounce off the atom like a tennis ball hitting a basketball, but will pass right through if the atom's electric fields are weak enough to permit it. Thomson's model predicted that the electric fields in an atom are too weak to affect a passing alpha particle much, given how fast and heavy alpha particles are. Both the negative and positive charges within the Thomson atom are spread out over the atom's entire volume, and Rutherford had calculated that this volume was too large for strong deflection to happen.[8] According the Coulomb's Law, if this sphere were to be smaller yet with the same amount of charge, the electric field at its surface would be much more intense.
Consider an alpha particle passing along the edge of a gold atom, where it will experience the electric field at its strongest and thus experience the maximum deflection angle
Using classical physics, the alpha particle's lateral change in momentum
- qg = positive charge of the gold atom = 79 e = 1.266×10−17 C
- q
α = charge of the alpha particle = 2 e = 3.204×10−19 C - r = radius of the gold atom = 1.44×10−10 m
- v = velocity of the alpha particle = 1.53×107 m/s
- m = mass of the alpha particle = 6.645×10−27 kg
- k = Coulomb constant = 8.987×109 N·m2/C2
This in turn gives an approximation of the deflection angle:
One could obtain a more accurate estimate for the deflection angle using the impact parameter equation, but this simpler calculation is sufficient to show the order of magnitude. For the alpha particle to be deflected by more than 1 degree, the sphere of positive charge would have to be several orders of magnitude smaller.
Now consider an alpha particle passing through the middle of the same atom.
As the alpha particle approaches the center of the atom, the atom's electric field pushes back on it. If the alpha particle passes the center of the atom, the atom will then start pushing the alpha particle forwards instead of back.
Let x be the distance between the alpha particle and the center of the atom. The amount of work that the atom exerts on the alpha particle up to the point that they make contact (ie when x ≥ r) will at most be
The amount of work exerted on the alpha particle as it passes through the atom from the surface to the center (ie when x ≤ r) is given by[10]
Add these two figures together, and the total amount of work exerted on the alpha particle as it approaches the center of the atom is 3.80×10−16 J.
The initial kinetic energy of the alpha particle is given by
The calculations above use modern measurements, but Rutherford had sufficiently accurate estimates. He assumed that the radius of atoms in general to be on the order of 10−10 m (perhaps after reading Jean Perrin's studies on Brownian motion[11]) and the positive charge of a gold atom to be about 100 times that of hydrogen (100 e).[12] He knew that gold has an atomic weight of 197. From an experiment in 1906, Rutherford measured alpha particles to have a charge of 2 e and an atomic weight of 4, and alpha particles emitted by radon to have velocity of 1.70×107 m/s.[13] In 1906, Robert Millikan measured the value of e to be 1.59 × 10-19 C. Jean Perrin in 1909 measured the mass of hydrogen to be 1.43×10−27 kg,[14] and if alpha particles are four times as heavy as that, they would have an absolute mass of 5.72×10−27 kg.
The outcome of the experiments[edit]
Between 1908 and 1913, Rutherford, Geiger, and Marsden ran a series of experiments where they pointed a beam of alpha particles at thin foils of various metals and studied the scattering pattern of the alpha particles with the aid of a fluorescent screen. They discovered that the metal foils could scatter some alpha particles in all directions, sometimes more than 90 degrees. This should have been impossible according to Thomson's model; the alpha particles should have all gone straight through. Obviously, those particles had encountered an electrostatic force far greater than Thomson's model suggested they would.[15]
These bizarre results led Rutherford to conclude in 1911 that the atom is a largely open structure containing a tiny nucleus at its center where its positive charge and most of its mass was concentrated. Only such a high concentration of charge, anchored by its high mass, could produce the strong deflection observed.[16]
Legacy[edit]
Hantaro Nagaoka, who had once proposed a Saturnian model of the atom, wrote to Rutherford from Tokyo in 1911: "I have been struck with the simpleness of the apparatus you employ and the brilliant results you obtain."[17] The astronomer Arthur Eddington called Rutherford's discovery the most important scientific achievement since Democritus proposed the atom ages earlier.[18] Rutherford has since been hailed as "the father of nuclear physics".
In a lecture delivered on October 15, 1936 at Cambridge University,[19][20] Rutherford commented on his reaction to the results of the 1909 experiment (see below for details):
Then I remember two or three days later Geiger coming to me in great excitement and saying, "We have been able to get some of the
α -particles coming backwards...". 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 centre, carrying a charge.[21]
According to classical Newtonian physics, Rutherford's model of the atom is impossible. Accelerating charged particles radiate electromagnetic waves, so an electron orbiting an atomic nucleus in theory would spiral into the nucleus as it loses energy. Obviously this was not happening, which meant that the classic laws of physics do not apply at the atomic scale. This eventually led Niels Bohr to incorporate quantum mechanics into the model of the atom. These developments came roughly at the same time Albert Einstein produced his theory of general relativity, which showed that the classic laws of physics do not apply at the cosmic scale either.
The experiments[edit]
Background[edit]
Ernest Rutherford was Langworthy Professor of Physics at the Victoria University of Manchester[22] (now the University of Manchester). He had already received numerous honours for his studies of radiation. He had discovered the existence of alpha rays, beta rays, and gamma rays, and had proved that these were the consequence of the disintegration of atoms. In 1906, he received a visit from a German physicist named Hans Geiger, and was so impressed that he asked Geiger to stay and help him with his research.[23] Ernest Marsden was a physics undergraduate student studying under Geiger.
Alpha particles are tiny, positively charged particles that are spontaneously emitted by certain substances such as uranium and radium. Rutherford had discovered them in 1899. In 1908, he was trying to precisely measure their charge. To do this, he first needed to know just how many alpha particles his sample of radium was giving off (after which he would measure their total charge and divide one by the other). Alpha particles are too tiny to be seen with the naked eye or even a microscope, but Rutherford knew that alpha particles ionize air molecules, and if the air is within an electric field, the ions will produce an electric current. On this principle, Rutherford and Geiger designed a simple counting device which consisted of two electrodes in a glass tube. Every alpha particle that passed through the tube would create a pulse of electricity that could be counted. It was an early version of the Geiger counter.[23]
The counter that Geiger and Rutherford built proved unreliable because the alpha particles were being too strongly deflected by their collisions with the molecules of air within the detection chamber. The highly variable trajectories of the alpha particles meant that they did not all generate the same number of ions as they passed through the gas, thus producing erratic readings. This puzzled Rutherford because he had thought that alpha particles were just too heavy to be deflected so strongly (in 1906, he measured alpha particles as having the same weight as helium atoms[24]). Rutherford asked Geiger to investigate just how much matter could scatter alpha rays.[25]
The experiments they designed involved bombarding a metal foil with alpha particles to observe how the foil scattered them in relation to their thickness and material. They used a fluorescent screen to measure the trajectories of the particles. Each impact of an alpha particle on the screen produced a tiny flash of light. Geiger worked in a darkened lab for hours on end, counting these tiny scintillations using a microscope.[8] Rutherford lacked the stamina and patience for this work, being in his late 30s, which is why he left it to his younger colleagues.[26] For the metal foil, they tested a variety of metals, but they preferred gold because they could make the foil very thin, as gold is very malleable.[27] As a source of alpha particles, Rutherford's substance of choice was radon, a substance several million times more radioactive than uranium.
The 1908 experiment[edit]
A 1908 paper by Geiger, On the Scattering of
The 1909 experiment[edit]
In a 1909 paper, On a Diffuse Reflection of the
Geiger and Marsden then wanted to estimate the total number of alpha particles that were being reflected. The previous setup was unsuitable for doing this because the tube contained several radioactive substances (radium plus its decay products) and thus the alpha particles emitted had varying ranges, and because it was difficult for them to ascertain at what rate the tube was emitting alpha particles. This time, they placed a small quantity of radium C (bismuth-214) on the lead plate, which bounced off a platinum reflector (R) and onto the screen. They found that only a tiny fraction of the alpha particles that struck the reflector bounced onto the screen (in this case, 1 in 8,000).[29]
The 1910 experiment[edit]
A 1910 paper[30] by Geiger, The Scattering of the
From the measurements he took, Geiger came to the following conclusions:
- the most probable angle of deflection increases with the thickness of the material
- the most probable angle of deflection is proportional to the atomic mass of the substance
- the most probable angle of deflection decreases with the velocity of the alpha particles
- the probability that a particle will be deflected by more than 90° is vanishingly small
Rutherford mathematically models the scattering pattern[edit]
Considering the results of the above experiments, Rutherford published a landmark paper in 1911 titled "The Scattering of
Rutherford developed a mathematical equation that modeled how the foil should scatter the alpha particles if all the positive charge and most of the atomic mass was concentrated in a point at the center of an atom.
- 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 - X = total number of particles falling on the scattering material
- n = number of atoms in a unit volume of the material
- t = thickness of the foil
- qn = positive charge of the atomic nucleus
- q
α = positive charge of the alpha particles - m = mass of an alpha particle
- v = velocity of the alpha particle
From the scattering data, Rutherford estimated the central charge qn to be about +100 units (see Rutherford model)
The 1913 experiment[edit]
In a 1913 paper, The Laws of Deflexion of
- csc4(
Φ /2) - thickness of foil t
- magnitude of the square of central charge Qn
- 1/(mv2)2
Their 1913 paper describes four experiments by which they proved each of these four relationships.
To test how the scattering varied with the angle of deflection (i.e. if s ∝ csc4(
Geiger and Marsden then tested how the scattering varied with the thickness of the foil (i.e. if s ∝ t). They constructed a disc (S) with six holes drilled in it. The holes were covered with metal foil (F) of varying thickness, or none for control. This disc was then sealed in a brass ring (A) between two glass plates (B and C). The disc could be rotated by means of a rod (P) to bring each window in front of the alpha particle source (R). On the rear glass pane was a zinc sulfide screen (Z). Geiger and Marsden found that the number of scintillations that appeared on the zinc sulfide screen was indeed proportional to the thickness as long as said thickness was small.[31]
Geiger and Marsden reused the above apparatus to measure how the scattering pattern varied with the square of the nuclear charge (i.e. if s ∝ Qn2). Geiger and Marsden did not know what the positive charge of the nucleus of their metals were (they had only just discovered the nucleus existed at all), but they assumed it was proportional to the atomic weight, so they tested whether the scattering was proportional to the atomic weight squared. Geiger and Marsden covered the holes of the disc with foils of gold, tin, silver, copper, and aluminum. They measured each foil's stopping power by equating it to an equivalent thickness of air. They counted the number of scintillations per minute that each foil produced on the screen. They divided the number of scintillations per minute by the respective foil's air equivalent, then divided again by the square root of the atomic weight (Geiger and Marsden knew that for foils of equal stopping power, the number of atoms per unit area is proportional to the square root of the atomic weight). Thus, for each metal, Geiger and Marsden obtained the number of scintillations that a fixed number of atoms produce. For each metal, they then divided this number by the square of the atomic weight, and found that the ratios were more or less the same. Thus they proved that s ∝ Qn2.[31]
Finally, Geiger and Marsden tested how the scattering varied with the velocity of the alpha particles (i.e. if s ∝ 1/v4). Using the same apparatus again, they slowed the alpha particles by placing extra sheets of mica in front of the alpha particle source. They found that, within the range of experimental error, that the number of scinitillations was indeed proportional to 1/v4.[31]
Rutherford determines the nucleus is positively charged[edit]
In his 1911 paper (see above), Rutherford assumed that the central charge of the atom was positive, but a negative charge would have fitted his scattering model just as well.[32] In a 1913 paper,[33] Rutherford declared that the "nucleus" (as he now called it) was indeed positively charged, based on the result of experiments exploring the scattering of alpha particles in various gases.
In 1917, Rutherford and his assistant William Kay began exploring the passage of alpha particles through gases such as hydrogen and nitrogen. In an experiment where they shot a beam of alpha particles through hydrogen, the alpha particles knocked the hydrogen nuclei forwards in the direction of the beam, not backwards. In an experiment where they shot alpha particles through nitrogen, he discovered that the alpha particles knocked hydrogen nuclei (i.e. protons) out of the nitrogen nuclei.[32]
See also[edit]
- Atomic theory
- Rutherford backscattering spectroscopy
- Rutherford scattering
- List of scattering experiments
References[edit]
- ^ J. J. Thomson (1907). The Corpuscular Theory of Matter, p. 103: "In default of exact knowledge of the nature of the way in which positive electricity occurs in the atom, we shall consider a case in which the positive electricity is distributed in the way most amenable to mathematical calculation, i.e., when it occurs as a sphere of uniform density, throughout which the corpuscles are distributed."
- ^ J. J. Thomson, in a letter to Oliver Lodge dated 11 April 1904, quoted in Davis & Falconer (1997):
"With regard to positive electrification I have been in the habit of using the crude analogy of a liquid with a certain amount of cohesion, enough to keep it from flying to bits under its own repulsion. I have however always tried to keep the physical conception of the positive electricity in the background because I have always had hopes (not yet realised) of being able to do without positive electrification as a separate entity and to replace it by some property of the corpuscles.
When one considers that, all the positive electricity does, on the corpuscular theory, is to provide an attractive force to keep the corpuscles together, while all the observable properties of the atom are determined by the corpuscles one feels, I think, that the positive electrification will ultimately prove superfluous and it will be possible to get the effects we now attribute to it from some property of the corpuscle.
At present I am not able to do this and I use the analogy of the liquid as a way of picturing the missing forces which is easily conceived and lends itself readily to analysis." - ^ Giora Hon; Bernard R. Goldstein (6 September 2013). "J. J. Thomson's plum-pudding atomic model: The making of a scientific myth". Annalen der Physik. 525 (8–9): A129–A133. Bibcode:2013AnP...525A.129H. doi:10.1002/andp.201300732.
- ^ Thomson (1907). The Corpuscular Theory of Matter, p. 106: "The general problem of finding how n corpuscles will distribute themselves inside the sphere is very complicated, and I have not succeeded in solving it"
- ^ Daintith & Gjertsen (1999), p. 395
- ^ Hantaro Nagaoka (1904). "Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity". Philosophical Magazine. Series 6. 7 (41): 445–455. doi:10.1080/14786440409463141.
- ^ Ernest Rutherford (1906). "The Mass and Velocity of the
α particles expelled from Radium and Actinium". Philosophical Magazine. Series 6. 12 (70): 348–371. doi:10.1080/14786440609463549. - ^ a b Cavendish Laboratory.
- ^ Hyperphysics.
- ^ "Electric Field, Spherical Geometry". hyperphysics.phy-astr.gsu.edu. Retrieved 2023-07-12.
- ^ Perrin (1909), p. 50
- ^ a b Rutherford (1911)
- ^ Rutherford (1906).
- ^ Perrin (1909), p. 49
- ^ Manners (2000). Quantum Physics, p. 28
- ^ Rutherford (1936): "From these observations, I was led in 1911 to the idea that the atom was a very open electronic structure containing at its centre a very minute charged nucleus in which most of the mass of the atom was concentrated."
- ^ Letter from Hantaro Nagaoka to Ernest Rutherford, 22 February 1911. Quoted in Eve (1939), p. 200
- ^ Reeves (2008)
- ^ Report on the Activities of the History of Science Lectures Committee 1936–1947, Whipple Museum Papers, Whipple Museum for the History of Science, Cambridge, C62 i.
The report lists two lectures, on October 8 and 15. The lecture on atomic structure was likely the one delivered on the 15th. - ^ Cambridge University Reporter, 7 October 1936, p. 141
The lecture took place in the lecture room of the Physiological Laboratory at 5 pm. - ^ The Development of the Theory of Atomic Structure (Rutherford 1936). Reprinted in Background to Modern Science: Ten Lectures at Cambridge arranged by the History of Science Committee 1936
- ^ 'Inward Bound' by Abraham Pais, Oxford University Press, 1986
- ^ a b Heilbron (2003), p. 59
- ^ Rutherford (1906)
- ^ Heilbron (2003)
- ^ Letter from Ernest Rutherford to Henry Bumstead, 11 July 1908, quoted in Eve (1939), p. 180: "Geiger is a demon at the work and could count at intervals for a whole night without destroying his equanimity. I damned vigorously after two minutes and retired from the conflict."
- ^ Tibbetts (2007), p. 127
- ^ Geiger (1908)
- ^ a b c Geiger & Marsden (1909)
- ^ a b Geiger (1910)
- ^ a b c d e f g Geiger & Marsden (1913)
- ^ a b AIP
- ^ Rutherford & Nuttal (1913)
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