Rutherford scattering experiments

• 1. Introduction

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  The Rutherford scattering experiments stand as one of the most startling reversals in the history of science. Between 1906 and 1913, a team working in the Physical Laboratories of the University of Manchester fired a beam of invisible particles at a thin sheet of gold foil, and what came back changed everything scientists thought they knew about matter. Most particles sailed straight through. But some bounced backward. Ernest Rutherford, the man directing the work, later recalled that moment as the most incredible event of his life. He compared it to firing a fifteen-inch artillery shell at a piece of tissue paper and having it fly back and strike you. How could something so tiny ricochet off something that should have been nearly empty? That question, and the answer the team eventually built from it, gave the world a new picture of the atom: not a soft diffuse cloud of charge, but a structure with a dense, almost inconceivably small nucleus at its core. The story runs through three scientists, a series of painstaking experiments, and a 1911 paper that few people read at first, yet eventually launched the entire field of nuclear physics.

• 2. The World Before the Nucleus

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  J. J. Thomson had discovered the electron through his work on cathode rays, and from that discovery he built a tentative model of the atom. Positive charge, he supposed, was spread uniformly throughout a sphere, with electrons distributed inside it in rough balance, like raisins in a pudding. Thomson likened the substance of this positive sphere to a liquid; the sphere itself was more of an abstraction than anything material. He never proposed a positively charged subatomic particle as a counterpart to the electron. The model could not predict emission spectra or chemical valencies, and Thomson was never able to develop a version of it that was both complete and stable. A Japanese physicist named Hantaro Nagaoka rejected the Thomson model on the grounds that opposing charges cannot penetrate each other, and proposed instead that electrons orbit the positive charge the way Saturn's rings circle the planet. That Saturnian model was also known to be mechanically unstable, which is why it was set aside. What mattered for the experiments to come was what Thomson's model predicted about scattering: an incoming particle should experience only the tiniest deflections as it passed through many atoms in succession, and the total deflection, even after thousands of collisions, should remain below one degree.

• 3. Geiger, Marsden, and the Apparatus

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  Ernest Rutherford held the Langworthy Professorship of Physics at the Victoria University of Manchester. He had already established that radiation came in three distinct forms, alpha, beta, and gamma, and had proved these were the consequence of atomic disintegration. In 1906 he received a visit from Hans Geiger, a German physicist, and was so impressed that he asked Geiger to stay on and assist his research. Ernest Marsden was a physics undergraduate working under Geiger. In 1906, Rutherford had already noticed that alpha particles passing through sheets of mica were deflected by as much as two degrees, a result he published that year with the observation that atoms must be the seat of very intense electrical forces. A 1908 paper by Geiger described a glass tube nearly two metres long, with a source of alpha particles at one end and a phosphorescent screen at the other. When Geiger pumped out the air, the particles left a sharp, clean image on the screen corresponding to the slit they passed through. Allowing air back in made the image spread. Adding gold foil made it spread further. The early experiments were confusing because the angular spread varied greatly depending on the apparatus's shape and internal pressure. Rutherford then asked Marsden to look specifically for alpha particles that bounced backward, even though no one expected to find any.

• 4. The 1909 Experiment

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  Geiger and Marsden constructed a small conical glass tube containing radium emanation, radium A, and radium C, with an open end sealed with mica as their alpha particle source. They placed a lead plate in front of a fluorescent screen so that particles from the tube could not strike the screen directly. When they added a metal foil to the side of the plate and aimed the tube at the foil, the number of scintillations on the screen increased. They tested lead, gold, tin, aluminium, copper, silver, iron, and platinum. Metals with higher atomic mass, such as gold, reflected more alpha particles than lighter ones such as aluminium. After refining their counting method to use a fixed quantity of radium C on the lead plate, they concluded that approximately one in every eight thousand alpha particles that struck the reflector bounced back onto the screen. They also confirmed, by measuring thin foils of varying thickness, that the reflection was a volume effect rather than a surface effect. These results were published in a 1909 paper titled On a Diffuse Reflection of the alpha-Particles. The fraction was small, but it was incomparably larger than anything Thomson's model could account for; in Thomson's model, there was no mechanism capable of turning a heavy, fast-moving alpha particle around.

• 5. Rutherford's 1911 Paper

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  Rutherford published his landmark paper in 1911 under the title The Scattering of alpha and beta Particles by Matter and the Structure of the Atom. He began by reviewing Thomson's beta particle scattering results and then proposed a model that would explain what his team had observed: place all of the positive charge at the centre of the atom, and treat the electrons as too diffuse to matter for scattering purposes. From this he derived a mathematical equation predicting how the scattering intensity should vary with angle. The concentrated charge explained two things at once: why most alpha particles pass through the foil undeflected, flying too far from the tiny nucleus to feel its pull, and why a rare few are flung back at steep angles after a direct close encounter. Rutherford estimated the central charge of a gold atom to be about one hundred units. He was careful to acknowledge that his calculations assumed the charge was positive, but admitted he could not yet prove this and would need further experiments. The paper did not propose the familiar orbital model of electrons circling a nucleus; Rutherford explicitly noted the unresolved problem of electron arrangement and only mentioned Nagaoka's previously rejected Saturnian model in passing. The term nucleus, which Rutherford introduced in 1912, became the accepted name for the core of the atom.

• 6. Confirming the Equation

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  In 1913, Geiger and Marsden published The Laws of Deflexion of alpha Particles through Large Angles, a paper describing four separate experiments designed to verify each term of Rutherford's scattering equation. To test how scattering varied with angle, they built a hollow metal cylinder mounted on a turntable, with the microscope and zinc sulfide screen able to rotate a full circle around the foil, allowing measurement of deflections up to one hundred and fifty degrees. They tested silver and gold foils and confirmed that the number of deflected particles was proportional to the fourth power of the cosecant of the scattering angle, exactly as Rutherford's formula predicted. A second apparatus with a disc holding six windows covered by foils of varying thickness confirmed proportionality to thickness, as long as the foils remained thin. Using foils of gold, tin, silver, copper, and aluminium, and accounting carefully for each metal's stopping power and its atomic weight, they confirmed proportionality to the square of the nuclear charge. Finally, by placing extra sheets of mica in front of the source to slow the particles, they confirmed the velocity dependence. In the same year, a separate paper declared the nucleus positively charged, based on scattering experiments in various gases. Together the 1913 results turned Rutherford's 1911 proposal into established quantitative physics.

• 7. Legacy and What Came After

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  There was little reaction to Rutherford's 1911 paper in its first years. Particle scattering was not yet a primary tool for physics, and the probability techniques and the wide range of observations in the paper were not immediately compelling. The first results from a cloud chamber, by C. T. R. Wilson, showed alpha particle scattering and also appeared in 1911, but the broader shift came gradually. Niels Bohr arrived at Manchester as a post-doctoral student at Rutherford's invitation and dropped his work on the Thomson model in favour of Rutherford's nuclear model. Over the following years, Bohr incorporated early ideas of quantum mechanics, allowing prediction of electronic spectra and chemical concepts that the 1911 paper had deliberately left aside. The historian Silvan S. Schweber has argued that Rutherford's approach marked a shift to viewing all interactions in physics as scattering processes. Rutherford's concept of a cross section, introduced in the 1911 paper, now dominates the language of experimental particle physics. In a lecture at Cambridge University on the 15th of October 1936, Rutherford re-enacted the moment when Geiger ran to him saying some of the alpha particles had come backwards, calling it quite the most incredible event that has ever happened to me in my life. The astronomer Arthur Eddington called Rutherford's discovery the most important scientific achievement since Democritus proposed the atom. Rutherford's work on nuclear size estimates, which placed the closest approach of an alpha particle to a gold nucleus at about 27 femtometres against a true nuclear radius of 7.3 femtometres, also opened the path to understanding nuclear structure, a line of inquiry that has continued in accelerator-based experiments ever since.