Particle Scattering Device

In 1909 Ernest Rutherford suggested an experiment that led to the first modern model of the atom. Hans Wilhelm Geiger, a German postdoctoral researcher working in Rutherford's laboratory, had been studying the passage of alpha particles through a metal foil. Most of the positively charged particles passed through the foil directly, striking a detector screen on the other side. A few particles were deflected slightly by electrical forces as they went through atoms in the foil. The deflections never amounted to more than a few degrees because the particles carried appreciable energy and momentum.

Nevertheless, Rutherford suggested to Geiger that Ernest Marsden, then a student working with Geiger, look hard for alpha particles deflecting at greater angles. No one, including Rutherford, expected that any would be found. Within days, however, Geiger returned to Rutherford with the startling news that some of the particles were scattered at large angles, even directly back toward the source. Rutherford later commented: "It was quite the most incredible event that has ever happened to me. 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.'

The deflection of alpha particles in that experiment is now called Rutherford scattering. It revealed that the contemporary model of the atom was wrong. This plum-pudding model, as it was often called, envisioned a roughly uniform distribution of positively and negatively charged particles. If an alpha particle penetrated such an atom, it would be attracted by the negatively charged particles and repelled by the positively charged ones. The net deflection, if any, would be small.

When Geiger announced that some alpha particles were deflected considerably, Rutherford realized they must be experiencing a strong electric repulsion when they entered an atom. That meant the charged components of an atom are not uniformly distributed. Instead the positively charged ones are collected in a highly compact core called the nucleus and negatively charged ones orbit the nucleus at distances that are large compared with the diameter of the nucleus.

Imagine following an alpha particle as it penetrates an atom made according to Rutherford's model. As it approaches the atom it experiences essentially no electric force because the atom as a whole is neutral. Once it passes through the orbits of the electrons, it begins to be repulsed by the nucleus because both the particle and the nucleus carry a positive charge. Suppose it travels directly toward the nucleus. The continuously increasing repulsion slows the particle to a momentary stop and then propels it back along the path of entry. The angle of deflection is 180 degrees.

An alpha particle entering an atom along a path offset from the nucleus is deflected less. The larger the offset, the smaller the angle of deflection. Since the nucleus is tiny, a small deflection is likelier than a large one. That is why Geiger and Marsden originally observed small deflections.

The distribution of the particles striking the detection screen is described in terms of the density of strikes per unit of screen area. The density depends on the scattering angle. The major strength of Rutherford's model for the atom was that it correctly predicted how the strikes would vary in density. Although several earlier workers had proposed similar solar-system models of the atom, Rutherford is credited with the first modern model because of his success in explaining the scattering of the alpha particles.

In last year's finals of the International Science and Engineering Fair, Rudy Timmerman of Wickes, Ark., won first place in the physics division with his experiments on the scattering of alpha particles from a thin gold foil. He set out to repeat the basic features of the experiment by Geiger and Marsden. In particular he wanted to verify Rutherford's mathematical prediction concerning the angular dependence of the scattering.

Timmerman relied on a detection scheme developed by Charles W. Leming of Henderson State University in Arkansas. Leming's apparatus, which is now manufactured commercially by the Daedalon Corporation (35 Congress Street, Salem, Mass. 01970), incorporates a special type of film that is sensitive to the impact of alpha particles. When it is developed, it has a small hole at every point where a particle struck it.

Timmerman constructed his own version of the apparatus. It consisted of three aluminum plates held by four long bolts. In each plate he drilled a small central hole. Above the hole in the top plate he positioned a source of alpha particles. Below the hole in the central plate he mounted a metal foil. On the upper surface of the bottom plate he placed the detection film.

He expected that the alpha particles would pass through the holes in the top two plates, forming a beam. When the particles passed through the foil, most of them would continue undeflected, but some would scatter into a small region surrounding the center of the detection film. Timmerman planned to measure the distribution of holes around the center in order to determine how the density of particles depended on the scattering angle. Although his plan was simple, he had to overcome several problems before he finally obtained the data he submitted at the fair.

Leming supplied Timmerman with the detection film. Leming also worked out a procedure for developing the film. After exposure the film is kept for 24 hours in a 2.5-molar solution of sodium hydroxide that is maintained at a temperature of 40 degrees Celsius (104 degrees Fahrenheit). Timmerman built an apparatus for developing the film. He puts the film and the sodium hydroxide solution in a canister that is lowered into a water bath inside a bucket. An aquarium heater warms the water and hence the contents of the canister. A cover and some insulation around the bucket slow the loss of heat to the room. A thermometer mounted on the inside of the bucket monitors the water temperature.

Before beginning his experiments on scattering Timmerman tested the strength of his source of alpha particles by putting a small piece of film near the source for a few minutes. He developed the film and put it in a microfilm machine to magnify it. The film had hundreds of holes, indicating that the source was strong enough for his plans.

He then positioned the source and a new sheet of film in his apparatus but still did not insert the metal foil. The apparatus was placed in a bell jar, which was then evacuated with a pump so that the alpha particles would not be scattered by air molecules. After five minutes the film was removed, developed and examined. Again Timmerman found numerous holes spread over the center of the film. The apparatus seemed to be suitable for the scattering experiments.

Timmerman's next move was to put his thin gold foil in the apparatus. (He had acquired the foil from a painter of window signs.) The apparatus was evacuated and the film was exposed for two hours. When he looked at the film later, he discovered that the vacuum had been lost during the test. After he developed the film he found it was covered with holes, indicating that the alpha particles had scattered from air molecules and heavily showered the film.

Timmerman concluded that the bell jar surrounding the scattering apparatus was leaking air and therefore would have to be evacuated several times during a test. He tried to rig an automatic pump control by attaching an electronic switch to an input port of a home computer, which he programmed to turn on the pump every 30 minutes. The arrangement resulted in a burned-out switch. Timmerman rigged a switch to control a relay on the pump, but the relay began to stick. Eventually he discovered that the leak was not in the bell jar but in the vacuum pump. From then on he closed off the hose from the pump as soon as the air had been removed from the bell jar.

The next problem was a malfunction of the aquarium heater that resulted in the ruin of several sheets of film. Unable to find a replacement for the heater, Timmerman wired it to an interface with the computer. The computer was to monitor a temperature probe in the water bath and turn on the heater as needed. This procedure failed because the temperature probe did not function properly. Timmerman then decided to buy a new aquarium heater.

With a fresh supply of film he set out to determine the proper exposure time for his experiments. Seven hours seemed to work well. When a sheet of exposed film was placed in the microfilm machine, he could easily see the holes created by the alpha particles. Measuring the distribution of the holes with the microfilm machine proved to be too difficult, and so he decided to try a more automatic procedure incorporating his computer.

He enlarged his view of the holes in the film by projecting the film onto a wood screen he built. The holes appeared as bright spots. To chart the location of the spots Timmerman pivoted a wood arm around one of the lower corners of the screen. The arm bore a slide with a small aperture. He rotated the arm and moved the slide until a bright spot fell on the aperture.

Wires in the slide and the arm constituted a voltage divider. When the slide was near the pivot of the arm, the voltage across the wires was low. It increased as Timmerman moved the slide to the far end of the arm. Hence the voltage across the wires was proportional to the distance between the aperture in the slide and the pivot point of the arm.

Timmerman arranged for the center of the film, the point reached by undeflected alpha particles, to project directly onto the pivot. He next moved the arm and the slide until the aper aperture in the slide was aligned with a bright spot. The voltage across the wires was then proportional to the distance between the center of the film and the point where the particle responsible for the bright spot struck the film.

Timmerman was interested in the distribution of alpha particles within a scattering angle of 10 degrees. Therefore he set up his apparatus so that a bright spot from a particle deflected at 10 degrees fell at the outermost position of the slide. With the help of James A. Wisman of the University of Arkansas at Fayetteville, Timmerman constructed an interface between the voltage divider and his computer. The interface sectioned the maximum voltage from the divider into 256 steps. Thus each step corresponded to 10/256 degree of scattering.

To measure the scattering distribution on a film Timmerman moved the arm and slide to each bright spot in the projection. When the aperture in the slide was aligned with a spot, he triggered a switch so that a signal was sent to the computer from the interface. The signal indicated which voltage step (and so which angle of scattering) should be assigned to the spot. The computer recorded the information.

Timmerman then wrote programs that calculated the density of holes in the film and printed a histogram of the density versus the angle of scattering. Not satisfied with the results, he repeated the experiments with longer exposure times (10 hours and 18 hours). These tests generated such an abundance of holes in the film that hours were needed to measure their locations. Timmerman also corrected for a background of holes in the film, which were presumably due to alpha particles unrelated to his source. He tried various "best fit' functions to the data to find the angular dependence of the scattering.

Timmerman concluded that the angular dependence seemed to follow Rutherford's prediction. Nevertheless, he still had reservations about the collimation of the particle beam before it reached the foil, and so he tested his conclusion with two procedures. He weighed the gold foil in order to determine its thickness. Then with Rutherford's formula for scattering he calculated the thickness from his measurements of the density of holes in the film. The two findings agreed to better than an order of magnitude.