The Rutherford-Geiger-Marsden Experiment

What made by Rutherford and his assistants Geiger and Marsden is perhaps one of the most important experiments of nuclear physics.

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.

In the experiment, Rutherford sent a beam of alpha particles (helium nuclei) emitted from a radioactive source against a thin gold foil (the thickness of about 0.0004 mm, corresponding to about 1000 atoms).

Surrounding the gold foil it was placed a zinc sulfide screen that would show a small flash of light when hit by a scattered alpha particle. The idea was to determine the structure of the atom and understand if it were what supposed by Thomson (atom without a nucleus, also known as pudding model) or if there was something different.

In particular, if the atom had an internal nucleus separated from external electrons, then they would have been able to observe events, or particles, with large angle of deviation. Obtained, actually, these results, the New Zealand physicist concluded that the atom was formed by a small and compact nucleus, but with high charge density, surrounded by an electron cloud.
In the image below it is depicted the interaction of the alpha particles beam with the nuclei of the thin gold foil; one can see how the majority of the particles passes undisturbed, or with small angles of deflection, through the “empty” atom, some particles, however, passing close to the nucleus are diverted with a high angle or even bounced backwards.

The interaction between an alpha particle and the nucleus (elastic collision) is also known as Coulomb scattering, because the interaction in the collision is due to the Coulomb force. In the diagram below it is shown the detail of the interaction between an alpha particle and the nucleus of an atom.

Experimental Setup

In the PhysicsOpenLab “laboratory” we tried to replicate the famous Rutherford experiment. With the equipment already used in alpha spectroscopy we built a setup based on an alpha solid-state detector, a 0.9 μCi Am 241 source and a gold foil as a scatterer. In these post we describe the equipment used : Alpha Spectrometer, Gold Leaf Thickness .
The main purpose is not to make precision measurements but to make a qualitative assessment of the scattering as a function of deflection.
The images below show the experimental setup:

 

The alpha source is actually 0.9 μCi of Am 241 (from smoke detector) which emits alpha particles with energy of 5.4 MeV. The alpha particle beam is collimated by a simple hole in a wooden screen. Source and collimator are fixed on a arm free to rotate around a pivot, which hosts the gold foil that acts as a scatterer. The whole is placed inside a sealed box that acts as a vacuum chamber with the help of an ordinary oil rotary vacuum pump. The images below show the “vacuum chamber” and the electronic part for amplification and acquisition connected to the PC for counting events.

Results

With the experimental setup described above, we have carried out a series of measurements. We chose a measurement time of 10 min = 600 s. It is a rather short interval, especially for higher angles that give a few events, but sufficient to have a result of a qualitative nature. With a few events the statistical uncertainty is high, and then the corresponding data should be regarded only as a qualitative indication. In addition has been placed a threshold of minimum energy of 700 KeV so as to exclude from the count any spurious events that may occur, but that usually remain confined within the energy values of less than 1 MeV.
The results obtained are shown in the table. The rotating arm has been positioned at different angles, starting from a null angle up to a value of 75°, with steps of 15°. At angles greater than 45° events counted have been reduced to a few units. For these angles it would be necessary to increase the measurement time, or increase the power of the source so as to acquire a greater number of events and thus have a greater statistical significance.
The results of measurements are shown in the following graphs, in a linear scale and in a semi-logarithmic scale.

Linear Scale :

Semilog Scale

The results obtained in our experiment approach, albeit with obvious limitations, to the expected theoretical results, represented in the following graph:

For completeness, we report also at the side the formula that describes the distribution of the number of the counted particles in function of the scattering angle. Interestingly, this depends on the power of two the atomic number of the target and is inversely proportional to the fourth power of the sin (θ/2).

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