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Rutherford Scattering


Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon static electric (Coulomb) forces, and the minimal distance between particles is set only by this potential. The classical Rutherford scattering of alpha particles against gold nuclei is an example of “elastic scattering” because the energy and velocity of the outgoing scattered particle is the same as that with which it began.

The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment in collaboration with Rutherford, in which they fired a beam of alpha particles (helium nuclei) at layers of gold leaf only a few atoms thick. At the time of the experiment, the atom was thought to be analogous to a plum pudding (as proposed by J. J. Thomson), with the negative charges (the plums) found throughout a positive sphere (the pudding). If the plum-pudding model were correct, the positive “pudding”, being more spread out than in the current model of a concentrated nucleus, would not be able to exert such large columbic forces, and the alpha particles should only be deflected by small angles as they pass through.

However, the intriguing results showed that around 1 in 8000 alpha particles were deflected by very large angles (over 90°), while the rest passed straight through with little or no deflection. From this, Rutherford concluded that the majority of the mass was concentrated in a minute, positively charged region (the nucleus/ central charge) surrounded by electrons. When a (positive) alpha particle approached sufficiently close to the nucleus, it was repelled strongly enough to rebound at high angles. The small size of the nucleus explained the small number of alpha particles that were repelled in this way. Rutherford showed, using the method below, that the size of the nucleus was less than about 10−14m (how much less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size).

The image below shows the layout of the famous Rutherford – Geiger – Marsden experiment on the scattering of alpha particles by a thin gold foil.



With the DIY alpha spectrometer we tried to replicate, in a qualitative way, the famous Rutherford experiment on the scattering of alpha particle. In particular we have tried to make the detection of back scattering, that is, those alpha particles that are spread to angles greater than 90 °, in practice bounce backwards.
In the image below is presented the experiment setup: the alpha source of americium, collimated through a wooden screen, is placed in the upper part of the vacuum chamber and is directed toward the target, in our case a lead plate, the target is placed directly below the detector.


In the picture below you see the basic diagram of the experimental setup.



The alpha spectrometer was run for about an hour, and it has obtained the following spectrum:


In the energy range from 2,000 KeV to 5500 KeV we note about 30 pulses which can be attributed with reasonable certainty to the same number of back scattering events originated from the lead target, the energy variation depends on the depth within the target where the alpha particle has been scattered. There is then a maximum of events around the energy of 500 keV, the interpretation of which has yet to be analyzed.

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