# Rutherford scattering

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In physics, Rutherford scattering is a phenomenon that was explained by Ernest Rutherford in 1911[1], and led to the development of the Rutherford model (planetary model) of the atom, and eventually to the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering. Rutherford scattering is also sometimes 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.

Rutherford also later analyzed inelastic scattering when he projected alpha particles against hydrogen nuclei (protons), and this latter process is not classical Rutherford scattering, although it was first observed by him. At the end of such processes, non-coulombic forces come into play. These forces, and also energy gained from the scattering particle by the lighter target, change the scattering results in fundamental ways which suggest structural information about the target. A similar process probed the insides of nuclei in the 1960s, and is called deep inelastic scattering.

The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment under the direction of 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 coulombic 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) 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 10−14 m (how much less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size).