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This paper discusses Rutherford’s experiments in studying the structure of an atom. The conducted study is based on the previous experiments carried out by Geiger, Marsden, and Crowther. Initially, in the 19th century, the structure of the atom was barely known by the researchers who only tabulated the atomic models. To achieve his goal, Rutherford repeated Geiger, Marsden and Crowther’s experiments to check their validity and accuracy. This paper discusses how Rutherford discovered the structure of the atom examining the researches he conducted and their results.

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Discovery of Nuclear Structure by Rutherford

The structure of the atom had largely remained unknown by the middle of the 19th century. Sir Joseph J. Thomson came up with an atomic model that was made of evenly distributed electrons which were surrounded by the positive charges. However, experiments conducted by Geiger and Marsden that involved the scattering of particles through large angles after encountering atoms raised questions to Thomson’s model (Benguria, 2011). In a search for a possible explanation to the scattering of particles, Rutherford worked with the experimental data including those from Geiger’s experiments to prove his theoretical model of the atom which consisted of negative charges surrounding a central charge which is referred to as the nucleus of the atom

Alpha and beta particles suffer deflection when they encounter atoms. Beta particles are deflected over larger angles than the alpha particles due to the smaller energy and momentum of the beta particles (Rutherford, 1911). Rutherford attributes the deflections of the particles to the strong electric field that the particles encounter in the atomic system. Previously, the deflection of particles had been supposed to be caused by the overall effect of scattering by atoms in the material being traversed by the particles. However, it was later discovered that some alpha particles could suffer deflection of more than 90 degrees on one encounter. However, it was found that the great deflection had a small probability. In building his proposition for the atomic model with the nucleus, Rutherford supposed that the deflection through large angles was due to the encounter of the alpha particles with a single atom; a proposition which would mean that the atom should be possessing a strong electric field in order to cause such a great deflection.

Furthermore, Rutherford made reference to J.J. Thomson’s structure of the atom. Thomson had proposed that the atom had a number of negatively charged particles and an equal quantity of positive matter which were uniformly distributed around the sphere. As such, the scientists proposed that the alpha particles had been scattered because the negative particles located all over the atom repelled the alpha particles and because the positive matter attracted the negative particles being directed to the atom. Thomson had worked with the assumption that the particles were deflected through small angles with every encounter of an atom. The large-angle resulted due to the multiple scattering of the particles by several atoms. Rutherford further asserts that the only other explanation that would befit the small scatterings of the alpha particles by Sir Thomson’s model of the atom would be that the diameter of the positive matter in the sphere was very minute when compared to the atomic sphere of influence (Rutherford, 1911).

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The Theoretical Model

Rutherford believed that the nature of the scatterings of the alpha particles, especially since the particles could be singled out, was useful in determining the nature of the atoms. The scientist proposed a simple structure of the atom with charge Ne at its center and opposite charges Ne at the atomic radius R that are scattered around the central charge (Benguria, 2011). Rutherford deduced his workings not depending on the sign of the central charge since no experiment had yet made clear if it was positive or negative. The scientist chose to work with a positive charge for convenience. His main interest was not only to explain the scattering of the alpha and beta particles through smaller angles but also to account for the deflections through the larger angles. Rutherford determined the probability of a deflection happening through a particular angle, the dynamic changes that occur when a moving particle encounters the atom, and the comparison of single and compound scattering theories.

Methods and Materials

In determining the structure of the atom, Rutherford relied on previous experiments on atomic scattering carried out by different scientists to justify his theory of single scattering and thus prove the presence of a single massive charge at the center of the atom that was responsible for the large-angle deflections (Kragh, 2012). He first outlined the theoretical foundation of his model using equations. Later, Rutherford conducted an experiment that was done by Geiger, two experiments carried out by Geiger and Marsden and one experiment done by Crowther to compare the theory with their results.

Rutherford used the theory of compound scattering proposed by Sir Thomson in order to justify his own theory since Thomson’s approach could not account for large deflections.

Previous Experiments Used

Firstly, Rutherford used Geiger’s experiment about which Geiger and Marsden had previously reported that about 1 of 8 000 of the alpha particles directed at thick platinum was scattered back in the direction of incidence. Notably, the experiment was termed as not very accurate for the calculation by Rutherford, since the fraction was made out of the assumption that the particles were being evenly scattered in every direction.

Secondly, Rutherford carried out Geiger’s experiment. Geiger and Marsden had conducted it using different thick layers of metals and determined the approximate number of the alpha and beta particles that were diffused by the metals under the same conditions.

Thirdly, Rutherford also analyzed Geiger’s experiment which involved the scattering of the alpha particles by thin foils of metal. Through the scintillation method and working with known thicknesses of metal, Geiger determined the most probable angles through which the alpha particles suffered deflections. The probable angle was arrived at by noting the angle which had the most scattered alpha particles. Possibilities for compound scattering are considered in cases where almost half of the alpha particles are scattered at a particular angle. Due to the combined effects of the two kinds of scatterings, both the probabilities of the scatterings and the probability of combined effects are taken into account. Through calculations, Geiger determined the various thicknesses and atomic numbers of the metals and proved that the atomic weight of metal and the most probable angle of deflection were almost proportional.

The fourth experiment that Rutherford applied was Crowther’s experiments on scattering the beta rays of various velocities. The theory of single scattering, which was based on the assumption that the alpha particles were scattered by a single massive scat was used to explain the findings of Crowther in a bid to understand how far the theory could be used. In this experiment, compound scattering was also found viable in explaining the results. Rutherford argued that the results indicated that the same laws of scattering that apply to the alpha particles also apply to beta particles. The value of N was measured by determining the fractions of the beta particles that were deflected through large angles. However, the values of the beta rays were slightly different from those of the alpha rays due to their differences in the mass and relative velocity of the particles.

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From Crowther’s experiment and his theory of the absorption of the beta rays, he deduced the value of the constant, which is the small fraction of the beta particles that are either reflected or scattered backward along the direction of incidence of the various elements to be proportional to nA2. n is the atomic number in a particular volume, and A is the atomic weight of the metal. In a condition where there is proportionality between the central charge and the atomic weight, then Rutherford’s theory of single scattering is expected to deliver the same relation that was derived by Crowther. The results of his experiment are shown in Table 2.


From Geiger’s experiments, only one out of 8 000 alpha particles were scattered at large angles. Table 1 demonstrates Geiger and Marsden’s results of the second experiment that Rutherford used, with z being the approximate number of the scattered alpha particles measured per minute as made possible by the scintillations on the zinc sulfide screen.

Table 1

Scattering of Alpha Particles by Different Metals

Metal Atomic Weight Z z/A3/2
Lead 207 62 208
Gold 197 67 242
Platinum 195 63 232
Tin 119 34 226
Silver 108 27 241
Copper 64 14.5 225
Iron 56 10.2 250
Aluminum 27 3.4 243
Average of 233

From the theory of single scattering, it was deducted that the atomic weight of the atoms was in direct proportion to the central charge since the fraction of the alpha particles that were scattered at any angle through a metal thickness t was proportional to n.A2t. Using the notion of the stopping power which had been more elaborated by Bragg, the number of the alpha particles scattered from the thick layers of metals was found to be proportional to z/A3/2, for which the values of individual metals were indicated in the last column of Table 1. The large scattering of the alpha particles had an effect on Bragg’s ionization curve. However, the impact was only taken into consideration where the alpha rays traversed the screens of the metals, which occurred mostly in metals with higher atomic weights since those metals with lower atomic weights were less affected.

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From the third experiment, Geiger found the value of N of gold to be 97 and 114 respectively when he used gold of varying thickness. In the first instance, the stopping power of the metal was about 0.76 cm of air, while in the second instance, it was about 2.12 cm of air.

By comparing atomic weights, Geiger thus proved that single scattering was the most reliable way to explain the average small-angle scattering of the alpha particles as well as the diffuse reflection of the alpha particles at angles more than 90 degrees, as the particles interacted with the gold foil in question (Rutherford, 1911, pp. 682,683).

Table 2

Crowther’s Results

Element Atomic Weight / tm N
Aluminum 27 4.25 22
Copper 63.2 10.0 42
Silver 108 15.4 78
Platinum 194 29.0 138


From the previous experimental data, Rutherford worked with the assumption that the atom had a central charge that was concentrated at a point. This central charge was responsible for the large deflections of the alpha and beta particles that had encountered its field. Rutherford also argued that the charge balance of the atom, given the negative charges that balance the positive central charge, has no effect on the deflection of the alpha and beta particles. The mass, the kinetic energy and the momentum for a rapidly moving electron are way less than the corresponding values for an alpha particle moving with high speed through an atom. The mass great difference, kinetic energy and the momentum of the two particles make it almost impossible to come up with the conclusion that the alpha particles are scattered as an effect of the field of the electrons. As such, the only possibility left is that the alpha particles encounter repulsion due to the central charge of the atom (Rutherford, 1911).

In order to establish the charge distribution at the center of the atom, the repulsions of the alpha particles were studied. Rutherford first hypothesized the central charge consisted of several unit charges. In this instance, the alpha particles would be suffering deflection as a result of the effect of multiple interactions with the electric fields of individual charges instead of suffering deflection as the result of the external field of the combined charges. Given the first scenario, the fraction of the alpha particles scattered through a large angle would be proportional to Ne2 which is unlike the proportion for the central charge which was calculated at N2e2, where N is the number of constituent charges of the central charge. In this calculation involving the single charges, only the electric field of the constituent charge can be used to determine its effect on the alpha particle while overlooking the mass of the charge.

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With calculations of the central point charge of about 100 for gold, Rutherford found out that at least 10, 000 distributed charges should be present for large deflections to occur. However, the mass of the constituent charge would then be too small to even result in the deflection of the alpha particle through the large angles. It has also been proven that the combined effect of several charges is more probable in causing large deflections than the effect of single scattering. Rutherford thus predicted that the deflection of the alpha particles over a gold foil would give a larger angle than the deflection given by a single atom. From the arguments against the possibility of the scattering being caused by the constituent charges, Rutherford stated that the atom could be best described as having a central charge that is spread and confined to a small volume which as a whole is responsible for the deflection of the alpha particles through a larger volume.

It was also found out that the central charge for any particular atom, especially of a higher atomic mass than aluminum, is relative of the same value as the atomic weight. Despite the fact that Rutherford had not yet determined the sign of the central charge, he proposed that a positive sign would possibly account for the rapid motion of the alpha particles as they are being expelled from the atom since a positively charged particle, say the alpha particle, would acquire greater velocity as it moves through the electric field of the positive central charge. Rutherford also suggested that the central charge was likely positive since the effect of radiation in velocity reduction of the beta particle would be more noticeable and impactful in a positive rather than a negative center.


Rutherford successfully proved, basing on previous experiments of Geiger, Marsden, and Crowther, that the atom has the nucleus, which is a concentration of charged matter at the center of the atom. The study carried out by Rutherford had limitations, since it could not yet prove whether or not there were any carriers for some fraction of the positive charge for some distance away from the center of the atom. It is proposed that the evidence could be obtained by the determination of the involvement of the central charge in the large deflections of the alpha and beta particles since it was found that the alpha particles moving with the same speed as the beta particles had to move closer to the center of the atom before suffering deflections of larger angles as the beta particles.

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