We note the condition of arbitrariness in statements of atomic size : an atom has no sharp boundaries. Similarly, some convention must be adopted in speaking of the size of the nucleus of the atom. Either we can make an attempt to estimate the distance between the centres of the nucleus of an atom and of the a-particle at the moment of closest approach, the a-particle having a given velocity, or we can investigate the distance from the centre at which the inverse-square law of repulsion breaks down. Whether this dis tance be called the size of the nucleus is a matter of definition, and in any case it becomes necessary to state within what degree of accuracy we require the inverse-square law to be obeyed outside the boundary so specified. As with the atom, what we call the size is, within limits, a convention.
The investigations of the scattering of a-particles, to which extensive reference has already been made, shows that with gold, for instance, the inverse-square law holds in cases where the angle of scattering is anything between 5° and since the formula (I) is based upon the assumption of an inverse-square law, and it represents experimental fact within this range of angle. For an actual head-on collision, the distance b of closest approach of centres is given by from which b can be calculated, and for an angle of scattering of 150° the distance of closest approach is only slightly greater. This gives 3 X 1 cm. as an upper limit for the radius of the gold nucleus. A study of the photographs of the forked ray tracks also enables us to estimate limits within which the inverse-square law holds, and leads to the conclusion that it is still valid for a distance 7X cm. between centres of nucleus and a-particle in the case of argon and 3 X cm. in that of air. The dimensions of the helium nucleus are probably smaller than those of the heavier nucleus, so that the general results of these estimates is 3 X cm. as the order of nuclear radius, as compared to 2 X cm. as the order of atomic radius. It may be added that the approach for the smaller angles at which the scattering law holds indicates that the inverse-square law is still valid at distances as great as .36X cm. for gold, 5X cm. for air and cms. for argon, or a space surrounding the nucleus of the order cm. in radius is free from any marked concentration of electrons.
Rutherford studied experimentally the impact of a-particles on hydrogen nuclei, as further described when the disruption of the nucleus is considered. He came to the conclusion that, while for very slow a-particles the number of hydrogen nuclei (to which the name protons, suggested by Rutherford, is often applied) knocked forward at different angles agrees with that calculated on the assumption of an inverse-square law of repulsion between the striking and the struck nuclei, with fast a-particles the num ber thrown directly forward is much larger than is to be anticipated on this basis, a fact which he explained by supposing that at very close approach of a-particles and hydrogen nucleus the a-particle (helium nucleus) behaves as if flattened into a plate-like form, the plane of the plate being normal to the path of the nucleus, or, since the collision in such cases of very close approach is prac tically "head-on," to the line joining the centres of the two nuclei.
This would clearly give a preferential projection of the struck nucleus in the line of motion of the a-particle. Chadwick and Bieler expefimented on the direction in which hydrogen nuclei were thrown forward by a-particles, by letting a-particles pass through a thin film of paraffin wax : the fact that the hydrogen atoms are here combined with carbon atoms has no effect on the behaviour of the nuclei, the forces of chemical binding being negligible compared to those involved in these collisions. Applying Rutherford's line of argument to these experiments, they came to the conclusion that an a-particle behaves in these collisions like an oblate spheroid of semi-axes 8 X and 4 X cm., the proton being treated as a point charge, on account of its presumably very simple structure.
To investigate in detail the departure of the field of force sur rounding a nucleus from the inverse-square law it is clearly neces sary to force the a-particle which acts as our probe as close to the nucleus as possible. The energy of the a-particle cannot be made to exceed that offered by the natural radioactive sources, so that two courses are open : (I) to investigate the scattering by light elements, where the nuclear charge is low, and so the nuclear field comparatively weak; (2) to work with very large angles of scattering, which corre spond to intimate approach.
Rutherford and Chadwick therefore examined the scattering by foils of aluminium and magnesium, choosing fixed large angles, namely 135° and They used a-particles of different energy, obtained from Radium C by the interposition of absorbing screens of various thickness, to vary the distance of approach. They found that the inverse-square law was followed with both these elements for distances of approach greater than 1.5 X cm., but that the ratio of the number actually scattered to the number calculated on the inverse-square law rapidly decreased for closer approach, then attained a minimum and increased again. The minimum was found at 7 X cm. for magnesium (Z and for a slightly greater distance of approach in the case of aluminium (Z= 13). The closest distance of approach measured was 6X r cms. With gold and silver (Z= 79 and Z=47), where the nuclear field is strong, the inverse-square law was obeyed up to the closest dis tance of approach obtainable, about 3 X cm. and 2X cms. respectively. If we may treat in these experiments the a-particle as a point-charge these results can be interpreted to mean that, with the aluminium and magnesium nuclei at any rate, the repulsive force exerted by the nucleus decreases for distances between 15X and 7X 1 cm., but increases again for closer distances, the inverse-square formula being taken as a standard of comparison. A physical explanation can be given by supposing that the outer parts of the nucleus consist of a layer of positive charge, within which is a layer of negative charge ; when the a-particle penetrates the positive layer the effective nuclear charge is diminished, but when it goes further and penetrates the negative layer, the effective nuclear charge increases again. This conception receives further reference when the radioactive nuclei are discussed.