In these points the formula was satisfactorily confirmed. The proportionality to thickness is particularly important. Quite apart from the formula, it is easy to see that the theory of single scattering gives this result, since the number of nuclei behind a given surface area of foil is proportional to the thickness, and the chance that the close approach needed for large angle scattering shall take place with more than one nucleus is negligibly small with the thicknesses of foil which are practicable. On the other hand any theory of multiple scattering gives a proportionality to the square root of the thickness of foil.
To help the reader to form an idea of the chance of a single scattering through a large angle, and of the unlikelihood that a single particle shall make two encounters of the type which lead to such scattering, the following picture may be offered. One of the thicker gold foils used in the scattering experiments, actually some few hundred-thousandths of an inch thick, may be considered to be magnified until it is a mile thick. The centres of the individual gold atoms will then be about a yard apart. The a-particle on the same scale will be represented by a tiny grain of dust, something less than a thousandth of an inch across. To be deflected through this grain, in its passage through the mile-thick foil, must pass within four thousandths of an inch of one of the yard-separated centres. For larger angles of scattering an even closer approach is necessary.
The large angle scattering of a-particles thus afforded, at the hands of Rutherford, certain evidence as to the nuclear structure of the atom. The great advantage of the a-particle as a probe to investigate the fields of force which make up atomic structure is, firstly, that a single radioactive element gives a beam of homo geneous velocity, and, secondly, that single particles can be detected. A great deal of work has been done on the scattering of 0-particles, from which a degree of confirmation of these views as to the mechanism of single scattering and multiple scattering can be derived. The intermediate case, where the number of deflec tions suffered by a particle is neither one, nor very large, also comes into account with 0-particles with a certain thickness of foil and a certain angle of scattering. The problem of 0-ray scattering, while of considerable interest, has not, however, on the whole, given us any fresh information on the nucleus, and therefore only receives passing reference here. It should not, however, be forgotten that, as a result of experiments on the absorption by matter of electrons of different speeds, including 0-rays, Lenard, as long ago as 1903, put forward the view that the impenetrable part of the atom was very small. This impenetrable part, however, he considered to be located in a large number of small electrical doublets, which he called dynamids, each dynamid being, as a whole, electrically neutral. While this view has perforce been abandoned it is of great historical importance.
magnitude of the electronic charge e. That this is so was first sug gested by van den Broek in 1913, and confirmation of his hypoth esis was speedily furnished by the experiments of Moseley. Mose ley used the method of crystal reflection, which had just been discovered by W. H. and W. L. Bragg (see under article X-RAYS), to measure the wave length of the characteristic X-rays given out by different elements subjected to suitable elec tronic bombardments, and found that the X-ray spectrum of every element conformed to a single type, consisting of a group of a few lines of shorter wave length and another grotip of a few lines of longer wave length. These groups corresponded to the so-called K and L radiations discovered by Barkla from the dif ference of their penetrating power, and were accordingly called the K and the L series.
The K and L radiations are characteristic of the atom, not of the molecule : they are not affected by the state of chemical combina tion in which the atom may be held (except for certain small secondary effects, discussed under X-rays, Röntgen). Moseley found that the wave length of a given line in the X-ray spectrum decreased from element to ele ment, taken in order of increasing atomic weight, and also that the frequency of such a line fol lowed a simple law. This law, known as Moseley's Law is that, if corresponding lines be selected in the spectra of the various elements, then the square root of the frequency increases by a constant amount from element to successive element. Now while the atomic number, as defined, in creases by i from element to element, the atomic weight in creases by irregular steps. The law is exhibited in fig. 2, where v/R is plotted above against atomic weight, below against atomic number : it is obvious that regularity exists in the latter case only. Here v is the frequency of the selected line, in the case of fig. 2 the so-called Ka line, and R is the constant, of fundamental importance for the theory of line spectra, known as Rydberg's constant. (See SPECTROSCOPY.) These results clearly show that there is some fundamental feature of the atom which is proportional to the atomic number, but has no reference to the atomic weight. A comparison of the simple formulae found by Moseley for the relationship between the frequency of the X-ray lines and the atomic number Z, which can be written with the general formula, deduced by Bohr, for a series in the line spectrum of a hydrogen-like atom (see AToM), namely where Ze is the nuclear charge, shows that Moseley's Z, multi plied by e, must also be the nuclear charge. The constants sub tracted from Z in Moseley's formula represent, speaking roughly, a shielding effect of the inner electrons. (See X-RAYS.) Thus Moseley's work, as represented by fig. 2, proves that the net positive charge on the nucleus is given by the atomic number, which thus has a fundamental significance for the nuclear theory of the atom. Moseley's linear relation is shown by more recent experiment not to be exact, but the departure, which is in the sense of a slightly more rapid increase of - V v with increasing Z, does not affect in any way this deduction, the curve remaining smooth, and the deviation from linearity being attributable to secondary effects.