The magnitude of the nuclear charge can be deduced directly from experiment by applying the formula (1) for single scattering, whose verification has already been discussed. A can be experi mentally determined, by counting the scintillations due to particles scattered through a given large angle; n is known from the atomic weight and the density; the thickness t of the foil can be easily measured ; e, E, M, v are all known ; and r and so merely express details of the experimental disposition. The only unknown in the equation is therefore Z. Rutherford in his original paper merely made a rough estimate, from which he conjectured that Z was about half the atomic weight, which is, in fact, a fair approxima tion. In 192o Chadwick carried out the scattering experiments in a modified form, with greater accuracy, and obtained for platinum, silver, and copper values of Z which were respectively 77.4, and 29.3. The atomic numbers of the elements in question are 78, 47, and 29 respectively, so that the hypothesis that the number of electronic charges, of positive sign, in the nucleus is equal to the atomic number has been confirmed by the scattering experi ments for elements of widely different atomic number.
The nuclear theory of the atom has been confirmed by another method of studying single scattering.. The Wilson cloud chamber (q v.) gives us a method of rendering visible the path of an a-particle, by means of a condensation of minute droplets of water on the ions produced by its passage. A study of photographs of these so-called ray tracks shows that some of the tracks end in forks, both prongs of the fork making an angle with the original direction of the a-ray. The one prong is due to the a-particle itself, turned through a large angle by collision with a nucleus of a gas atom, the other prong is due to the struck nucleus, which likewise produces ionisation, and consequent condensation, along its path. A single photograph will not enable us to measure accurately the angle which the forked tracks make with one another and with the original ray, since the plane containing the three paths makes an unknown angle with the direction from which the photograph is taken. If, however, two photographs are taken of a single ray track, from mutually perpendicular directions, it is a simple matter of geometry to find these angles. Now, on the assumption that the collision of a-particles obeys the ordinary laws of mechanics for the collision of perfectly elastic bodies (conserva tion of energy and momentum) it is easy to calculate a theoretical value for the angles involved in the collision, but such a calculation involves the ratio of the mass of the struck particle to that of the striking particle. Comparison of the theoretical and experimental values enables us to find a value for this ratio. Blackett, from a
study of the passage of a-particles through oxygen, obtained in this way for the mass of the oxygen nucleus 16.72, which is in good enough agreement with the chemically known value 16. Examples of his photographs are given in the article WILSON CLOUD CHAM BER. Calculation shows that if the masses of striking and struck particles are equal, a case that can be realized experimentally by letting a-particles pass through helium, the two branches of the fork should always be at right angles to one another, no matter what angle the a-particle itself be turned through. This result has also been confirmed experimentally, the actual value found being, for instance, 89° 27' in one case. Since all the calculations are based upon the assumption that the whole mass of the atom is concentrated in a minute nucleus these ray track experiments give a brilliant confirmation of this feature of the theory.
The Size and Field of Force of the Nucleus.—In the case of an entity like the nucleus, whose existence is revealed to us by experiments on the deflection of particles, no definite boundary is defined by the conditions, and we must discuss what we mean by its size before we can attempt to form an estimate of it. Let us first consider what we mean by size in the case of other entities. In the case of an ordinary body, such as a metal wire, we can measure the thickness either by visual methods, such as the use of a reading microscope, depending upon the fact that there is an abrupt change of optical properties at the surface of a metal (revealing itself, for instance, by a reflection of the light taking place at a definite plane) or by mechanical methods, such as a micrometer screw. The reading of the micrometer depends to a slight extent upon how hard we screw it up, or the recorded size of the wire depends upon the force we exert. In other words, what we are really measuring is the place at which the resistance to the jaws changes abruptly, the force being negligibly small just outside the surface, and increasing rapidly but continuously as we force the jaws together. In the case of the dimensions of an atom, as measured by methods depending on the kinetic theory of gases, the diameter of the atom is taken as the distance between the centres of two atoms at the moment of closest approach. This depends markedly upon the relative speed of the two atoms, decreasing as the speed increases, that is, as the temperature of the gas is raised. The size of the atom usually accepted is that given by the distance of closest approach in a gas at ordinary temperatures, but some other methods, such as the distance of closest approach of atoms in a crystal of known structure, may also be used, and give somewhat different values.