Nucleus

Studying the scattering in this way Geiger and Marsden found that the distribution of the scattered particles in the neighbour hood of the original beam was such as to accord with the view that each particle had suffered a large number of encounters, each encounter producing a small deflection in a random direction. In other words, the scattering through small angles obeys a law which can be calculated from the theory of probability, applied to calculate the final effect of many scatterings in chance direc tions. In addition to these a-particles scattered through small angles there are a few scattered through large angles, and among these there are even some that have been so far deflected from their original direction that they issue from the foil on the same side as they went in, being thus, in a sense, "reflected." It might at first be supposed that a large number of small deflections con spire to produce such a very large deflection, but, from the probability considerations that give the distribution for small angle scattering, the number of particles to be anticipated at any given large angle can be calculated, and turns out to be far less than the number of large angle scatterings actually observed. In other words, there are far too many particles scattered through large angles for it to be possible to explain them on the basis of a multiple scattering through small angles in random directions. It was from this apparently insignificant quantitative observation that the nuclear theory sprang.

In 1911 Rutherford pointed out that large angle scatterings of the a-particle, in the number actually observed, could only be explained as the result of single encounters with very intense centres of force. To provide those centres of force he assumed that each atom contained a central positive charge, with which the mass of the atom was associated, the remainder of the atom being made up of rings of electrons, maintained in a stable position by rotation. The central charge (or nucleus, as it was called later) was assumed to occupy a very small space, the diameter being taken as of the order 1 cm. in Rutherf ord's original paper. It becomes clear that in this case very few of the a-particles passing through a thin foil, which may be some thou sands of atoms thick, will approach near the nucleus : rather they will pass near outlying electrons in several atoms, experiencing a small deflection at each near passage. This accounts for the distri bution of the particles deflected through small angles. An occa sional a-particle, however, will pass close to the nucleus, and will then experience, owing to the intense field of force caused by the big positive charge, a deflection which will be the larger the closer the approach. We thus distinguish between two different processes,

multiple scattering, which denotes repeated small deflections in the majority of the particles which traverse the foil, and single scatter ing, which denotes the occasional very large deflection due to passage close to the nucleus. With foils such as are used in the experiment the chance of a given a-particle experiencing more than one close approach to a nucleus, and hence more than one large deflection, is negligibly small.

This theory of single scattering survives severe quantitative tests. With the help of the simple theory of the dynamics of a particle, as applied in elementary considerations of planetary mo tion, the behaviour of a particle projected towards another particle repelling it with an inverse-square law of force can be easily worked out. Let the mass of the nucleus be so large that it may be considered infinite, and let its charge be Ze, where e is the magni tude of the electronic charge : let the mass, charge and velocity of the a-particle be M, E and v.

Then

it can be shown that where p is the length of the per pendicular from the centre of the nucleus onto the original direc tion of motion, and yo is the angle through which the particle is de viated. (Fig. I.) This gives a relation which can clearly be used to find the chance of a given large angle of deviation, since the probability of a given p can be found immediately if we know the number of nuclei (i.e., of atoms) per unit area of foil. If n be the number of atoms per unit volume, t the thickness of the scattering foil, the chance q of a particle having an original direc tion such that p lies between and th is so that the fraction of the incident particles deviated at an angle between cal and is Since it is usual to arrange the little phosphorescent screen so as to be normal to the particular direction of scattering which is being investigated the equation is usually transformed so as to give the number A of particles turned through a given angle (p which fall per unit of area on such a screen placed at distance r from the point where the original beam hits the foil. This is when Q is the number of particles in the original beam. Now this *formula can be checked experimentally : (I ) By measuring the number of particles turned through dif. ferent large angles, to investigate the proportionality to cosec 4 (P.

(2) By investigating the connection between the number scat tered at a given fixed angle (p and the velocity : the number should be inversely as the fourth power of the velocity.

(3) By varying the thickness of the foil, and measuring the variation of the number of particles scattered at a given fixed angle, which should be proportional to the thickness.