RUTHERFORD'S EXPERIMENT

Scattering of α-particles by atoms of metal.

Existence in atom of heavy positively charged nucleus was discovered by English physicist E.Rutherford in 1906-1912 as a result of experiments with scattering of a-particles on the atoms of gold and other metals. These experiments showed that some of  a-particles (1 per 20000) passing through very thin metal layers were scattered by big angles, while the most of the particles were not deviated. Rutherford concluded that rare scattering of particles (which moves with velocity just 20 times lees that the velocity of light) at big angles may be explained by the presence in the matter the massive nucleus the size of which is much smaller as compared to the atom size. Animation shows the simulation of Rutherford's experiment. The beam of particles moving with about the same velocities collides several big balls simulating the atoms in metal. We see in animation that small part of the particles are scattered by big angles.

Differential section of scattering. Rutherford's formula.

The scattering of particles by nucleus occurs due to Coulomb's electrostatic forces. Sighting parameter is the distance between the line of initial motion of particle and the center of the force center (nucleus). It is clear that not only the particles with sighting parameter smaller than the radius of nucleus will be scattered (see animation). Rutherford supposed that all mass of atom is concentrated in the positively charged small nucleus and obtained on this basis the expression for differential section of scattering :

 ds/dW = (Qe/2vp)²/(sin(j/2) )⁴

where Q is the charge of nucleus, v, p is the velocity and impulse of a-particle respectively, j  is the angle of scattering, ds is differential section of scattering which has dimensionality of area, dW is the spatial angle in which we observe the scattering. This expression is called Rutherford's formula. The calculated section for a-particles proved to be in very good correspondence with experimental results if we substitute in this formula Q= Ze, where Z is the atom number of the element.

For the better understanding of Rutherford's formula let us consider the animation, which shows several beams of particles colliding the nucleus at different sighting parameters r. It is seen from animation that different beams are deviated by different angles. Let us consider the beam deviated by angle j. Changing slightly the sighting parameter by dr the angle of scattering  will change by dj. All particle with sighting parameters from r to r + dr will be scattered by the angles from j to j + dj. Scattering of particles occurs in spherically symmetrical field, so it is more convenient to define the differential scattering section through the spatial angle formed by all directions of the particles scattering limited by angles from j to j + dj. If all particles are scattered in a spatial angle dW, then ds = 2prdr - differential section is equal to the area of the ring in which the particles moved before scattering. In difference of differential section of scattering the value s is called the effective section defined as area the probability of hit in which is equal to the probability of collision. For example, the effective section of the collision of the rigid balls s = p(r₁+r₂)², where r₁ and r₂ - radiuses of the colliding balls.