In 1911 Rutherford proposed the nuclear model of atomic structure. He suggested that an atom consists of a central nucleus (where most of the mass of the atom is concentrated) having a positive charge, surrounded by moving electrons carrying negative charge. Geiger and Marsden carried out an experiment to verify his proposal.

The apparatus is illustrated in the diagram below.

The apparatus was in an evacuated container. The detector was a ZnS screen observed through a low power microscope. Each time an alpha particle hit the screen, a small flash of light was produced.

The detector was mounted on a support such that it could be rotated to measure the angular deflection of the alpha particles as they passed through a very thin sheet of gold. They measured the numbers of particles deflected through various angles.

It was found that most of the a particles pass through the gold undeflected; only a relatively small number are deflected (scattered).

Their results were considered to confirm Rutherford’s model and allowed them to estimate the size of the nucleus (»10^-14m) and the size of the atom (»10^-10m), thus producing the slightly surprising conclusion the most of the space occupied by an atom is empty space!

For a given speed of alpha particle, the closest approach to a nucleus, r_min, will occur when the initial direction of motion of the particle is along the line joining the centres of particle and nucleus.

In this case, at the point of closest approach, the speed of the particle is zero.

As the particle approaches the nucleus, kinetic energy is being converted to electrical potential energy.

Electrical potential at a distance r from a point charge Q is given by

For a nucleus of atomic number Z, the charge is Ze, where e is the magnitude of the charge on one proton (the same as the magnitude of the charge on an electron).

The magnitude of the charge on an alpha particle is 2e

Therefore, the energy, w, possessed by an alpha particle placed at distance, r_min, from a charge Ze is given by

So, we have
 

which gives
 

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