In 1911 Rutherford, Geiger and Marsden were studying the passage of alpha particles through thin (1 mm) pieces of gold foil. As they expected, some of the alpha particles were able to pass through the film. They then noticed something that they did not expect.
Some of the alpha particles were being deflected from their original path and more surprising still about 1 in 8000 were actually knocked backwards! You must remember that although alpha particles are very small they are travelling at a tenth the speed of light.
The animation shows the scattering of alpha particles by a gold nucleus.
If an alpha particle with a kinetic energy Eo is fired directly towards a gold nucleus it will feel a repulsion which increases as it gets closer - climbing the potential hill surrounding the nucleus. When all the kinetic energy has been converted to potential energy the alpha particle (charge q) has reached its distance of closest approach (dc) and comes to rest. At that point :
Ea = qVE =(1/4peo)qQ/dc so therefore dc = (1/4peo)qQ/Ea